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(7p707 4 @7x708 x808  4 @88`8  @9 9$  % 8  8  9   919 9 9 Fq   9  5 78ÜĜŜƜǜȜ_w6(50567Յ 8ՅbOX7kvU kݙ:HOV]d(>p>0>+@>x>0? x?0?ݙ +@??h?  @`@ @@@?  ?  O@&`@@ x@,  P@ A$ `A0BA@BA OЎC0CC CC& CL (C XCPB@CD`D (D pDC E0EEEE6 EL EȎE`DF0XF@FЎFF':F:8FbHFȎFF# /C0G!- !G`GG 9؎GG# G#3GO_<  > ?@BDF"=(<0<=>Յ ?Յ|'(@zKRXF"+Ig ),7.k1!j  ]ݙHqFt0C (%p%0% 4 @%x%0&x&0& չ4 @&&`&  @' '(  ) &  &  '   ',' '  8c s  '  # %% ÜĜŜƜǜȜ_w$($չ0$%  %TALz|k~kA Rչչ&-4չ;B(*p*0*+@*x*0*x*0*+@**h+  +`,  +, ,+  +  /+&`,  , x,+.  H, ,( ,,  (-/-`- (- p--$  6 , - /  0/.  .   ./K\( **+,,i)((չ0(*6 *f(+-0,(,f,kj oj %չ ~Oչ3:AչHOP1,P11(`2022@2X2,3Џ3033 33& 3 K(3 X33 3 `3   @4 4 `4 E545 0122381 (00(1^<02PDH,~7jor2 %X. (7p707 4 @7x708 x808  4 @88`8  @9 9(  ) 8  8  9   919 9 9 Fq   9  5 78ÜĜŜƜǜȜ_w6(50567 8jW`7kvU s#:HOV]d(>p>0>+@>x>0? x?0? +@??h?  @`@ @@@?  ?  O@&`@@ x@,  P@ A( `A0BA@BA OЏC0CC CC& CL (C XCPB@CD`D (D pDC E0EEEE6 EL EȏE`DF0XF @FЏFF'=F:8F WjHFȏFF# /C0G!- !G`GG 9؏GG# G#3GO_<  > ?@BDF"=(<0<=> ?7(@SZXF řǙșəʙ˙G*R{9 qz ps7ukxhjG  /en><:AHOV] (%p%0% 4 @%x%0&x&0& չ4 @&&`&  @' '0  1 &  &  '   ',' '  8c s  '  # %% ÜĜŜƜǜȜ_w$($չ0$%  %dQ\z|k~kA bչչ&-4չ;B(*p*0*+@*x*0*x*0*+@**h+  +`,  +, ,+  +  /+&`,  , x,+.  H, ,0 ,,  (-/-`- (- p--,  > , - 7  0/.  . - >N/k|( **+,,i)((չ0(*;V * %(+M0,(,v,kj oj Eչ7*_չSZaչhoP1,P110`202ۼ2@2X2,3А3033 33& 3  S(3 X33 3 `3   @4 4 `4 E545 0122381 (00(1nL02PDH,~7jor2 %ۼ`6 (7p707 4 @7x708 x808  4 @88`8  @9 90  1 8  8  9   919 9 9 Fq   9  5 78ÜĜŜƜǜȜ_w6(50567 8zgp7kvU 3:HOV]d(>p>0>+@>x>0? x?0? +@??h?  @`@ @@@?  ?  O@&`@@ x@,  P@ A0 `A0BۼA@BA OАC0CC CC& CL (C XCPB@CD`D (D pDC E0EEEE6 EL EȐE`DF0XF @FАFF'=F:8F WjHFȐFF# /C0G!- !G`GG 9ؐGG# G#3GO_<  > ?@BDF"=(<0<=> ?G(@SZXF řǙșəʙ˙G*R{9 qz ps7ukxhjG  /e~#ۼ><:AHOV] (%p%0% 4 @%x%0&x&0& չ4 @&&`&  @' '!  " &  &  '   ',' '  8c s  '  # %% ÜĜŜƜǜȜ_w$($չ0$% %yD1:vxkzi= @չչ")0չ7>(*p*0*+@*x*0*x*0*+@**h+  +`,  +, ,+  +  /+&`,  , x,H, ,! ,,ɨ (-'-`-(- p--   2  , -  + 0/ ,.   .  /( **+,,iٗ)((չ0(* *v(+l0,(,jBkj o jz +չɨG չչP11P11$`2022@2X223Б3033 33& 3 K(3 X33 3 `3   @4 4 `4 E545 0122381 (00(1,;02,ZNR6)7jow2 /b8 (7p707 4 @7x708 x808  4 @88`8  @9 9!  " 8  8  9   919 9 9 Fq   9  5 78ÜĜŜƜǜȜ_w6(50567 8\IR7kvU ˫e:HOV]d(>p>0>˫+@>x>0? x?0? +@??h?  @`@ @@@?  ?  O@&`@@ x@@  P@ A$ `A0BA@BA OБC0CC CC& CL (C XCPB@CD`D (D pDC E0EEEE6 EL EȑE`DF0XF@FБFF':F:8FbHFȑFF# /C0G!- !G`GG 9ؑGG# G#3GO_<  > ?@BDF"=(<0<=> ?w"(@,zPWXF'0Nl .173k6&j  "˫]HvKy5H  (%p%0% 4 @%x%0&x&0& չ4 @&&`&  @' '"  # &  &  '   ',' '  8c s  '  # %% ÜĜŜƜǜȜ_w$($չ0$%  %}H5>xzk|i? 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O@&`@ @ x@P@ A$ `A0BA@BA OГC0CC CC& CL (C XCPB@CD`D (D pDC E0EEEE6 EL EȓE`DF0XF@FГFF':F:8FbHFȓFF# /C0GG`GG-ؓGG# G#3GO_<  > ?@BDF  =(<0<=> ?Z(@Pp5|<vXF G, 7k!j    *ˊ R'U8 (%p%0% 4 @%x%0&x&0& չ4 @&&`&  @' '(  ) &  &  '   ',' '  8c s  '  # %% ÜĜŜƜǜȜ_w$($չ0$% %R?Hvxkzi= Nҡ չ չ")0չ7>(*p*0* +@*x*0*x*0*ҡ +@**h+  +`,  +, ,+  +  /+&`,  , x,H, ,( ,, (-'-`-(- p--$  6  , -  / 0/ .   .  /( **+,,i )((չ0(* *x (+n0,(,^6kj o j|r ҡ ϩ %չת 3 չչP1P11(`2022@2X23Д3033 33& 3 K(3X333`3  @4 4 `4ת  145 01223 81 (00(1022&w*f7gjiob2 2ת x (7p707 4 @7x708 x808  4 @88`8  @9 9(  ) 8  8  9   919 9 9 Fq   9  5 78ÜĜŜƜǜȜ_w6(50567 8jW`7kvU s #: HOV]d(>p>0> +@>x>0? x?0?  +@??h?  @`@ϩ  @@ @?  ?  O@&`@ת  @ x@P@ A( `A0BA@BA OДC0CC CC& CL (C XCPB@CD`D (D pDC E0EEEE6 EL EȔE`DF0XF@FДFF':F:8FbHFȔFF# /C0GG`Gת G-ؔGG# G#3GO_<  > ?@BDF  =(<0<=> ?b (@Xp5|<vXF G, 7k!j    2 ϩ ת R'Uת 8 (%p%0% 4 @%x%0&x&0& չ4 @&&`&  @' '0  1 &  &  '   ',' '  8c s  '  # %% ÜĜŜƜǜȜ_w$($չ0$%  % dQZxzk|i? ` չ չ$+2չ9@(*p*0* +@*x*0*x*0* +@**h+  +`,  +, ,+  +  /+&`,  , x,H, ,0 ,, (-'-`-(- p--,  >  , -  7 0/ .   .  /%6( **+,,i )((չ0(*  * @(+0,(,nFkj o j|r   Eչ Cչչ P1P110`2022@2X23Е3033 33& 3 K(3X333`3  @4 4 `4  145 01223 81 (00(1022&w*f7gjiob2 2 x (7p707 4 @7x708 x808  4 @88`8  @9 90  1 8  8  9   919 9 9 Fq   9  5 78ÜĜŜƜǜȜ_w6(50567  8 zgp7kvU  3: HOV]d(>p>0> +@>x>0? x?0?  +@??h?  @`@  @@ @?  ?  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Kߊ ] ]5D44   base +7~?L,ĉ *kM̖ \  X >G P&< o ڧ  ʼL|ř Lf! ]̖ d 7cache T+,0PJ     W Ԛ0 ީ  4 ;E c  sJڧQXڧ_̖ f< $ ř4 <    !? p ԏL Q <\г  P<< 0{?i bg    Q          , $ ' < l ř U8 d G <   4  ^U +$ wl4+\ U*D RppYp opopo2ЫߵLd &oT &t#1!řǙșəʙ˙G*R{9 \M wDřǙșəʙ˙G*R{9  1 #     ׶|D7hmk T]i9EI$+oٴd  4* ׶ |A3g, T\ K0(  8z4't 3{< _77/7 6wQ?m!؆UO=F|  %ÜĜŜƜǜȜ_ww| L  l  [ÜĜŜƜǜȜ_wXu %ÜĜŜƜǜȜ_w |  Lm[}OD^!ÜĜŜƜǜȜ_wYq PBOo'm w #( (   f 4 =U  e mM   g  "=" ,#(-"q"  "U17 ,U& Xh  "  - 6?errhZf gyH")\ N Կ\ g 8/#4 dZDv ,  dd DebugTupleddd dddd empty_named(5&:?R,''t'4( KD( (('Z '7y,+++\+ >l++*Y7Y䍲?Mݻ*0m,1 *1AF,1 1d1 K1 110 16 1,03<aj,i,555\5 G 5t5 554?$5 4K,<<<*d< HL<\=<$ == "zero",! i if i > 0 => "positive",Č _ => "negative",< }); // Ranged sampling: use std::f32::consts::PI;?< println!("Angle: {} radians", rand::random_range(-PI..PI));<ZW See also [The Book: Quick Start](https://rust-random.github.io/book/quick-start.html).%https://www.rust-lang.org/favicon.ico9https://www.rust-lang.org/logos/rust-logo-128x128-blk.pnglt  stsrih]G Q K 7J 9I HG#FYvy| s hY\L JM?B),l<9 Generating random samples from probability distributions # Quick start< use rand::RngExt; let mut rng = rand::rng();KH eprintln!("A letter: {}", rng.sample(rand::distr::Alphabetic) as char);IF let percent_range = rand::distr::Uniform::try_from(0..=100).unwrap();=: eprintln!("Percentage: {}%", rng.sample(&percent_range));<Ԕ # `Distribution` traitIF Abstractly, a [probability distribution] describes the probability of1. occurrence of each value in its sample space./, More concretely, a sampler `X` implementingNK [Distribution][]<T> is an algorithm for choosing valuesKH from the sample space `T` (or a subset of `T`) using randomness from and [`Rng`]. OL Typically the sampler `X` emulates some like-named probability distribution ,) (for example, [`Bernoulli`] emulates the TQ [Bernoulli distribution](https://en.wikipedia.org/wiki/Bernoulli_distribution)).  (% ## The Standard Uniform distribution  OL The [`StandardUniform`] distribution is perhaps the most important sampler, C@ representing the "default" probability distribution for a type. NK Its distribution is expected to be uniform. For `bool`, `char` and integer PM types the sample space equals that of the type (i.e. any valid value of that JG type may be yielded), but for floating-point types the sample range is" arbitrarily set to `0.0..1.0`.IF Implementing [`Distribution`] for [`StandardUniform`] for type `T`IF enables sampling type `T` using [`RngExt::random`] and (by extension) [`rand::random`].,) ### Other standard uniform distributionsJG [`Alphanumeric`] is a simple distribution to sample random letters andTQ numbers of the `char` type; in contrast [`StandardUniform`] may sample any valid\ `char`.\Y There's also an [`Alphabetic`] distribution which acts similarly to [`Alphanumeric`] butܠ doesn't include digits.NK For floats (`f32`, `f64`), [`StandardUniform`] samples from `[0, 1)`. AlsoHE provided are [`Open01`] (samples from `(0, 1)`) and [`OpenClosed01`]NK (samples from `(0, 1]`). No option is provided to sample from `[0, 1]`; itNK is suggested to use one of the above half-open ranges since the failure toKH sample a value which would have a low chance of being sampled anyway is  rarely an issue in practice.*' ## Parameterized Uniform distributionsKH The [`Uniform`] distribution provides uniform sampling over a specifiedHE range on a subset of the types supported by the above distributions.52 Implementations support single-value-sampling via74 [`Rng::random_range(Range)`](RngExt::random_range).NK Where a fixed (non-`const`) range will be sampled many times, it is likely;8 faster to pre-construct a [`Distribution`] object usingB? [`Uniform::new`], [`Uniform::new_inclusive`] or `From`. ## Non-uniform samplingMJ Sampling a simple true/false outcome with a given probability has a name:MJ the [`Bernoulli`] distribution (this is used by [`RngExt::random_bool`]).IF For weighted sampling of discrete values see the [`weighted`] module.JG This crate no longer includes other non-uniform distributions; insteadGD it is recommended that you use either [`rand_distr`] or [`statrs`].VS [probability distribution]: https://en.wikipedia.org/wiki/Probability_distribution74 [`rand_distr`]: https://crates.io/crates/rand_distr/, [`statrs`]: https://crates.io/crates/statrs# [`rand::random`]: crate::random7ԑ/ [`Rng`]: crate::Rng, HXWL"Xt"d"Cd##Y$#Y#[4#[Zd#Z_T# _ _d# _ ΂<$  4$ lL  d#   4 c ԘW,GI57L&\ , $g8  ggg cgcثq1ȡB  $ *t7JG Construct a new `Bernoulli` with the given probability of success `p`.| # PrecisionHE For `p = 1.0`, the resulting distribution will always generate true.IF For `p = 0.0`, the resulting distribution will always generate false.LI This method is accurate for any input `p` in the range `[0, 1]` which isB? a multiple of 2-64. (Note that not all multiples of?< 2-64 in `[0, 1]` can be represented as a `f64`.)B *X!B? Construct a new `Bernoulli` with the probability of success of"EB `numerator`-in-`denominator`. I.e. `from_ratio(2, 3)` will return"JG a `Bernoulli` with a 2-in-3 chance, or about 67%, of returning `true`.##JG For `numerator == denominator`, the resulting distribution will always$FC return `true`; for `numerator == 0` it will always return `false`.$HE For `numerator > denominator` or `denominator == 0`, this returns anT% error.%l% # Example%<%% use rand::distr::Bernoulli;&&1. let d = Bernoulli::from_ratio(2, 3).unwrap();&.+ assert!((d.p() - 2.0 / 3.0).abs() < 1e-9);&& // Edge cases:'MJ assert_eq!(Bernoulli::from_ratio(3, 3).unwrap().p(), 1.0); // always true'NK assert_eq!(Bernoulli::from_ratio(0, 3).unwrap().p(), 0.0); // always false(YV assert!(Bernoulli::from_ratio(4, 3).is_err()); // numerator > denominator)RO assert!(Bernoulli::from_ratio(1, 0).is_err()); // denominator == 0<)T*B .-63 Returns the probability (`p`) of the distribution...KH This value may differ slightly from the input due to loss of precision. . B . $.0%%0640  B 0400 $07 0 d  #C 4I!$8"T=@T3̤ NK Types (distributions) that can be used to create a random instance of `T`.A> It is possible to sample from a distribution through both theJG `Distribution` and [`RngExt`] traits, via `distr.sample(&mut rng)` andOL `rng.sample(distr)`. They also both offer the [`sample_iter`] method, which<9 produces an iterator that samples from the distribution.NK All implementations are expected to be immutable; this has the significantDA advantage of not needing to consider thread safety, and for mostIF distributions efficient state-less sampling algorithms are available.  KH Implementations are typically expected to be portable with reproducible :7 results when used with a PRNG with fixed seed; see the NK [portability chapter](https://rust-random.github.io/book/portability.html) NK of The Rust Rand Book. In some cases this does not apply, e.g. the `usize` C@ type requires different sampling on 32-bit and 64-bit machines.  .+ [`sample_iter`]: Distribution::sample_iterd #$#$  #,2%')%'))'%46 4 LI Generate a random value of `T`, using `rng` as the source of randomness.4   B#&& #4   %$ 7  b JG Create an iterator that generates random values of `T`, using `rng` as the source of randomness.C@ Note that this function takes `self` by value. This works sinceDA `Distribution` is impl'd for `&D` where `D: Distribution`,IF however borrowing is not automatic hence `distr.sample_iter(...)` mayEB need to be replaced with `(&distr).sample_iter(...)` to borrow orC@ `(&*distr).sample_iter(...)` to reborrow an existing reference.l<LI use rand::distr::{Distribution, Alphanumeric, Uniform, StandardUniform}; // Vec of 16 x f32:OL let v: Vec = StandardUniform.sample_iter(&mut rng).take(16).collect();t // String:  let s: String = Alphanumeric .sample_iter(&mut rng) .take(7) .map(char::from) .collect(); // Dice-rolling::7 let die_range = Uniform::new_inclusive(1, 6).unwrap();74 let mut roll_die = die_range.sample_iter(&mut rng);)& while roll_die.next().unwrap() != 6 {,) println!("Not a 6; rolling again!");, }<\B#((# ϸ, 'K7U:<g" Map sampled values to type `S`l<-* use rand::distr::{Distribution, Uniform};41 let die = Uniform::new_inclusive(1, 6).unwrap();2/ let even_number = die.map(|num| num % 2 == 0);1. while !even_number.sample(&mut rand::rng()) {.+ println!("Still odd; rolling again!");,<B#*+*+#  #T# , )fZplnhj;8-.-. 4#|/%/46 34  ͸B,00 ,͸4͸ /8͸$7* "R234423 " " "#|"#567QQQ67egac]_L#$#11#$# ɿB1 #1 6$#&-L& B1 &1 7$&&]9:;9:; & & &|''(*-/24)e=>?@>@?=#ۼ *ۼ * * *|*#ۼT* )A%AQSVX[]*34*  B<BB +<4** Aۼ$+7 *,+! Sample or extend a [`String`]++EB Helper methods to extend a [`String`] or sample a new [`String`].,̼,d,CC,C!DFDFDF.W,)& Append `len` random chars to `string`--JG Note: implementations may leave `string` with excess capacity. If this-IF is undesirable, consider calling [`String::shrink_to_fit`] after this\. method.l.   BCEE .C4..$.7.4// .1K//, Generate a [`String`] of `len` random chars//LI Note: implementations may leave the string with excess capacity. If this0I\1l1  BCGG 1C411 F$17R[ 1L ,  T#\HJ"tHK#LHLd#HN|HOHOHQ 4HR HSd{},]_KML<t4LTTT!UVUVU<V4 TT<HE Helper method to combine the fraction and a constant exponent into aT float.JG Only the least significant bits of `self` may be set, 23 for `f32` and 52 for `f64`.JG The resulting value will fall in a range that depends on the exponent.30 As an example the range with exponent 0 will be41 [20..21), which is [1..2).ĖBTT V$D\  0  !,   , 8 $& 8 $- $ , 8& 8,$ , 8uty& 8,$ , 8f_scalarD& 8,$ , 8u_scalarD& 8$ , 8 fraction_bitsl& 8$$ , 8 exponent_biasl& 8$*  0-,   +   8  , 8 $- 8$8L8 , 8  8!$8  , 8% +   84  848 8  8$$ 8D& 8(, 8  88l& , 8D     , 8l 8D8, 8D, 8l% , 8'8 from_bitsL  8$ , 8'8,  8l,   +   8  , 8 $- 8$8d , 8 8 8|  $8 84 8 & 8 - 8,    8$$ 87&  88 (, 8  $B8!8T! !8 !'!88%48B $9 ,99%49B $9 ,99T9B $9L9$99,<:B $: ,:<3|<B $<$<L>$>>(l>B  >@#\@,@ A,AB _7B!LB,B B,BB 7BCC"TC,C CCB $CCDDB  8DD D P D E , D8D& D8,D$ E, E8E& E8,E*E E P8$E8"tE8 E, E8E E L=8!$E8"$E E8$E% E8!$E8#$E E, E8E% E+ F F F84F F F84F8 F8"4F F F8$F$ F8 ,F& F8$F(F8$F F F8$F F8 ,F+ G G G84G G G84G8 G8"4G G G8$G$ G8 ,G& G8$G(G8$G G G8$GG8 ,G+ H H H84H H H84H8 H8"TH H H8$H(H8$H H H8$H H8 is_finiteLH H H+ H H I84H I I84I8 I8"` to support passing in values by reference orI F by value. In the implementation of these functions, you can choose toT Q simply use the reference returned by [`SampleBorrow::borrow`], or you can chooseF C to copy or clone the value, whatever is appropriate for your type. < ̢  use rand::prelude::*;6 3 use rand::distr::uniform::{Uniform, SampleUniform,? < UniformSampler, UniformFloat, SampleBorrow, Error};   struct MyF32(f32); !  #[derive(Clone, Copy, Debug)]+ ( struct UniformMyF32(UniformFloat); * ' impl UniformSampler for UniformMyF32 {  type X = MyF32; @ = fn new(low: B1, high: B2) -> Result4 1 where B1: SampleBorrow + Sized,3 0 B2: SampleBorrow + SizedL  {W T UniformFloat::::new(low.borrow().0, high.borrow().0).map(UniformMyF32)L  }J G fn new_inclusive(low: B1, high: B2) -> Result4 ɵ3 L öa ^ UniformFloat::::new_inclusive(low.borrow().0, high.borrow().0).map(UniformMyF32)L C @ fn sample(&self, rng: &mut R) -> Self::X {% " MyF32(self.0.sample(rng))L ,  "  impl SampleUniform for MyF32 {$ ! type Sampler = UniformMyF32;,  7 4 let (low, high) = (MyF32(17.0f32), MyF32(22.0f32));3 0 let uniform = Uniform::new(low, high).unwrap();- * let x = uniform.sample(&mut rand::rng());<  ; 8 [`SampleUniform`]: crate::distr::uniform::SampleUniform= : [`UniformSampler`]: crate::distr::uniform::UniformSampler5 2 [`UniformInt`]: crate::distr::uniform::UniformInt9 6 [`UniformFloat`]: crate::distr::uniform::UniformFloat? < [`UniformDuration`]: crate::distr::uniform::UniformDurationI F [`SampleBorrow::borrow`]: crate::distr::uniform::SampleBorrow::borrow to ensure that samples from `[low, high)` are always strictlyA<7 less than `high`, this approach may be very slow where:<0 `scale.abs()` is much smaller than `high.abs()`3</ (example: `low=0.99999999997819644, high=1.`).28 8l\  8k& , 8$ 8$& , 8$ 88k,& , 8(8$  88D  , 8 '8,   78, 8D , 8D'8<% 8$  88$   8k, 8D 8k 8"<  8$% 88$ 8    8,% 8k, 8k, 8"|   8$% 8d     , 8 '8,  70.0 8"4  8k,% 8kd  8k$ 8k,,   +   8  , 8 $- 8$8-l8 , 8   8!$8'< 8kd , 8 % ,   +   8  , 8 $- 8$8-t8 8kd , 8   =8!$8  , 8% 8 8  8'$ 8'   8,& 8'$ 84& 8'(84 8$$ 8/, 8$,8'& 8/d 8$'8   8,$ 8'& 8/d 8$'8   8,$   ",88k  8, 8/4  % 88$  84 8/4  % +   8  88   8k 8"T     8$ 8"T    848  8/,'8L% 8    8k  8"4   8$   84 8   8/, ' 8ށT % 8 8k,  8$  !8k!% !8! ! ! !8k,! !8"T! ! ! ! !84!8! ! !8/,!'!8L!% !8" " "8$"'"8l\" " "8k"$ "8$"$ "8k,"8 "8(l" "8'"$ "8'" " " "8,"& "8'"$ "84"& "8'"("84" #8$#$ #8/,# #8$,#8'#& #8/d# #8$#'#8 # # #8,#$ #8'#& #8/d# #8$#'#8 # # $8,$$ $ $ )D8$8k$ $ $8,$ $8/4$ $ $% $8$8$$ $ $84$ $8/4$ $ $% $+ % % %8% % %8%8% % % %8k% %8"T% % %% % % %8$% %8"T% % % % &84%8% % &8/,%'%8L&% &8& &8k& &8"4& & &8$& & '84&8& & &8/,&'&8ށT&% &8'8j,' '8$' '8k'% '8' '8j,' '8"T' ' ' ' (84'8' ' (8/,''(8L(% (8(8D( ( (, (8( ('(8,( ( ( 7(8(, (8D( (, (8D('(8<(% (8)8k,) )8j,) )8D)% )8) ) )8$)')8l\) ) )8k)$ )8$)$ )8k,)8 )84) *8 *& *8* *- *8,* * * * *8$*$ *87*& * *8*8 *(*8$*'*8 * * 08*8D* + + +87+ +874+'+ +, +8+ + + ++, +8+'+8,+ + +, +8|+ +8+ + +7 +% +8,8D, ,8D, , ,, ,8, ,',8,, , ,7,% ,8D0 08$0 08k,0 08$0 08k0+ 0 0 08408 08(l0 08 0& 080 0- 18,1$ 18'1$ 18'1 1 1 1 8,1& 18'1$ 1841& 18'1$ 1871& 1 1818 1(1841 18$1'18 1$ 18/,1 18$,18'1& 18/d1 28$2'28 2 2 28,2$ 28'2& 28/d2 28$2'28 2 2 28,2$ 2 2 38$2'28(2 3 38,3$ 3843$ 3873+ 3 3 38438 38(3 38 3& 383 3- 38,3$ 38'3$ 38'3 3 3 4 8,3& 48'4$ 4844& 48'4$ 4874& 4 4848 4(4844 48$4'48 4$ 48/,4 48$,48'4& 48/d4 48$4'48 4 4 48,4$ 48'5& 58/d5 58$5'58 5 5 58,5$ 5 5 =M858k5 5 58,5 58/45 5 5% 5858$5 6 6846 68/46 6 6% 6+ 6 6 686 6 68686 68k6 68"T6 6 66 68$6 68"T6 6 6 6 784787 7 78/,7'78L7% 787 78k7 78"47 7 78$7 7 884788 8 88/,8'88ށT8% 8888k,8 88$8 88k8% 888 88k,8 88"T8 8 8 8 984989 9 98/,9'98L9% 98:8D: : : :87: :874:': :, :8: : : ::, :8:':8,: : :, :8|: :8: : ;7 ;% ;8;8D; <8D< < <, <8< <'<8,< < <7<% <8= = =8D= =8k,= =8k=% = t T$<   /, /d-l-t! 4,y{hj%\,MO9;  W  , 8& 8$ , 8& 8$ , 8 sample_tyL& 8,*  W8$8oT , 8   < Get the maximum possible value"+   8,  8unused4+   848  8,8 8p   8$(, 8   88$ 8j,7   84 , 8 '8MAX% 8$  88p 8$ 8k 8d  8$ 8j, 8d  7 % 88p 8$ 8k   , 8 '88$  8p8$8-l8 , 8   8!$8'<  8oT  , 8  % 8$ 8-t 8  8oT  , 8    W8!$"8 " ", "8"% "+ # # #84#8 #8 $ $8'$$ $8'$ $ $ $8,$& $8'$$ $84$& $8'$($84$ $8$$$ $8/,$ $8$,$8'$& $8/d$ $8$$'$8 $ $ $8,$$ $8'%& %8/d% %8$%'%8 % % %8,%$ % % '8%8k% % %8,% %8/4% % %% %8%8$% & &84& &8/4& & &% &8& & & &8k& &8$& & &84&8& & &8/,&'&8ށT&% &8-t'''8(l' ' '8k'$ '8$' '7 '+ ' ' '84'8 (8(l( (8'($ (8'( ( ( )8,(& (8'($ (84(& (8'(()84) )8$)$ )8/,) )8$,)8')& )8/d) )8$)')8 ) ) )8,)$ )8')& )8/d) )8$)'*8 * * *8,*$ * * /18*8k* * *8,* *8/4* * *% *8*8$* * *84* *8/4* * *% *8+ + + +8k++8$+ + +84+8+ + +8/,+'+8ށT+% +8+8j,+ +8$+ ,8d, , ,8k, ,8d, , ,7 ,8,, ,8,% ,8,8o4, ,8,8j,, ,7 , , - 8,8j,, ,, ,8L,'-8$- - -8j,-% - - -8j,- -8 wrapping_negd- - - -8j,-8$- - .7 -% .8. . /8oT. . /8k.$ .8j,.& .8j,.8., .8.$ .8o4/& /8o4/8/, /8/8/, /8/$ /<4 Sample from distribution, Lemire's method, unbiased/7+ 0 0 08408 0840 08 0& 080 0- 08,0 0 0 0 08$0$ 0870& 0 0808 0(18$1'18 1 1 5+818j,1 18$1 18j,181, 18181, 18L1% 1818j,117 1 1 2841872 28742 2 2% 2828o42 28$2 28o4282, 28282, 28L2% 28282 28$3 3 483 3 383$ 383 3873 38743'3 3, 38L3 3 3 3 38!$3 3 38j,3% 3838338o43 3 48,484% 4% 48$4 48k4 48d4 4 48484, 484+ 5 5 58458 58(l5 58 5& 585 5- 58,5$ 58'5$ 58'5 5 5 68,5& 58'5$ 5845& 68'6$ 6876& 6 6868 6$ 6(6846 68$6'68 6$ 68/,6 68$,68'6& 68/d6 68$6'78 7 7 78,7$ 78'7& 78/d7 78$7'78 7 7 78,7$ 7 7 9878k7 7 78,7 78/47 7 7% 7888$8 8 8848 88/48 8 8% 888 8 8 88k8 88$8 8 984888 8 88/,8'88ށT8% 88$9'98(9 9 98k9$ 98$9 97 9$ 9879<, Sample single value, Canon's method, biased9/<:<> In the worst case, bias affects 1 in `2^n` samples where n is:A<= 56 (`i8`), 48 (`i16`), 96 (`i32`), 64 (`i64`), 128 (`i128`).;@+ ; ; ;8; ; ;8 ; ; ;8<; ;7unbiasedT;+ < < <84<8 <8(< <8 <& <8< <- <8,<$ <8'<$ <8'< < < =8,<& <8'<$ <84<& =8'=$ =87=& = =8=8 =$ =(=84= =8$='=8 =$ =8/,= =8$,=8'=& =8/d= =8$='>8 > > >8,>$ >8'>& >8/d> >8$>'>8 > > >8,>$ > > GF8>8k> > >8,> >8/4> > >% >8?8$? ? ?84? ?8/4? ? ?% ?8? ? ? ?8k??8$? ? @84?8? ? ?8/,?'?8ށT?% ?8@8j,@ @8$@ @8d@ @ @8k@ @8d@ @ @7 @8@, @8@8@, @8L@% @8@8j,@A7 A A B84A8A A B87A B874B B B% B8B B C8B8 4B$ C8DC C87C C874C'C C, C8LC C C C C8!$C C C8j,C% C8C8DC D8j,D D8ȤdD D D D G8D D E8dD$ E8 E E E E 87E E874E'E E, E8LE E E E E8!$E E E8j,E8E, E8LE% E8F8\F F8DF F8 checked_add\F F F8dF8F, F8LF F8is_none= high`, or if `low`, `high` or the range `high - low` isF; 8 non-finite. In release mode, only the range is checked.G  B'',G |G ,H |G kG G J HL I Create a new `Uniform` instance, which samples uniformly from the closedI$ ! range `[low, high]` (inclusive).I IK H Fails if `low > high`, or if `low`, `high` or the range `high - low` isJ; lJ  B'',K ه|K ,K |K kBLJ J L5  L lL %M3 4M   B M 4M M $M 7 M O MI F Helper trait for creating objects using the correct implementation ofN- * [`UniformSampler`] for the sampling type.N NH E See the [module documentation] on how to implement [`Uniform`] rangeO  sampling for a custom type.O O1 . [module documentation]: crate::distr::uniformlP ,P  P' P DQ -"P& P< 9 The `UniformSampler` implementation supporting type `X`.

Usually users should not call this directly but prefer to useX  [`Uniform::new`].X  B'',Y  Y ,Z  Y kY $Y X X [ Z8 5 Construct self, with inclusive bounds `[low, high]`.Z ZA Η[  [`Uniform::new_inclusive`].l[  B'',\ \ ,\ \ k[ $[ [ [ ]: \  Sample a value.4]    B ] 4] ] $] 7] ] f ]K H Sample a single value uniformly from a range with inclusive lower bound^, ) and exclusive upper bound `[low, high)`.^ ^L ‚_N _D ķ` ` `( % By default this is implemented usingaI F `UniformSampler::new(low, high).sample(rng)`. However, for some typesaJ G more optimal implementations for single usage may be provided via thisb7 4 method (which is the case for integers and floats).b!  Results may not be identical.c cK H Note that to use this method in a generic context, the type needs to bec6 3 retrieved via `SampleUniform::Sampler` as follows: ; use rand::distr::uniform::{SampleUniform, UniformSampler};d  # #[allow(unused)]e? < fn sample_from_range(lb: T, ub: T) -> T {e"  let mut rng = rand::rng();eO L ::Sampler::sample_single(lb, ub, &mut rng).unwrap(),f  Immutably borrows from an owned value. See [`Borrow::borrow`]u u3 0 [`Borrow::borrow`]: std::borrow::Borrow::borrow4u   B u  $u uU /Du lv #%v 4v  ܶB v  $v wV 8/Dw lw #%w 4w   B x  8$x } x? < Range that supports generating a single sample efficiently.x xO L See [`RngExt::random_range`] for examples; the method provides a convenienty  interface over this type.y ty # Examplesy `] exists.  Error cases:E B - [`Error::InvalidInput`] when the iterator `weights` is empty.K H - [`Error::InvalidWeight`] when a weight is not-a-number or negative.K H - [`Error::InsufficientNonZero`] when the sum of all weights is zero. B ? - [`Error::Overflow`] when the sum of all weights overflows.  2 / [`Uniform`]: crate::distr::uniform::Uniform!  B ! P d! ֣ |" 4"  4MO*  5 +G D Update a subset of weights, without changing the number of weights., ,. + `new_weights` must be sorted by the index., ,X U Using this method instead of `new` might be more efficient if only a small number of-V S weights is modified. No allocations are performed, unless the weight type `X` usesԉ.  allocation internally.. .: 7 In case of error, `self` is not modified. Error cases:.E B - [`Error::InvalidInput`] when `new_weights` are not ordered by/' $ index or an index is too large./K 0K 1K H Note that due to floating-point loss of precision, this case is not1L I always correctly detected; usage of a fixed-point weight type may be2  preferred.2B 3 3P M Updates take `O(N)` time. If you need to frequently update weights, consider3c ` [`rand_distr::weighted_tree`](https://docs.rs/rand_distr/*/rand_distr/weighted_tree/index.html)44 1 as an alternative where an update is `O(log N)`.t5      B 5  5#  6# ,6 <6 $5  75 6 A  L? L $ L lL TL $L$ 21wIy$wIyL ttL  $ց dM ,M Mr 8 M lM TM g,N g,N gKMN8 N   ggg cgcثq1ȡB N  8$N @7PS 8 P lP TP #%P ,P  B P  8$P R 8 R  R# lR TR ,S QQQjlR LS $S S( $S  řǙșəʙ˙G*R{9 QB S  8$S U- LU  B U  8$U V 8 V  W# lW TW ,W EGW W<  W lW TX ,X )+\i X8 5 Returns the weight at the given index, if it exists.X X; 8 If the index is out of bounds, this will return `None`.Y lY Y >(), vec![1, 2, 3]);d- * dist.update_weights(&[(0, &2)]).unwrap();dB ? assert_eq!(dist.weights().collect::>(), vec![2, 2, 3]);R: [Rng][]. L I This trait must usually be brought into scope via `use rand::RngExt;` or  `use rand::prelude::*;`.   # Generic usage E B The basic pattern is `fn foo(rng: &mut R)`. Some!  things are worth noting here: J G - Since `RngExt: Rng` and every `RngExt` implements `Rng`, it makes no G D difference whether we use `R: Rng` or `R: RngExt` for `R: Sized`. N K - Only `Rng` is dyn safe, supporting `&mut dyn Rng` and `R: Rng + ?Sized`.  O L An alternative pattern is possible: `fn foo(rng: R)`. This has some P M trade-offs. It allows the argument to be consumed directly without a `&mut`;  also it still works directly N K on references (including type-erased references). Unfortunately within the L I function `foo` it is not known whether `rng` is a reference type or not, J G hence many uses of `rng` require an extra reference, either explicitly O L (`distr.sample(&mut rng)`) or implicitly (`rng.random()`); one may hope the4 1 optimiser can remove redundant references later. d Example: <   use rand::{Rng, RngExt}; 1 . fn foo(rng: &mut R) -> f32 {  rng.random(),  $ ! # let v = foo(&mut rand::rng());< 4 @  , 8,P C @ Return a random value via the [`StandardUniform`] distribution. l  <      let x: u32 = rng.random();  println!("{}", x);2 / println!("{:?}", rng.random::<(f64, bool)>());<    # Arrays and tuples 8 5 The `rng.random()` method is able to generate arraysG D and tuples (up to 12 elements), so long as all element types can bet generated. I F For arrays of integers, especially for those with small element typesI F (< 64 bit), it will likely be faster to instead use [`RngExt::fill`],2 / though note that generated values will differ. <    I F let tuple: (u8, i32, char) = rng.random(); // arbitrary tuple support D A let arr1: [f32; 32] = rng.random(); // array construction  let mut arr2 = [0u8; 128];9 6 rng.fill(&mut arr2); // array fill<  / , [`StandardUniform`]: distr::StandardUniform4  B    #| $ +- = : Return an iterator over [`random`](Self::random) variates ? < This is a just a wrapper over [`RngExt::sample_iter`] using  [`distr::StandardUniform`]. 0 - Note: this method consumes its argument. Use: 7 `(&mut rng).random_iter()` to avoid consuming the RNG. l  < 4 1 use rand::{rngs::SmallRng, RngExt, SeedableRng}; ) & let rng = SmallRng::seed_from_u64(0);: 7 let v: Vec = rng.random_iter().take(5).collect();  assert_eq!(v.len(), 5);< \  B  , | L(*+n  / , Generate a random value in the given range.! !H E This function is optimised for the case that only a single sample is!D A made from the given range. See also the [`Uniform`] distribution"H E type which may be faster if sampling from the same range repeatedly.# #A > All supported types may be sampled with `low..high_exclusive`#F C ([`Range`]) and `low..=high` ([`RangeInclusive`]) syntax. Unsigned$C @ integer types also support `..high_exclusive` ([`RangeTo`]) and$, ) `..=high` ([`RangeToInclusive`]) syntax.% d% # Panics% %J G Panics if the range is empty, or if `high - low` overflows for floats.& l& & <& & & & ' '  // Exclusive range'5 2 println!("{}", rng.random_range::(..10));'3 0 println!("{}", rng.random_range(-40.0..1.3e5));( (  // Inclusive range(/ , println!("{}", rng.random_range(-10..=10));(0 - println!("{}", rng.random_range('a'..='z'));<) ) )( % [`Uniform`]: distr::uniform::Uniform)  [`Range`]: std::ops::Range*0 - [`RangeInclusive`]: std::ops::RangeInclusive*"  [`RangeTo`]: std::ops::RangeTo*4 1 [`RangeToInclusive`]: std::ops::RangeToInclusive|+ d+  B +  +  + l+ t, $+ jQPRUW1) -7 4 Return a bool with a probability `p` of being true.- -C @ See also the [`Bernoulli`] distribution, which may be faster if.2 / sampling from the same probability repeatedly.. l. .  1`.0 0# [`Bernoulli`]: distr::Bernoulli|1 \1  B 1  $1 aP9D 2H E Return a bool with a probability of `numerator/denominator` of beingL3  true.3 3H E That is, `random_ratio(2, 3)` has chance of 2 in 3, or about 67%, of4J G returning true. If `numerator == denominator`, then the returned value4F C is guaranteed to be `true`. If `numerator == 0`, then the returned5& # value is guaranteed to be `false`.5 5C 6D A sampling from the same `numerator` and `denominator` repeatedly.7 d7 7 77 4 If `denominator == 0` or `numerator > denominator`.7 l7 8 <8 8 8 8 8+ ( println!("{}", rng.random_ratio(2, 3));<9 9 9# |9 d9  B 9  $9 PP@: <5 2 Sample a new value, using the given distribution.< |< ### Example= <= = = ʤ= = >9 6 let x = rng.sample(Uniform::new(10u32, 15).unwrap());>I F // Type annotation requires two types, the type and distribution; the?$ ! // distribution can be inferred.?@ = let y = rng.sample::(Uniform::new(10, 15).unwrap());<@ 4@  B @  @  @ |@ $@ CQ=?9;Iz @J G Create an iterator that generates values using the given distribution.A A1 . Note: this method consumes its arguments. UseB< 9 `(&mut rng).sample_iter(..)` to avoid consuming the RNG.B lB B  ; use rand::distr::{Alphanumeric, Uniform, StandardUniform};C C C D ؽDQ N let v: Vec = (&mut rng).sample_iter(StandardUniform).take(16).collect();D tD ݾE8 5 let s: String = (&mut rng).sample_iter(Alphanumeric)E ſE ޿E F F  // Combined valuesFD A println!("{:?}", (&mut rng).sample_iter(StandardUniform).take(5)GA > .collect::>());G G G: H9 6 let mut roll_die = (&mut rng).sample_iter(die_range);H) I, ,I ACP+ K8 5 Fill any type implementing [`Fill`] with random dataK KJ G This method is implemented for types which may be safely reinterpretedLJ G as an (aligned) `[u8]` slice then filled with random data. It is oftenLB ? faster than using [`RngExt::random`] but not value-equivalent.M MI F The distribution is expected to be uniform with portable results, butN> ; this cannot be guaranteed for third-party implementations.N lN N  TV   B V 4V V  ?[7=[ V ԍW DW  X LX  X e  X X *X  X X % X  X X 8to_le,X  X 8plain,X , X 8 X & X 8,X *X  X Y , Y 8 Y  Y 8,Y  Y Y % Y  Y Y 8,Y  Y 8wrappingDY , Y 8 Y & Y 8,Y *Y  Y Y 8DY  Y Y , Y 8 Y  Y 7 Y  Y 8,Y  Y Y % Y  Y Z  89TY  Y , Y 8 Y & Y 8Y $ Y , Y 8,Y & Z 8Z *Z  Z a  8 Z 89TZ  Z 8 Z & Z 8Z Z - Z 8,Z  Z  Z Z  8 $Z & Z  Z 8Z  Z Z 8$Z $ Z 87Z & Z  Z 8Z 8 Z  Z a 8Z 8 $Z  Z 8Z  Z Z  Z 7 Z  Z a 8[ 8$[ [ 8 [ '[ 8\[  [ [ 8 $[ % [ 87[  [ 8 fill_bytesT[  [ ` 8"4_  _ ` 8,_ '_ 8from_raw_parts_mut_  _ `  8 $_  _ 8 as_mut_ptrT_  _ _ 8` ` 8` 8` $ ` 8$` % ` 8 a 8 a 8a 8 $a  a a  a 8 a a 89La  a  a a 8,a  a , a 8,a 8 a % a % a  a b , a 8 b & b 8b *b  b d  b d 89Db  b b % b 8$b 89$b 8 b , b 8 b  b c 89Lb  c  c c 89Tc  c , c 8 c $ c 8,c % c 8$c 89$c 8 c 8Dc  c , c 8 c  c  c d 89Lc  c  c d 89Tc  c , c 8 c $ c 8Dc % d % d  d d , d 8 d & d 8d $ d , d  d d , d 8d & d 8d $ d  d *d  d e  d e 89Ld  d  d d , d 8 d % d 89Le  e  e e , e  e e , e 8e $ e  e % e \f f \g g d)& Random number generators and adapters ## Generators85 This crate provides a small selection of generators.>; See also [Types of generators] and [Our RNGs] in the book.&# ##### Non-deterministic generatorsUR - [`SysRng`] is a stateless interface over the operating system's random numberOL source. This is typically secure with some form of periodic re-seeding.EB - [`ThreadRng`], provided by [`crate::rng()`], is a handle to aRO thread-local generator with periodic seeding from [`SysRng`]. Because thisKH is local, it is typically much faster than [`SysRng`]. It should be74 secure, but see documentation on [`ThreadRng`]. ##### Standard generatorsOL These use selected best-in-class algorithms. They are deterministic but not EB portable: the algorithms may be changed in any release and may be  platform-dependent.  PM - [`StdRng`] is a CSPRNG chosen for good performance and trust of security HE (based on reviews, maturity and usage). The current algorithm is KH [`ChaCha12Rng`], which is well established and rigorously analysed. KH [`StdRng`] is the deterministic generator used by [`ThreadRng`] but B? without the periodic reseeding or thread-local management. NK - [`SmallRng`] is a relatively simple, insecure generator designed to be FC fast, use little memory, and pass various statistical tests of GD randomness quality. The current algorithm is one of the XoshiroA> generators below, depending on the target's pointer size.# ##### Named portable generatorsMJ These are similar to the [standard generators](#standard-generators), but85 with the additional [guarantees of reproducibility]:MJ - [`Xoshiro256PlusPlus`] is a very fast 64-bit insecure generator usingOL 256 bits of state with good performance in statistical tests of qualityMJ - [`Xoshiro128PlusPlus`] is a very fast 32-bit insecure generator usingOL 128 bits of state with good performance in statistical tests of qualityOL - [`ChaCha8Rng`], [`ChaCha12Rng`] and [`ChaCha20Rng`] are generators overEB the ChaCha stream cipher designed by Daniel J. Bernstein[^1]. ### Additional generatorsKH - The [`rdrand`] crate provides an interface to the RDRAND and RDSEED<9 instructions available in modern Intel and AMD CPUs.IF - The [`rand_jitter`] crate provides a user-space implementation ofJG entropy harvesting from CPU timer jitter, but is very slow and hasJG [security issues](https://github.com/rust-random/rand/issues/699).LI - The [`rand_pcg`] crate provides portable implementations of a subset96 of the [PCG] family of small, insecure generatorsKH - The [`rand_xoshiro`] crate provides portable implementations of the63 [xoshiro] family of small, insecure generators1. For more, search [crates with the `rng` tag]. ## Traits and functionalityEB All generators implement [`TryRng`]. Most implement [`Rng`] (i.e.EB `TryRng`) and thus also implement [`RngExt`].52 See also the [Random Values] chapter in the book.C@ Secure RNGs may additionally implement the [`CryptoRng`] trait.@= Use the [`rand_core`] crate when implementing your own RNGs.YV [^1]: D. J. Bernstein, [*ChaCha, a variant of Salsa20*](https://cr.yp.to/chacha.html)YV [guarantees of reproducibility]: https://rust-random.github.io/book/crate-reprod.htmlLI [Types of generators]: https://rust-random.github.io/book/guide-gen.htmlB? [Our RNGs]: https://rust-random.github.io/book/guide-rngs.htmlIF [Random Values]: https://rust-random.github.io/book/guide-values.html [`RngExt`]: crate::RngExt  [`TryRng`]: crate::TryRng  # [`CryptoRng`]: crate::CryptoRng '$ [`SeedableRng`]: crate::SeedableRng!/, [`rdrand`]: https://crates.io/crates/rdrand!96 [`rand_jitter`]: https://crates.io/crates/rand_jitter!30 [`rand_pcg`]: https://crates.io/crates/rand_pcg";8 [`rand_xoshiro`]: https://crates.io/crates/rand_xoshiro"?< [crates with the `rng` tag]: https://crates.io/keywords/rng#*' [chacha]: https://cr.yp.to/chacha.html#&# [PCG]: https://www.pcg-random.org/#(% [xoshiro]: https://prng.di.unimi.it/$D%%&4&ݑL'SysErrorD(SysRng4(L$,$ InfallibleT \ G4  BL 13 "D  #   HIJL $  & L HB j  $ l B  T , 5 d  B   $ 5 d  B  $ !G t!   B !  $!  $$T\G4!,2VLEG46#%'HIJL$ 2KH Create a new `Xoshiro128PlusPlus`. If `seed` is entirely 0, it will be  mapped to a different seed.L B  $  ( 85 Create a new `Xoshiro128PlusPlus` from a `u64` seed.  2/ This uses the SplitMix64 generator internally.l B ,t "T,5d B  $5d B  $Ft  B  h3$$T\G4!,2VLEG46#%'HIJL$ 2KH Create a new `Xoshiro256PlusPlus`. If `seed` is entirely 0, it will be L B  $  ( 85 Create a new `Xoshiro256PlusPlus` from a `u64` seed.  2l B ,t "T,5d B  $,5d B  $Ft  B  ]͈<$Ф$$$T\Gd4mL\^KM9;,T,5d B  $5d B  $Ft  B  $HIL$&LHB %%$4%T2T,Id̺D4\GD GeneratorLd4$3$D\,Դ}Lpr^` ! L $ Еd< Еlet:o\,Е   \4-D  B  $,4 ÜĜŜƜǜȜ_w/ hՙB  $DЕUܣl B ̗$t()0($! Immediately reseed the generator))96 This discards any remaining random data in the cache.4) B ) $),,52 Debug implementation does not leak internal stateg,6,  ggg cgcثq1ȡB , $,,̆71,) Access a fast, pre-initialized generator110- This is a handle to the local [`ThreadRng`].11.+ See also [`crate::rngs`] for alternatives.2l22<22б22 # fn main() {22&# let mut numbers = [1, 2, 3, 4, 5];3&# numbers.shuffle(&mut rand::rng());3%" println!("Numbers: {numbers:?}");33JG // Using a local binding avoids an initialization-check on each usage:44485 println!("True or false: {}", rng.random::());5B? println!("A simulated die roll: {}", rng.random_range(1..=6));<5 # }<55t5 # Security55$! Refer to [`ThreadRng#Security`].6d666LI This method panics in case of [`SysRng`] failure during initial seeding.7B7 U7̎8<8B 8T8,895d9 B 9 $9;5d; B ; $;=Gt=  B = $= @%j%&_&&T&Ф&ܲ&\'&&dL(sys_rng(܀(,(j.,}\" Sequence-related functionality̐ This module provides:GD * [`IndexedRandom`] for sampling slices and other indexable listsRO * [`IndexedMutRandom`] for sampling slices and other mutably indexable lists+( * [`SliceRandom`] for mutating slices1. * [`IteratorRandom`] for sampling iteratorsGD * [`index::sample`] low-level API to choose multiple indices from `0..length`l Also see:MJ * [`crate::distr::weighted::WeightedIndex`] distribution which provides  weighted index sampling.MJ In order to make results reproducible across 32-64 bit architectures, allKH `usize` indices are sampled as a `u32` where possible (also providing a+( small performance boost in some cases). WeightError\ Et t N| K Gl L\ dT%\ ,*,TT,|ܑ ԳB 79 B  $, :d  B $  %.d% B %$% % 4,24 + j,.T4 T,|! "B 7vu %T  B  >+B)#,BĬ<dD GlB\ 4Cu c,TV@B|B*DA Extension trait on iterators, providing random sampling methods.NK This trait is implemented on all iterators `I` where `I: Iterator + Sized` and provides methods for=: choosing one or more elements. You must `use` this trait:<" use rand::seq::IteratorRandom;+( let faces = "😀😎😐😕😠😢";JG println!("I am {}!", faces.chars().choose(&mut rand::rng()).unwrap());<'$ Example output (non-deterministic):\ ```nonet I am 😀!<t,QD* 6,\  Uniformly sample one elementEB Assuming that the [`Iterator::size_hint`] is correct, this method HE returns one uniformly-sampled random element of the slice, or `None` GD only if the slice is empty. Incorrect bounds on the `size_hint` may IF cause this method to incorrectly return `None` if fewer elements than HE the advertised `lower` bound are present and may prevent sampling of KH elements beyond an advertised `upper` bound (i.e. incorrect `size_hint` B? is memory-safe, but may result in unexpected `None` result and  non-uniform distribution).  KH With an accurate [`Iterator::size_hint`] and where [`Iterator::nth`] is HE a constant-time operation, this method can offer `O(1)` performance. Where no size hint isEB available, complexity is `O(n)` where `n` is the iterator length.?< Partial hints (where `lower > 0`) also improve performance.JG Note further that [`Iterator::size_hint`] may affect the number of RNGJG samples used as well as the result (while remaining uniform sampling).EB Consider instead using [`IteratorRandom::choose_stable`] to avoidLI [`Iterator`] combinators which only change size hints from affecting thed results.l<"41 let words = "Mary had a little lamb".split(' ');<9 println!("{}", words.choose(&mut rand::rng()).unwrap());<4 B 4 $7e ,c!)& Uniformly sample one element (stable)""DA This method is very similar to [`choose`] except that the result"IF only depends on the length of the iterator and the values produced by#HE `rng`. Notably for any iterator of a given length this will make the$JG same requests to `rng` and if the same sequence of values are produced$JG the same index will be selected from `self`. This may be useful if you%KH need consistent results no matter what type of iterator you are working%>; with. If you do not need this stability prefer [`choose`].&&DA Note that this method still uses [`Iterator::size_hint`] to skip'IF constructing elements where possible, however the selection and `rng`'GD calls are the same in the face of this optimization. If you want to(IF force every element to be created regardless call `.inspect(|e| ())`.((&# [`choose`]: IteratorRandom::choosel, B ,4-- $,7p ,$1ߛ=l7=: Uniformly sample `amount` distinct elements into a buffer77FC Collects values at random from the iterator into a supplied buffer8  until that buffer is filled.88IF Although the elements are selected randomly, the order of elements in9HE the buffer is neither stable nor fully random. If random ordering is9  desired, shuffle the result.::NK Returns the number of elements added to the buffer. This equals the length:NK of the buffer unless the iterator contains insufficient elements, in which;63 case this equals the number of elements available.< Complexity is `O(n)` where `n` is the length of the iterator.<1. For slices, prefer [`IndexedRandom::sample`].\=  B =4==$=7 =HhB>; Uniformly sample `amount` distinct elements into a [`Vec`]CCC@ This is equivalent to `sample_fill` except for the result type.CCIDHE EEIF The length of the returned vector equals `amount` unless the iteratorFIF contains insufficient elements, in which case it equals the number ofF elements available.FFAG1GG4H B H4HH$H7JJ HNqM1. Deprecated: use [`Self::sample_fill`] instead0.10.0Renamed to `sample_fill`ԡNMBNϳٳ-  B N4OO ޮ7ܮۮ NPmO,) Deprecated: use [`Self::sample`] insteadP̙PϳRenamed to `sample`PP=|Pϳ- B Q4QQ 9777 QR6,RQDR RL , C,/d-l\54 4Index,IndexMutD#,d۬(&̹,+),L%JG Extension trait on indexable lists, providing random sampling methods.JG This trait is implemented on `[T]` slice types. Other types supportingMJ [`std::ops::Index`] may implement this (only [`Self::len`] must be| specified).lOd0 <,88#QQ 85( 8Y 84řǙșəʙ˙G*R{9 887#Q7Q 875( 8ߖ 846 6ÜĜŜƜǜȜ_wX t The length B $  True when the length is zeroD B $ \   B? Returns a reference to one uniformly-sampled random element of /, the slice, or `None` if the slice is empty.  %" For slices, complexity is `O(1)`. l  <  ! use rand::seq::IndexedRandom;  '$ let choices = [1, 2, 4, 8, 16, 32];  /, println!("{:?}", choices.choose(&mut rng)); 41 assert_eq!(choices[..0].choose(&mut rng), None);< 4   řǙșəʙ˙G*R{9  B 4   $ 7- wA> Return an iterator which samples from `self` with replacement41 Returns `None` if and only if `self.is_empty()`.l<!'B? for choice in choices.choose_iter(&mut rng).unwrap().take(3) {! println!("{:?}", choice);,<\  řǙșəʙ˙G*R{9 B 4 $7C Z88̊̊YϊЊD^)cOY7Y䍲?MݻU88W QS QL  t a 96 Uniformly sample `amount` distinct elements from selfKH Chooses `amount` elements from the slice at random, without repetition,FC and in random order. The returned iterator is appropriate both forIF collection into a `Vec` and filling an existing buffer (see example).A> If `amount > self.len()`, all available elements are sampled.IF In case this API is not sufficiently flexible, use [`index::sample`].<9 For slices, complexity is the same as [`index::sample`].l<!# let mut rng = &mut rand::rng();/, let sample = "Hello, audience!".as_bytes();)& // collect the results into a vector:C@ let v: Vec = sample.sample(&mut rng, 3).cloned().collect();̄ // store in a buffer:ܢ let mut buf = [0u8; 5];MJ for (b, slot) in sample.sample(&mut rng, buf.len()).zip(buf.iter_mut()) { *slot = *b;,<4  ]ʣ$hB 4,$7 $FC Uniformly sample a fixed-size array of distinct elements from self  FC Chooses `N` elements from the slice at random, without repetition,!JG and in random order. Returns `None` if (and only if) `N > self.len()`.!!B? For slices, complexity is the same as [`index::sample_array`]."l"<""!"###/##<9 let a: [u8; 3] = sample.sample_array(&mut rng).unwrap();<$d$  B $4%t$,%,%%7 $E $<&0&# Biased sampling for one element&'FC Returns a reference to one element of the slice, sampled according' to the provided weights.''DA The specified function `weight` maps each item `x` to a relative(JG likelihood `weight(x)`. The probability of each item being selected is)GD therefore `weight(x) / s`, where `s` is the sum of all `weight(x)`.))30 For slices of length `n`, complexity is `O(n)`.*85 For more information about the underlying algorithm,*+( see the [`WeightedIndex`] distribution.++%" See also [`choose_weighted_mut`].+l++<++б,,;8 let choices = [('a', 2), ('b', 1), ('c', 1), ('d', 0)];,,QN // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c',-$! // and 'd' will never be printed-RO println!("{:?}", choices.choose_weighted(&mut rng, |item| item.1).unwrap().0);<..%" [`choose`]: IndexedRandom::choose.B? [`choose_weighted_mut`]: IndexedMutRandom::choose_weighted_mut/<9 [`WeightedIndex`]: crate::distr::weighted::WeightedIndex0̇0|0  ÜĜŜƜǜȜ_w B 0 41 0 0 01# 1# 1|1l242l2 p74 02%l2,363$! Biased sampling with replacement44KH Returns an iterator which samples elements from `self` according to the4C@ given weights with replacement (i.e. elements may be repeated).55/, See also doc for [`Self::choose_weighted`].6̃66  ÜĜŜƜǜȜ_wB 6 47 6 6 67# 7# 8|8l848l8 i74 688̊̊YϊЊD^)cOY7Y䍲?MݻU88QQ8%l8,9Ռ:G:1. Biased sampling of `amount` distinct elements::;8 Similar to [`sample`], but where the likelihood of each;EB element's inclusion in the output may be specified. Zero-weighted;GD elements are never returned; the result may therefore contain fewer= amount`. The elements=41 are returned in an arbitrary, unspecified order.==D>J>G??MJ This implementation uses `O(length + amount)` space and `O(length)` time.@/, See [`index::sample_weighted`] for details.@l@@<@@бAA1. let choices = [('a', 2), ('b', 1), ('c', 1)];AA,) // First Draw * Second Draw = total oddsB // -----------------------B^[ // (50% * 50%) + (25% * 67%) = 41.7% chance that the output is `['a', 'b']` in some order.C^[ // (50% * 50%) + (25% * 67%) = 41.7% chance that the output is `['a', 'c']` in some order.D^[ // (25% * 33%) + (25% * 33%) = 16.6% chance that the output is `['b', 'c']` in some order.Dgd println!("{:?}", choices.sample_weighted(&mut rng, 2, |item| item.1).unwrap().collect::>());`].XXlX#|X?3&QE8ZhX&# Uniformly sample one element (mut)YYJG Returns a mutable reference to one uniformly-sampled random element ofY/ZZ%TZ  řǙșəʙ˙G*R{9  B Z4[[ $Z7Ƕ Zc\)& Biased sampling for one element (mut)]]NK Returns a mutable reference to one element of the slice, sampled according]^^D^J_G_`3`8`+aa! See also [`choose_weighted`].aa0- [`choose_mut`]: IndexedMutRandom::choose_mutb74 [`choose_weighted`]: IndexedRandom::choose_weightedb<c̍cc  ÜĜŜƜǜȜ_w B c 4d c c cd# d#å d|ele4ele 74 cdedeelf,fk'g;8 Extension trait on slices, providing shuffling methods.ggIF This trait is implemented on all `[T]` slice types, providing severalhKH methods for choosing and shuffling elements. You must `use` this trait:i; let mut bytes = "Hello, random!".to_string().into_bytes();j bytes.shuffle(&mut rng);j0- let str = String::from_utf8(bytes).unwrap();j println!("{}", str);= self.len()` this is equivalent to [`Self::shuffle`].ulvv`. Conversion may or may not be trivial.DB &<9 Iterate over the indices as a sequence of `usize` values$ s߬SvB  $PPPlDL$&MJ Convert into an iterator over the indices as a sequence of `usize` valuesLB ,&  B  $ ,tDUDU  $ B 2! ܏!!#!$!B @$"8QQQL$$$$#$$ B $ 8$$%%&Ό&-L& B ' 8$'(+8+"QQQL+$++($+ řǙșəʙ˙G*R{9 QB + $+,,ٝ---L- B - $../+8b0KH Randomly sample exactly `amount` distinct indices from `0..length`, and01. return them in random order (fully shuffled).11LI This method is used internally by the slice sampling methods, but it can1MJ sometimes be useful to have the indices themselves so this is provided as2 an alternative.22IF The implementation used is not specified; we automatically select the3HE fastest available algorithm for the `length` and `amount` parameters3LI (based on detailed profiling on an Intel Haswell CPU). Roughly speaking,4NK complexity is `O(amount)`, except that when `amount` is small, performance4KH is closer to `O(amount^2)`, and when `length` is close to `amount` then5 `O(length)`.55NK Note that performance is significantly better over `u32` indices than over6HE `u64` indices. Because of this we hide the underlying type behind an6 abstraction, `IndexVec`.77HE If an allocation-free `no_std` function is required, it is suggested785 to adapt the internal `sample_floyd` implementation.88  Panics if `amount > length`.|848 B 8499 7hhh 8? ? ? ?B C CLE>; Randomly sample `amount` distinct indices from `0..length`EENK The result may contain less than `amount` indices if insufficient non-zeroFOL weights are available. Results are returned in an arbitrary order (there isF+( no guarantee of shuffling or ordering).GGGD Function `weight` is called once for each index to provide weights.GGLHMIIIIQN - [`WeightError::InvalidWeight`] when a weight is not-a-number or negative,JLI or when infinite weights fill the reservoir before all elements haveJLI been processed (this always happens with more than `amount` infiniteKPM weights, and may also happen with exactly `amount`, depending on order).KKM|LL|L ۼB M4M L LM#ۼtN#ۼ NLN ۼ7ff4dd LY|YYY ۼB Z 4Z Y Y YZtZ [L[$[d[ ۼ74 Y[l[D[[T[\<\ \%"  "D\,\D]]]! ]]7\]  B ] $] Է^ ^^'^  B ^ $^ `  `a"a  B a $a sa a ,np`dp B p4qq7 p$tzbtz B z4{{77|7|7| z~W$~ ~ $~T~~L~~l~h$~L~͇݇wmcYLjJ͇݇Lj~$B B DB $$B ۀހB ԑDB |Ӂ́#$B ΂тB ԄDB { B  4ч$ˇ̖ d 7tttdf     L Ľ      ̥ , l  &# Low-level API for sampling indices,   4  I D ̔d"), y{l   t x C@ Randomly sample exactly `N` distinct indices from `0..len`, and1JG This is implemented via Floyd's algorithm. Time complexity is `O(N^2)`$! and memory complexity is `O(N)`..+ Returns `None` if (and only if) `N > len`.d B 4t 7nn : $׶ĝX XXXXdX%XX0.&X& Construct and seed an RNGPM This method yields a seeded RNG, using [`rng`] ([`ThreadRng`]) if enabled or̜ [`SysRng`] otherwise.tŹ<96 let mut rng: rand::rngs::SmallRng = rand::make_rng();,) # let _ = rand::Rng::next_u32(&mut rng);<dGD If [`SysRng`] fails to obtain entropy from the OS. This is unlikely74 outside of early boot or unusual system conditions.t$# [`SysRng`]: crate::rngs::SysRng)& [`ThreadRng`]: crate::rngs::ThreadRng;8 [`ThreadRng#Security`]: crate::rngs::ThreadRng#securityܣ|DB G\ ,]:7 Adapter to support [`std::io::Read`] over a [`TryRng`]tŹl ```no_run use std::{io, io::Read}; use std::fs::File;(% use rand::{rngs::SysRng, RngReader};l io::copy()& &mut RngReader(SysRng).take(100),74 &mut File::create("/tmp/random.bytes").unwrap()| ).unwrap();<|L 4_ԱBQ_`B z|,.| Ĥ4C$  B  $o,0| Ĥ4gB  ggg cgcثq1ȡB  $ l'CKH Generate a random value using the thread-local random number generator.SP This function is shorthand for [rng()].[random()](RngExt::random):  IF - See [`ThreadRng`] for documentation of the generator and security VS - See [`StandardUniform`] for documentation of supported types and distributions!t!Ź!();!""" let y = rand::random::();" println!("{}", y);"".+ if rand::random() { // generates a boolean",) println!("Better lucky than good!");,#<###IF If you're calling `random()` repeatedly, consider using a local `rng`$96 handle to save an initialization-check on each usage:$<$$52 use rand::RngExt; // provides the `random` method%%A> let mut rng = rand::rng(); // a local handle to the generator%% let mut v = vec![1, 2, 3];%% for x in v.iter_mut() {Ԍ& *x = rng.random();,&<&&&/&" [`ThreadRng`]: rngs::ThreadRng''4'B '|' *w(1. Return an iterator over [`random()`] variates((" This function is shorthand for(>; [rng()].[random_iter](RngExt::random_iter)().)l))<))<9 let v: Vec = rand::random_iter().take(5).collect();* println!("{v:?}");<***\*B *|+ 0{+^[ Generate a random value in the given range using the thread-local random number generator.,,",PM [rng()].[random_range](RngExt::random_range)(range).-l--<--/, let y: f32 = rand::random_range(0.0..=1e9);.­..IF let words: Vec<&str> = "Mary had a little lamb".split(' ').collect();.=: println!("{}", words[rand::random_range(..words.len())]);[rng()].[random_bool](RngExt::random_bool)(p).3l33<331. println!("{}", rand::random_bool(1.0 / 3.0));<33d44Ԕ444|4\4B fs<=5HL556H6J7F7&88C8D99"9li [rng()].[random_ratio](RngExt::random_ratio)(numerator, denominator).:d:::7:l:;<;;-* println!("{}", rand::random_ratio(2, 3));<;;;#;;|<d<B tt@$=8=="=?< [rng()].[fill](RngExt::fill)(dest).>l>><>>> rand::fill(&mut arr[..]);-64 can be represented.L 8%T ,  oookokoo B  o  lҊmgҊҊ  ggg cgcثq1ȡB  ҊҊnn  B   0- Error type returned from [`Bernoulli::new`].tM1 `p < 0` or `p > 1`.&:<oo B  pXqgXX  ggg cgcثq1ȡB XXrr  B  s B !'$ An iterator over a [`Distribution`]HE This iterator yields random values of type `T` with distribution `D`(% from a random generator of type `R`.  B? Construct this `struct` using [`Distribution::sample_iter`] or KH [`RngExt::sample_iter`]. It is also used by [`RngExt::random_iter`] andܶ! [`crate::random_iter`].$! ! ! !䍲?Mݻ2479<>D","4"""%<"itg!g!g!g;>BEILii  ggg cgcثq1ȡB! iiԊ)'<9 A [`Distribution`] which maps sampled values to type `S`((A> This `struct` is created by the [`Distribution::map`] method.(# See its documentation for more.) ) ) ) )9V^[:<?ADFIKD),)<)$)ۼ).<)Ơu  )gۼ))g)gjmqtx{ƠƠ  ggg cgcثq1ȡB) ۼƠƠ NK A distribution to sample floating point numbers uniformly in the half-open2/ interval `(0, 1]`, i.e. including 1 but not 0.JG All values that can be generated are of the form `n * ε/2`. For `f32`MJ the 24 most significant random bits of a `u32` are used and for `f64` theIF 53 most significant bits of a `u64` are used. The conversion uses theԙ multiplicative method.IF See also: [`StandardUniform`] which samples from `[0, 1)`, [`Open01`] LI which samples from `(0, 1)` and [`Uniform`] which samples from arbitrary\  ranges. l <   " use rand::distr::OpenClosed01;  41 let val: f32 = rand::rng().sample(OpenClosed01); )& println!("f32 from (0, 1): {}", val);<   63 [`StandardUniform`]: crate::distr::StandardUniform $! [`Open01`]: crate::distr::Open01 /, [`Uniform`]: crate::distr::uniform::Uniformd l|oSU*vv B    w%xg%%  ggg cgcثq1ȡB  %%yB  IF A distribution to sample floating point numbers uniformly in the open :7 interval `(0, 1)`, i.e. not including either endpoint.OL All values that can be generated are of the form `n * ε + ε/2`. For `f32`OL the 23 most significant random bits of an `u32` are used, for `f64` 52 from;8 an `u64`. The conversion uses a transmute-based method.OL See also: [`StandardUniform`] which samples from `[0, 1)`, [`OpenClosed01`]LI which samples from `(0, 1]` and [`Uniform`] which samples from arbitrary\l< use rand::distr::Open01;.+ let val: f32 = rand::rng().sample(Open01);)<60- [`OpenClosed01`]: crate::distr::OpenClosed01/4ٽkV;g*ٽzٽzٽ ٽٽB!  "{ٽX|ٽgXX ٽ ggg cgcثq1ȡB# XX}ٽٽB %UV0%%%7%B é%*%%50%  B%0%%  %7%%$'%%%50%%  B%%0%%%%  %%7%%%+!ٽ%%,50%, ٽ B%,0%,%,  %,7%,& UV0&&&7&B &* %&50&  B&0&&  &7&&$' %&%50&%  B&%0&%&%  &%7&%&+! ٽ%&,50&, ٽ B&,0&,&,  &,7&,'* %'50'  B'0''  '7'(* %(50(  B(0((  (7()* %)50)  B)0))  )7)** %*50*  B*0**  *7G*+*%+50+  B+0++  +7+,*%,50,  B,0,,  ,74,-*%-50-  B-0--  -7-.*%.50.  B.0..  .7c./*%/50/  B/0//  /7/0*%0500  B0000  0701*%1501  B1011  17112*%2502  B2022  2723*%3503  B3033  37q34*%4504  B4044  4745*%5505  B  5055  575HE Sample a `u8`, uniformly distributed over ASCII letters and numbers: a-z, A-Z and 0-9.l<" use rand::distr::Alphanumeric;SP let chars: String = (0..7).map(|_| rng.sample(Alphanumeric) as char).collect(); (% println!("Random chars: {}", chars);<   FC The [`SampleString`] trait provides an easier method of generating >; a random [`String`], and offers more efficient allocation:<  2/ use rand::distr::{Alphanumeric, SampleString}; B? let string = Alphanumeric.sample_string(&mut rand::rng(), 16); *' println!("Random string: {}", string);<  |  # Passwords  OL Users sometimes ask whether it is safe to use a string of random characters NK as a password. In principle, all RNGs in Rand implementing `CryptoRng` are LI suitable as a source of randomness for generating passwords (if they areHE properly seeded), but it is more conservative to only use randomnessHE directly from the operating system via the `getrandom` crate, or the/, corresponding bindings of a crypto library.MJ When generating passwords or keys, it is important to consider the threatLI model and in some cases the memorability of the password. This is out ofFC scope of the Rand project, and therefore we defer to the following| references:_\ - [Wikipedia article on Password Strength](https://en.wikipedia.org/wiki/Password_strength)[X - [Diceware for generating memorable passwords](https://en.wikipedia.org/wiki/Diceware)d2,qSƉ H*  ~ g   ggg cgcثq1ȡB 6    B 7  8  B  85 Sample a [`u8`], uniformly distributed over letters: a-z and A-Z.lOL You're able to generate random Alphabetic characters via mapping or via the30 [`SampleString::sample_string`] method like so:<0- use rand::distr::{Alphabetic, SampleString}; // Manual mappingQN let chars: String = (0..7).map(|_| rng.sample(Alphabetic) as char).collect();(,) // Using [`SampleString::sample_string`]@= let string = Alphabetic.sample_string(&mut rand::rng(), 16);*<|(% Refer to [`Alphanumeric#Passwords`].TD|fK C*   g   ggg cgcثq1ȡB :    B ;  <     B  DGQ % DHA0DH  B   DH 0DHDH  DH7DHFG   O#FH % &(FHA0FH  B   FH 0FHFH  FH7yFHHG    OHH# % PS;=HHA0HH  B   HH 0HHϸHH  HH7HHJG      aD OJH # % PRJHA0JH  ͸B   JH 0JHJH ͸ JH7SJHLG       u OLH #  % 58 #egLHA0LH  B   LH 0LHLH  LH7@LHNG          p# ONH #& %  #z|NHA0NH  B   NH 0NHNH  NH7NHPG            |_ OPH #, % vyPHA0PH  ދB   PH ދ0PHދPH ދ PH7*PHRG              ~1 ORH !#2 %     HKRHA0RH  B   RH 0RHRH  RH7$ RHTG                  TeF OTH !'#8 % t w _ b   THA0TH  B   TH 0THTH  TH7x THVG                  iL   v OVH !'-#> %     0 3   EHVHA0VH  B   VH 0VHVH  VH7&VHXG                   0   t% OXH !'-3#D % be  F I _ b HKXHA0XH  ֥B   XH ֥0XH֥XH ֥ XH7.XHZG                    ar S  OZH !'-39#J % NQ25K N 4 7 vyZHA0ZH  B   ZH 0ZHZH  ZH7ZH\G                     pb   O\H !'-39?#P % jmNQgjPS     \HA0\H  B   \H 0\H\H  \H7L\H]  X]0]  ]% ]B  m#w#^  X^0^  ^% ^B  I%S%_  X_0_  _% _B  !'+'`   X`0`  `% `B  ()a!  Xa0a  a% aB  2'2Y5Pab""  Xb"0b"  b#' b#B  66cE#  HcE cE  HcE cE  cF$0cFB  8 8cG$0cGB  8 9cHPcHB  9cI+8cIB  9 :cJ2xcJ׆ B  ;;cK'hcKB  <cP#jE$  HjE jE  HjE jE  jF$0jFB  < =jG$0jGB  v= =jHPjHB   >jI+8jIB  u> >jJ2xjJˋ B  @@jK'hjKB  @jP$ę:7 A distribution to uniformly sample elements of a sliceNK Like [`IndexedRandom::choose`], this uniformly samples elements of a sliceNK without modification of the slice (so called "sampling with replacement").NK This distribution object may be a little faster for repeated sampling (but)& slower for small numbers of samples).| ## Examples:7 Since this is a distribution, [`Rng::sample_iter`] and;8 [`Distribution::sample_iter`] may be used, for example:<30 use rand::distr::{Distribution, slice::Choose};+( let vowels = ['a', 'e', 'i', 'o', 'u']; 41 let vowels_dist = Choose::new(&vowels).unwrap();  " // build a string of 10 vowels *' let vowel_string: String = vowels_dist &# .sample_iter(&mut rand::rng())  .take(10)   ! println!("{}", vowel_string); '$ assert_eq!(vowel_string.len(), 10); ?< assert!(vowel_string.chars().all(|c| vowels.contains(&c)));<   DA For a single sample, [`IndexedRandom::choose`] may be preferred:<  !  +ϑ    52 println!("{}", vowels.choose(&mut rng).unwrap());< @= [`IndexedRandom::choose`]: crate::seq::IndexedRandom::choose41 [`Rng::sample_iter`]: crate::RngExt::sample_iter%4$    $tCx 795,  Ԙ,  \  @$   gq g @@  ggg cgcثq1ȡB q $@@D$    r  DD B r $D s$    s Error: empty sliceHE This error is returned when [`Choose::new`] is given an empty slice.&,?E! )  WL g WLWL  ggg cgcثq1ȡB t WLWLMMMM  MM B u M vJG The back-end implementing [`UniformSampler`] for floating-point types.OL Unless you are implementing [`UniformSampler`] for your own type, this type96 should not be used directly, use [`Uniform`] instead. # Implementation notesMJ `UniformFloat` implementations convert RNG output to a float in the rangeNK `[1, 2)` via transmutation, map this to `[0, 1)`, then scale and translate NK to the desired range. Values produced this way have what equals 23 bits of 30 random digits for an `f32` and 52 for an `f64`. ܨ  # Bias and range errors  MJ Bias may be expected within the least-significant bit of the significand. MJ It is not guaranteed that exclusive limits of a range are respected; i.e. KH when sampling the range `[a, b)` it is not guaranteed that `b` is neverd  sampled.   [`new`]: UniformSampler::new 41 [`new_inclusive`]: UniformSampler::new_inclusive 6  [`Uniform`]: super::Uniform(d   7  "4  D,  X  y  XX B y  X z   / zGJX  zg{ g XX  ggg cgcثq1ȡB { XXX[  |X[   C  X[X[  B | X[ X[}) };X}B  k} }k(}}) `}8}  }))  0}}  }}չB ' '    (}}(}չַ } չ__}}}"h}"չB ' '    (}#˷ }#(}$ }# չee}"}"})90})  ַ B   }* 0}*}*  }*7h}*}0h}0 ÜĜŜƜǜȜ_wַ B  ' '    }1 0}1}0(}2ַ }1(}2ַ }2 jjuj7j}0}1}1}3}3  B  ' '   }4 0}3}3(}4 }4(}5 }5 oo7o}3}3}3* ;XB  k k(Ђ* `8  )*  0  չB ' '   ((չ  չuu"h"չB ' '   (# #($ # չK{W{"")90)   B   * 0**  *7.*0h0 ÜĜŜƜǜȜ_w B  ' '    1 010(2 1(2 2 Ѐ܀701133  B  ' '   4 033(4 4(5 5 7333IJC@ The back-end implementing [`UniformSampler`] for integer types.O 9 ѥ JG For simplicity, we use the same generic struct `UniformInt` for allPM integer types `X`. This gives us only one field type, `X`; to store unsigned PM values of this size, we take use the fact that these conversions are no-ops.  LI For a closed range, the number of possible numbers we should generate is NK `range = (high - low + 1)`. To avoid bias, we must ensure that the size of LI our sample space, `zone`, is a multiple of `range`; other values must be 52 rejected (by replacing with a new random sample).  LI As a special case, we use `range = 0` to represent the full range of the ?< result type (i.e. for `new_inclusive($ty::MIN, $ty::MAX)`).  JG The optimum `zone` is the largest product of `range` which fits in ourPM (unsigned) target type. We calculate this by calculating how many numbers weVS must reject: `reject = (MAX + 1) % range = (MAX - range + 1) % range`. Any (large)MJ product of `range` will suffice, thus in `sample_single` we multiply by aGD power of 2 via bit-shifting (faster but may cause more rejections).NK The smallest integer PRNGs generate is `u32`. For 8- and 16-bit outputs weMJ use `u32` for our `zone` and samples (because it's not slower and becauseOL it reduces the chance of having to reject a sample). In this case we cannotJG store `zone` in the target type since it is too large, however we know*' `ints_to_reject < range <= $uty::MAX`.LI An alternative to using a modulus is widening multiply: After a wideningOL multiply by `range`, the result is in the high word. Then comparing the low?< word against `zone` makes sure our distribution is uniform.T # BiasNK Unless the `unbiased` feature flag is used, outputs may have a small bias.AMJ 56 (`i8` and `u8`), 48 (`i16` and `u16`), 96 (`i32` and `u32`), 64 (`i64`(% and `u64`), 128 (`i128` and `u128`). +T   d{uՆ "$  ,  L4          B      P ad  ܰ  g   ggg cgcثq1ȡB  V   V   D  VV  B  V V     B  ,  B   Ќ, `8    ',  0""  #$չB ' '   ($$(%չ % չ$$(h(չB ' '    () )(* ) չ((09/700   B   0 000  0705h5 ÜĜŜƜǜȜ_w B  ' '   6 055(7 6(7 7 7555<9/˷::A;@۸;;;!<  B  ' '    = 0<<(> =(> > ~7<<<-  B   Ѝ- `8    '-  0""  #$չB ' '   ($$(%չ % չ˩ש$$(h(չB ' '    () )(* ) չʮ֮((09/700   B   0 000  0705h5 ÜĜŜƜǜȜ_w B  ' '   6 055(7 6(7 7 p|7555<9/˷::A;@۸;;;!<  B  ' '   = 0<<(> =(> > IU7a<<<.  B   Ў. `8    '.  0""  #$չӄB ' '    ($$(%չŅ!% չ6B$$(h(չӄB ' '   ()!)(*!) չ#/((09/700  Ņ!B   0 000  0705h5 ÜĜŜƜǜȜ_wŅ!B  ' '   6 055(7Ņ!6(7Ņ!7 7555<9/˷::A;@۸;;;!< !B  ' '   = 0<<(>!=(>׋!> _k7w<<</  B   Џ/ `8    '/  0""  #$չB ' '   ($$(%չؒ!% չLX$$(h(չB ' '   ()͒!)(*!) չNZ((09/700  ؒ!B   0 000  0705h5 ÜĜŜƜǜȜ_wؒ!B  ' '   6 055(7ؒ!6(7ؒ!7 7555<9/˷::A;@۸;;;!< !B  ' '   = 0<<(>ʘ!=(>!> 7<<<0  B   А0 `8    '0  0""  #$չB ' '    ($$(%չ!% չ$$(h(չB ' '    ()!)(*!) չ ((09/700  !B   0 000  0705h5 ÜĜŜƜǜȜ_w!B  ' '    6 055(7!6(7!7 7555<9/˷::A;@۸;;;!< !B  ' '   = 0<<(>ݥ!=(>!> 7<<<1  B   Б1 `8    '1  0""  #$չٗB ' '   ($$(%չ!% չ  $$(h(չٗB ' '   ()!)(*!) չr~((09/700  !B   0 000  07(05h5 ÜĜŜƜǜȜ_w!B  ' '    6 055(7!6(7!7 7555<9/˷::A;@۸;;;!< !B  ' '   = 0<<(>!=(>!> 7<<<2  B   В2 `8    '2  0""  #$չB ' '    ($$(%չ!% չ##$$(h(չB ' '    ()!)(*!) չ9(E(((09/700  !B   0 000  07+05h5 ÜĜŜƜǜȜ_w!B  ' '   6 055(7!6(7!7 //7/555<9/˷::A;@۸;;;!< ˾!B  ' '   = 0<<(>!=(>!> c6o67{6<<<3  B   Г3 `8    '3  0""  #$չB ' '    ($$(%չ!% չM;Y;$$(h(չB ' '   ()!)(*!) չ?@((09/700  !B   0 000  07sC05h5 ÜĜŜƜǜȜ_w!B  ' '   6 055(7!6(7!7 GG7G555<9/˷::A;@۸;;;!< !B  ' '    = 0<<(>!=(>!> MM7M<<<4  B   Д4 `8    '4  0""  #$չ B ' '   ($$(%չ!% չRR$$(h(չ B ' '    ()!)(*!) չ?WKW((09/700  !B   0 000  07Z05h5 ÜĜŜƜǜȜ_w!B  ' '   6 055(7!6(7!7 X^d^7p^555<9/˷::A;@۸;;;!< !B  ' '    = 0<<(>!=(>!> ee7e<<<5  B   Е5 `8    '5  0""  #$չ B ' '   ($$(%չ!% չii$$(h(չ B ' '    ()!)(*!) չnn((09/700  !B   0 000  07Ur05h5 ÜĜŜƜǜȜ_w!B  ' '   6 055(7!6(7!7 u v7v555<9/˷::A;@۸;;;!< !B  ' '   = 0<<(>!=(>!> ||7|<<<Ã=: The back-end implementing [`UniformSampler`] for `usize`.ԅѥ LI Sampling a `usize` value is usually used in relation to the length of anMJ array or other memory structure, thus it is reasonable to assume that theKH vast majority of use-cases will have a maximum size under [`u32::MAX`].LI In part to optimise for this use-case, but mostly to ensure that results؆PM are portable across 32-bit and 64-bit architectures (as far as is possible),?< this implementation will use 32-bit sampling when possible.ܐ:E6dŌ3,HN T  dҍ,ҍ  l4  d܋#4  ~~~~  ~~ B  ~ S g SS  ggg cgcثq1ȡB ň SS    B ̈  Ѓ  ЃЃЃЃ B ׈ Ѓ < 9 The back-end implementing [`UniformSampler`] for `char`. O  9   N K This differs from integer range sampling since the range `0xD800..=0xDFFF`L I are used for surrogate pairs in UCS and UTF-16, and consequently are notN K valid Unicode code points. We must therefore avoid sampling values in thisT  range.:\ {8+8Պ Č <   4444  44 B   4   g   ggg cgcثq1ȡB   33  33  B   3 3   B   Խ$ "@ = The back-end implementing [`UniformSampler`] for `Duration`." "P M Unless you are implementing [`UniformSampler`] for your own types, this type#9  ;|$  ; $ $$   \$ 4$      B #   # T g TT  ggg cgcثq1ȡB #  TT    B #   L  LLLL B #  L% <% aiI    ,& <  L& $&   & ,&   4& <  & ,&   ,' <  l' D'   t' L'   ' $'    g   ggg cgcثq1ȡB %   %    B %  33  33  B %  3 3   B %  t" !B ? Error type returned from [`Uniform::new`] and `new_inclusive`.=," %j   T# "6 3 `low > high`, or equal in case of exclusive range.=F  Z\  L# #M J Input or range `high - low` is non-finite. Not relevant to integer types.=]  qs     B "   "  g   ggg cgcثq1ȡB "      B "      B "  \'/ , Sample values uniformly between two bounds.' '  # Construction' 'G D [`Uniform::new`] and [`Uniform::new_inclusive`] construct a uniform(O L distribution sampling from the given `low` and `high` limits. `Uniform` may)R O also be constructed via [`TryFrom`] as in `Uniform::try_from(1..=6).unwrap()`.) )P M Constructors may do extra work up front to allow faster sampling of multiple*I F values. Where only a single sample is required it is suggested to use*H E [`Rng::random_range`] or one of the `sample_single` methods instead.+ +H E When sampling from a constant range, many calculations can happen at,N K compile-time and all methods should be fast; for floating-point ranges and,O L the full range of integer types, this should have comparable performance to-A > the [`StandardUniform`](super::StandardUniform) distribution.- -  # Provided implementations. .Q N - `char` ([`UniformChar`]): samples a range over the implementation for `u32`.O L - `f32`, `f64` ([`UniformFloat`]): samples approximately uniformly within a/P M range; bias may be present in the least-significant bit of the significand0H E and the limits of the input range may be sampled even when an open0  (exclusive) range is used0J G - Integer types ([`UniformInt`]) may show a small bias relative to the1N K expected uniform distribution of output. In the worst case, bias affects2P M 1 in `2^n` samples where n is 56 (`i8` and `u8`), 48 (`i16` and `u16`), 962G D (`i32` and `u32`), 64 (`i64` and `u64`), 128 (`i128` and `u128`).32 / The `unbiased` feature flag fixes this bias.3F C - `usize` ([`UniformUsize`]) is handled specially, using the `u32`4P M implementation where possible to enable portable results across 32-bit and4  64-bit CPU architectures.5O L - `Duration` ([`UniformDuration`]): samples a range over the implementation5  for `u32` or `u64`5K H - SIMD types (requires [`simd_support`] feature) like x86's [`__m128i`]6G D and `std::simd`'s [`u32x4`], [`f32x4`] and [`mask32x4`] types are7I F effectively arrays of integer or floating-point types. Each lane is7O L sampled independently from its own range, potentially with more efficient8G D random-bit-usage than would be achieved with sequential sampling.8 l8 9 <9 9- 9 98 5 let between = Uniform::try_from(10..10000).unwrap();9 :  let mut sum = 0;:  for _ in 0..1000 {:( % sum += between.sample(&mut rng);,: :  println!("{}", sum);<; ; ;@ = For a single sample, [`Rng::random_range`] may be preferred:; <; ; ; < <, ) println!("{}", rng.random_range(0..10));<< < <  [`new`]: Uniform::new<- * [`new_inclusive`]: Uniform::new_inclusive=/ , [`Rng::random_range`]: RngExt::random_range=L I [`__m128i`]: https://doc.rust-lang.org/core/arch/x86/struct.__m128i.html>  [`u32x4`]: std::simd::u32x4>  [`f32x4`]: std::simd::f32x4>% " [`mask32x4`]: std::simd::mask32x4?H E [`simd_support`]: https://github.com/rust-random/rand#crate-features>   B   >!>  Q `Vڼ">  y|>>  B ?  > >   B (   RU B ?  $ ?  ҅I hՅ  B     0  7 з @  B     - ?  ͈I hЈ  B     0  7ވ з @  B     $ @  ҅I hՅ  B     0  l7y и @  B     - @  ͈I hЈ  B     0  7ވ и @  B     $ A  ҅I hՅ   B     0  E7R й @  B     - A  ͈I hЈ   B     0  7ވ й @  B     $ B  ҅I hՅ   B     0  &73 к @  B     - B  ͈I hЈ   B     0  7ވ к @  B     $ C  ҅I hՅ   B     0  '74 л @  B     - C͈I hЈ   B 0  7ވ л @  B    $ D҅I hՅ   B 0  07= м @  B    - D͈I hЈ   B 0   7 ވ м @  B    7 = : A distribution using weighted sampling of discrete items. K H Sampling a `WeightedIndex` distribution returns the index of a randomlyH E selected element from the iterator used when the `WeightedIndex` wasN K created. The chance of a given element being picked is proportional to theH E weight of the element. The weights can use any type `X` for which anO L implementation of [`Uniform`] exists. The implementation guarantees thatI F elements with zero weight are never picked, even when the weights are  floating point numbers.   # Performance  H E Time complexity of sampling from `WeightedIndex` is `O(log N)` where !  `N` is the number of weights. P  K   L I A `WeightedIndex` contains a `Vec` and a [`Uniform`] and so its O L size is the sum of the size of those objects, possibly plus some alignment.  L I Creating a `WeightedIndex` will allocate enough space to hold `N - 1` K H weights of type `X`, where `N` is the number of weights. However, sinceK H `Vec` doesn't guarantee a particular growth strategy, additional memoryJ G might be allocated but not used. Since the `WeightedIndex` object alsoR O contains an instance of `X::Sampler`, this might cause additional allocations,K H though for primitive types, [`Uniform`] doesn't allocate any memory. A > Sampling from `WeightedIndex` will result in a single call toP M `Uniform::sample` (method of the [`Distribution`] trait), which typicallyG D will request a single value from the underlying [`Rng`], though theG D exact number depends on the implementation of `Uniform::sample`. l  < ̾ б-  "  let choices = ['a', 'b', 'c'];  let weights = [2, 1, 1];5    for _ in 0..100 {T Q // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c'7 4 println!("{}", choices[dist.sample(&mut rng)]);,  5 2 let items = [('a', 0.0), ('b', 3.0), ('c', 7.0)];M J let dist2 = WeightedIndex::new(items.iter().map(|item| item.1)).unwrap(); "S P // 0% chance to print 'a', 30% chance to print 'b', 70% chance to print 'c'8 5 println!("{}", items[dist2.sample(&mut rng)].0);, <  ) & [`Uniform`]: crate::distr::Uniform ^ El   l T eO.o24  ̖ | d     ܰ  " g    ggg cgcثq1ȡB      "    B     ڼ" Zڼ"  B        <    B          <    B          <    B          <    B          <    B          <    B          <    B          <    B          <    B          <    B          <    B          <    B     H <   B  I <   B  t Invalid weight errors<9 This type represents errors from [`WeightedIndex::new`],GD [`WeightedIndex::update_weights`] and other weighted distributions.:J,;c`dDA The input weight sequence is empty, too long, or wrongly orderedJThjlOL A weight is negative, too large for the distribution, or not a valid numberJ_su>; Not enough non-zero weights are available to sample valuesJG When attempting to sample a single value this implies that all weightsIF are zero. When attempting to sample `amount` values this implies that52 less than `amount` weights are greater than zero.J@UXD0- Overflow when calculating the sum of weightsJ@TVRgRR  ggg cgcثq1ȡB RR(T(T(T(T(T(T B (T TTTT  B T TRURURURURU B RUԽG$%" The Standard Uniform distribution%%SP This [`Distribution`] is the *standard* parameterization of [`Uniform`]. Bounds%.+ are selected according to the output type.&&FC Assuming the provided `Rng` is well-behaved, these implementations&@= generate values with the following ranges and distributions:''C@ * Integers (`i8`, `i32`, `u64`, etc.) are uniformly distributed'OL over the whole range of the type (thus each possible value may be sampled( with equal probability).(NK * `char` is uniformly distributed over all Unicode scalar values, i.e. all)DA code points in the range `0...0x10_FFFF`, except for the range)B? `0xD800...0xDFFF` (the surrogate code points). This includes*&# unassigned/reserved code points.*UR For some uses, the [`Alphanumeric`] or [`Alphabetic`] distribution will be more+ appropriate.+B? * `bool` samples `false` or `true`, each with probability 0.5.+MJ * Floating point types (`f32` and `f64`) are uniformly distributed in the,[X half-open range `[0, 1)`. See also the [notes below](#floating-point-implementation).-NK * Wrapping integers ([`Wrapping`]), besides the type identical to their- normal integer variants..LI * Non-zero integers ([`NonZeroU8`]), which are like their normal integer.&# variants but cannot sample zero.//PM The `StandardUniform` distribution also supports generation of the following/;8 compound types where all component types are supported:00JG * Tuples (up to 12 elements): each element is sampled sequentially and0OL independently (thus, assuming a well-behaved RNG, there is no correlationķ1 between elements).1EB * Arrays `[T; n]` where `T` is supported. Each element is sampled2JG sequentially and independently. Note that for small `T` this usually2PM results in the RNG discarding random bits; see also [`RngExt::fill`] which3KH offers a more efficient approach to filling an array of integer types3 with random data.4KH * SIMD types (requires [`simd_support`] feature) like x86's [`__m128i`]4G"5Iګ"5MJ sampled independently, potentially with more efficient random-bit-usage6NK (and a different resulting value) than would be achieved with sequential7/, sampling (as with the array types above).77 ## Custom implementations77VS The [`StandardUniform`] distribution may be implemented for user types as follows:8<88 # #![allow(dead_code)]8952 use rand::distr::{Distribution, StandardUniform};99 struct MyF32 {|9 x: f32,,9992/ impl Distribution for StandardUniform {:A> fn sample(&self, rng: &mut R) -> MyF32 {:%" MyF32 { x: rng.random() }L;,;<;;; ## Example usage<;̽;б;%" use rand::distr::StandardUniform;;<74 let val: f32 = rand::rng().sample(StandardUniform);<)& println!("f32 from [0, 1): {}", val);<<<<# # Floating point implementation=WT The floating point implementations for `StandardUniform` generate a random value in=@= the half-open interval `[0, 1)`, i.e. including 0 but not 1.>>J>M?I@FC multiplicative method: `(rng.gen::<$uty>() >> N) as $ty * (ε/2)`.@@LI See also: [`Open01`] which samples from `(0, 1)`, [`OpenClosed01`] whichAOL samples from `(0, 1]` and `Rng::random_range(0..1)` which also samples fromAOL `[0, 1)`. Note that `Open01` uses transmute-based methods which yield 1 bitBPM less precision but may perform faster on some architectures (on modern IntelC;8 CPUs all methods have approximately equal performance).CC! [`Uniform`]: uniform::UniformC'$ [`Wrapping`]: std::num::WrappingD&# [`NonZeroU8`]: std::num::NonZeroU8DL"E"E"E%"FH"K|G5)z*UUUUUU BF U FUgUU  ggg cgcثq1ȡBF UUVVVB b c Z> PZ    BZ 0Z Z  fk7rkZ Z> PZ    BZ 0Z Z  p7pZ b c Z> PZ    BZ 0Z Z  t7tZ Z> PZ    BZ 0Z Z  Py7\yZ b c Z> PZ    BZ 0Z Z  }7}Z Z> PZ   BZ 0Z Z  7Z b Ёc Z> PZ   BZ 0Z Z  &72Z Z> PZ   BZ 0Z Z  Ћ7܋Z b Їc Z> PZ   BZ 0Z Z  7Z Z> PZ   BZ 0Z Z  N7ZZ b Ѝc Z> PZ   BZ 0Z Z  7Z Z> PZ   BZ 0Z Z  7Z b Гc Z> PZ   BZ 0Z Z  $70Z Z> PZ   BZ 0Z Z  Ϊ7ڪZ b Йc Z> PZ   BZ 0Z Z  d7pZ Z> PZ   BZ 0Z Z  7Z b Пc Z> PZ   BZ 0Z Z  7Z Z> PZ   BZ 0Z Z  N7ZZ 6 3 A small-state, fast, non-crypto, non-portable PRNG P M This is the "standard small" RNG, a generator with the following properties: J G - Non-[portable]: any future library version may replace the algorithm, ) and results may be platform-dependent.S P (For a small portable generator, use the [rand_pcg] or [rand_xoshiro] crate.)= : - Non-cryptographic: output is easy to predict (insecure)+ ( - [Quality]: statistically good qualityL I - Fast: the RNG is fast for both bulk generation and single values, with % " consistent cost of method calls  - Fast initialization I F - Small state: little memory usage (current state size is 16-32 bytes  depending on platform)   The current algorithm is O L `Xoshiro256PlusPlus` on 64-bit platforms and `Xoshiro128PlusPlus` on 32-bit E B platforms. Both are also implemented by the [rand_xoshiro] crate.   ## Seeding (construction)  H E This generator implements the [`SeedableRng`] trait. All methods are N K suitable for seeding, but note that, even with a fixed seed, output is not !  [portable]. Some suggestions:  K H 1. To automatically seed with a unique seed, use [`rand::make_rng()`]:\  ```!  use rand::rngs::SmallRng;1 . let mut rng: SmallRng = rand::make_rng();0 - # let _ = rand::Rng::next_u32(&mut rng);\ #N K 2. To use a deterministic integral seed, use `seed_from_u64`. This uses aJ G hash function internally to yield a (typically) good seed from anyt input.\ #2 / # use rand::{SeedableRng, rngs::SmallRng};- * let rng = SmallRng::seed_from_u64(1);  # let _: SmallRng = rng;\ #P M 3. To seed deterministically from text or other input, use [`rand_seeder`]. ( % See also [Seeding RNGs] in the book.   ## Generation > ; The generator implements [`Rng`] and thus also [`RngExt`].5  D A [portable]: https://rust-random.github.io/book/crate-reprod.htmlI F [Seeding RNGs]: https://rust-random.github.io/book/guide-seeding.htmlI I F [Quality]: https://rust-random.github.io/book/guide-rngs.html#quality# [`StdRng`]: crate::rngs::StdRng1 . [rand_pcg]: https://crates.io/crates/rand_pcg9 6 [rand_xoshiro]: https://crates.io/crates/rand_xoshiroD A [`rand_seeder`]: https://docs.rs/rand_seeder/latest/rand_seeder/ܩ  [`Rng`]: rand_core::Rng Ѵ) & [`rand::make_rng()`]: crate::make_rngQD 2M4Bg7B   B  g  ggg cgcثq1ȡB        B      B  +( A xoshiro128++ random number generator.NK The xoshiro128++ algorithm is not suitable for cryptographic purposes, but:7 is very fast and has excellent statistical properties.JG The algorithm used here is translated from [the `xoshiro128plusplus.c`NK reference source code](http://xoshiro.di.unimi.it/xoshiro128plusplus.c) by(% David Blackman and Sebastiano Vigna.RޣNP\  \g\\  ggg cgcثq1ȡB \\ B   B  $$$$$ B $ +( A xoshiro256++ random number generator.NK The xoshiro256++ algorithm is not suitable for cryptographic purposes, but:#JG The algorithm used here is translated from [the `xoshiro256plusplus.c`NK reference source code](http://xoshiro.di.unimi.it/xoshiro256plusplus.c) by($T!; Seeding via [`rand::make_rng()`] or [`rand::rng()`] may be\ faster:< # use rand::rngs::StdRng;+( let mut rng: StdRng = rand::make_rng();,<PM Any [`SeedableRng`] method may be used, but note that `seed_from_u64` is notMJ suitable where security is required. See also [Seeding RNGs] in the book.#>#5D#I#PM [unpredictable]: https://rust-random.github.io/book/guide-rngs.html#securityIwt [CSPRNG]: https://rust-random.github.io/book/guide-gen.html#cryptographically-secure-pseudo-random-number-generator1. [chacha20]: https://crates.io/crates/chacha20@= [rand issue]: https://github.com/rust-random/rand/issues/932#Ѵ)# [`rand::rng()`]: crate::rngV4,T PB7B g  ggg cgcثq1ȡB   B  22222 B 2'-* A reference to the thread-local generatorLI This type is a reference to a lazily-initialized thread-local generator.HE An instance can be obtained via [`rand::rng()`][crate::rng()] or via [`ThreadRng::default()`].JG The handle cannot be passed between threads (is not `Send` or `Sync`).tIF Security must be considered relative to a threat model and validationJG requirements. The Rand project can provide no guarantee of fitness for@= purpose. The design criteria for `ThreadRng` are as follows:GD - Automatic seeding via [`SysRng`] and after every 64 kB of output.WT Limitation: there is no automatic reseeding on process fork (see [below](#fork)).RO - A rigorously analyzed, unpredictable (cryptographic) pseudo-random generator`] (see [the book on security](https://rust-random.github.io/book/guide-rngs.html#security)).=: The currently selected algorithm is ChaCha (12-rounds).(% See also [`StdRng`] documentation.C@ - Not to leak internal state through [`Debug`] or serialization implementations.IF - No further protections exist to in-memory state. In particular, theNK implementation is not required to zero memory on exit (of the process or/, thread). (This may change in the future.)GD - Be fast enough for general-purpose usage. Note in particular thatIF `ThreadRng` is designed to be a "fast, reasonably secure generator"=: (where "reasonably secure" implies the above criteria).  KH We leave it to the user to determine whether this generator meets their >; security requirements. For an alternative, see [`SysRng`].!ԗ! # Forks and interrupts!!KH `ThreadRng` is not automatically reseeded on fork. It is recommended to"PM explicitly call [`ThreadRng::reseed`] immediately after a fork, for example:l" ```ignore" fn do_fork() {"*' let pid = unsafe { libc::fork() };# if pid == 0 {#30 // Reseed ThreadRng in child processes:#! rand::rng().reseed();L$,$<$$$OL Methods on `ThreadRng` are not reentrant-safe and thus should not be called$OL from an interrupt (e.g. a fork handler) unless it can be guaranteed that no%@= other method on the same `ThreadRng` is currently executing.&d&&&IF Implementations of [`TryRng`] and [`Rng`] panic in case of [`SysRng`]&/, failure during reseeding (highly unlikely).''##ܿ'#XL'=(,(    B'  g.at.&eeB ,0ЕUneOee ggStoragegfgf~[l(!e"Ne"e gg$gfgf~[l(Ή4-* An iterator over multiple slice elements.켈 This struct is created byڈHE [`IndexedRandom::sample`](trait.IndexedRandom.html#tymethod.sample).̣_tى$4 d]ʣ$h XZM, $&DNJ <NJz$g )geh{{  ggg cgcثq1ȡBƉ $X|`|  A vector of indices.30 Multiple internal representations are possible.`mm~BB}t 4 ` B$D   #t 4 ` B$D |www B wHvghvlv  ggg cgcثq1ȡB ww""$! 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#https://github.com/rust-random/rand%%%% std::num::NonZeroU84https://en.wikipedia.org/wiki/Bernoulli_distribution%%%%statrs__΂ ō%%%%std::numBernoulli distribution%%ώ%%#https://crates.io/crates/rand_distrZ__ %ō%rand%%9u32x4 crate::Rng%%std::num::Wrapping rand_distr[Z_ %%%ώ%%f32x4%6https://en.wikipedia.org/wiki/Probability_distribution% Wrapping%Ƒ%%[Zݑ%%%"%%% notes belowprobability distribution%%%Uniform::new_inclusive%ݑ%[Ƒ%%mask32x4uniform::Uniform%%ޓ%% Uniform::new%%%%%%ޓ%W%%%%% %%W%1% Rng::random_range(Range)%W1 #%%1 ҋ%% %% %  %WBernoulli::new%%W%W%%%%' Distribution::sample_iter'portability chapter3https://rust-random.github.io/book/portability.htmlRngExt::sample_iter%Distribution::mapcrate::random_iterString::shrink_to_fit #%%%%%% %% %%%%%%%)I%!crate::distr::StandardUniform crate::distr Zcrate::distr::Open01crate::distr::uniform::Uniform΂crate::distr::uniformcrate::distr::OpenClosed01[%Z%˜%΂% %%[Z%%˜%΂%%%[&Wikipedia article on Password Strength/https://en.wikipedia.org/wiki/Password_strength_ +Diceware for generating memorable passwords&https://en.wikipedia.org/wiki/DicewareSampleString::sample_stringAlphanumeric#Passwords%%%%_%ݠ%C%%%_%%Fݠ%I-crate::seq::IndexedRandom crate::seqRng::sample_iterj crate::RngExt::sample_iter crate::RngExt%'G Choose::newIndexedRandom::choosei!crate::seq::IndexedRandom::choose%%#%֢%%%j%Gi %ɣ%%%%֢%%%jG%%ɣ%i%%%΂% }%crate::distr::uniform::UniformSampler$crate::distr::uniform::SampleUniform%module documentationo  %%%΂ -}%%k%%%( Y%%super::StandardUniform%΂ %-} %kY(Rng::random_range% %%%9-k %Y(Ũ%%std::borrow::Borrow::borrow%%Ũ%Borrow::borrow%!crate::distr::uniform::UniformInt%%% std::borrow%%-#crate::distr::uniform::UniformFloat%%%%%Ҫ%%-&crate::distr::uniform::UniformDuration%% %%%%std::borrow::BorrowҪ%-#crate::distr::uniform::SampleBorrowث%% %%%ɬ%+crate::distr::uniform::SampleBorrow::borrow%ث%  ~ /%UniformSampler::sample_singleɬ%SampleBorrow::borrowڭ%%~  /ͦ%%̮%%%ڭ%o~  /%ͦ%% %̮%%%%o %% 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>ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789>+assertion failed: b.is_ascii_alphanumeric()+At least one lane must be setChooseslicerange num_choices Irand::distr::slice::Choose: index out-of-range (likely memory corruption)IEmpty UniformFloat lowscale UniformInt thresh UniformUsize mode64 UniformChar samplerZrand::distr::uniform::UniformChar: invalid Unicode scalar value (likely memory corruption)ZUniformDurationmodeoffsetLargemax_secs max_nanos secsMediumnanosSmall NonFinite EmptyRange Uniform WeightedIndex cumulative_weights total_weight weight_distributionWeightedIndexIterweighted_indexindexOverflowInsufficientNonZero InvalidWeight InvalidInput StandardUniformcannot sample empty range"p= is outside range [0.0, 1.0]"%p=/ is outside range [0.0, 1.0]%SmallRngXoshiro128PlusPlussXoshiro256PlusPlusStdRngassertion failed: c <= 32assertion failed: m > 0#iterator shorter than size_hint().0#IndexedSamples_phantomindicesU64U32:`amount` of samples must be less than or equal to `length`:-assertion failed: amount <= u32::MAX as usize-"assertion failed: amount <= length"!assertion failed: amount < length! 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the specified memory ranges do not overlap This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: ptr::replace requires that the pointer argument is aligned and non-null This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: hint::assert_unchecked must never be called when the condition is false This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: hint::unreachable_unchecked must never be reached This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.is_nonoverlapping: `size_of::() * count` overflows a usizeunsafe precondition(s) violated: slice::from_raw_parts requires the pointer to be aligned and non-null, and the total size of the slice not to exceed `isize::MAX` This indicates a bug in the program. 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getrandom::sys_rng::SysRngseedstorage*const std::sys::thread_local::native::lazy::Storage>, alloc::alloc::Global>, ()>keyivctr_sizeconst_dststate_remkey_dst_ctr_dstiv_dstleft_valright_valcodemhighmax_rand_weakx0x1x2x3ek&mut [[core::core_arch::x86::__m256i; 4]; 2]rol16_maskrol8_maskd&mut [[core::core_arch::x86::__m128i; 4]; 4]&mut core::core_arch::x86::__m128iret*mut ()zero_sizemsgaddrdiffsrc_usizedst_usizeu&mut core::slice::iter::ChunksExactidx&core::slice::iter::ChunksExactn&mut core::slice::iter::Iter&core::slice::iter::Iterexact&mut core::slice::iter::IterMut<[core::core_arch::x86::__m128i; 4]>&mut core::slice::iter::IterMut<[core::core_arch::x86::__m256i; 4]>&mut core::slice::iter::IterMut&mut core::slice::iter::IterMut&mut core::array::iter::IntoIter<[core::core_arch::x86::__m256i; 4], 2>isize&mut core::ops::range::Rangeold&core::num::error::TryFromIntErroravx2_tokensse2_token&mut std::sys::stdio::unix::StderrargstemplateNonNull*const core::fmt::rt::ArgumentNonNullArgumentsrustc 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/rustc/48a229ceaefd4985c50990b14116b6d856af0985src/root/.cargo/registry/src/index.crates.io-1949cf8c6b5b557f/chacha20-0.10.2/root/.cargo/registry/src/index.crates.io-1949cf8c6b5b557f/rand_core-0.10.1src/distr/root/.cargo/registry/src/index.crates.io-1949cf8c6b5b557f/cpufeatures-0.3.1library/core/src/result.rslibrary/core/src/fmt/rt.rslibrary/std/src/sys/thread_local/native/lazy.rslibrary/core/src/cell.rslib.rslibrary/core/src/option.rslibrary/core/src/ptr/metadata.rslibrary/core/src/mem/mod.rslibrary/core/src/mem/maybe_dangling.rslibrary/core/src/mem/maybe_uninit.rslibrary/core/src/ub_checks.rslibrary/core/src/ptr/mod.rslibrary/core/src/ops/function.rslibrary/core/src/mem/manually_drop.rslibrary/core/src/ptr/mut_ptr.rslibrary/std/src/thread/local.rslibrary/core/src/ptr/const_ptr.rssrc/backends/avx2.rssrc/backends/sse2.rslibrary/core/src/sync/atomic.rslibrary/core/src/../../stdarch/crates/core_arch/src/x86/avx2.rslibrary/core/src/../../stdarch/crates/core_arch/src/macros.rssrc/seedable_rng.rslibrary/core/src/iter/traits/iterator.rslibrary/core/src/iter/adapters/zip.rslibrary/core/src/num/f32.rslibrary/core/src/num/f64.rssrc/lib.rslibrary/core/src/io/error.rslibrary/core/src/io/error/repr_bitpacked.rslibrary/core/src/io/error/os_functions_atomic.rsuniform_float.rsutils.rslibrary/core/src/slice/iter.rslibrary/core/src/ptr/non_null.rslibrary/alloc/src/rc.rslibrary/alloc/src/boxed.rslibrary/core/src/convert/mod.rslibrary/core/src/../../stdarch/crates/core_arch/src/simd.rslibrary/core/src/intrinsics/mod.rslibrary/core/src/hint.rslibrary/core/src/num/uint_macros.rslibrary/core/src/slice/raw.rssrc/rng.rslibrary/core/src/iter/traits/collect.rslibrary/core/src/slice/mod.rslibrary/core/src/convert/num.rslibrary/core/src/mem/alignment.rslibrary/core/src/alloc/layout.rslibrary/core/src/slice/iter/macros.rslibrary/core/src/array/iter.rslibrary/core/src/slice/index.rslibrary/core/src/iter/range.rslibrary/core/src/cmp.rslibrary/core/src/num/error.rssrc/lib.rssrc/backends/soft.rslibrary/std/src/io/mod.rs 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D$'uE&H|$H5HD$HD$(HD$0qH|$Ht$HD$8H|$Ht$HD$8HD$8Hu,HD$PHD$HH HHL$(HD$0HD$(HT$0HH|$8H5HD$HL$8HL$PHL$PH$HL$HHL$HH$HL$@HL$@HL$H$H$H$H$H|$H5HD$HL$HL$(HD$0@@L$D$L$L$L$uD$D$D$ L$D$D$T$HH|$Ht$HHHH|$Ht$HHHH|$Ht$HHHL$HL$HT$Ht$H|$ H|$(Ht$PHT$XHL$`Hu+H$HHD$hHD$pH=7HD$HHL$HD$Ht$1HHHT$HD$xHH)H$H|$0LHT$HL$ HD$(LL$0LD$8L$L$H|$@Ht$HH$H$L LAHyHqHQ HĨH=HxLD$HL$HT$ Ht$(H|$0H|$8Ht$@HT$HHL$PHT$XHt$`HT$Ht$ H|$LD$HL$H|$(HHL$HD$ HT$(HH$HT$hH)HD$HD$pLD$HL$H<$HHD$8HL$0HT$H4$H|$LD$(LHyHqHQHxHL$HL$HT$Ht$H|$ H|$(Ht$pHT$xH$H9v1H$HH$HDŽ$ H=HL$HT$Ht$H|$PLHL$ HD$(HT$PHT$0HT$XHT$8HT$`HT$@HT$hHT$HHT$0HHT$8HQHT$@HQHT$HHQHĘH(H|$Ht$HT$HL$ H(HxLD$HL$HT$ Ht$(H|$0H|$8Ht$@HT$HHL$PHT$XHt$`HT$Ht$ H|$LD$HL$H|$(HHL$HD$ HT$(HHHH$HT$hH)HD$HD$pLD$HL$H<$HHD$8HL$0HT$H4$H|$LD$(LHyHqHQHxHH|$Ht$HHHH|$Ht$HH|$t$|$|$L$uD$D$D$ L$D$D$T$HHt$8H|$@H|$H7H$HHL$(D$4HL$(D$4H$$HD$PHL$PHHL$HD$ HL$HD$ HD$H9tHD$HHD$ HDŽ$@H@HD$HD$H$H$H$H$H$H$H$H$H$$un$$H=H LH+H$1HH$$H$$HL$(D$4 $D$$Ht$8D$D$PH$P@H$Ht$PH|$@H$H|$@HH$P@HD$HH%+H(H|$H|$ HHH$HD$HHuH$H$4u>H4$HH<$H|$1H<$HH(H=HfofHfofHfofH((N)O)H((N)O)H((N)O)H((N)O)H|$Ht$HH|$H|$L$uHD$HD$HD$H HHL$HD$HD$HT$H(H|$(Ht$0H|$8Ht$@HtHD$0H@HD$(HD$HHD$P@HDŽ$@@H$H$H$H$H$H$H$H$H$$uc$$H=H LH+H$&HH$$H$HD$  HD$($$H=HHD$(HHH|$H|$hHD$pH|$x HHD$HT$H$H$H9rHt$HHL$A$$H $ H H=r H|$Ht$(H|$HD$(HL$0HD$XHL$`1H9rH=)HHD$0H@wH|$0H$H$H$H$H$H$H$H$H$H$$u`$$H=H LH+H$#HH$$H$HD$  HD$($$H(H|$ ++NH|$H|$Ht$HT$LD$HL$HHt$LHT$HT$Ht$L$u(HD$HL$HT$HPHHH@H0HD$H5H=H HHxH0HPHHHD$H|$Ht$HH|$L$H|$uHD$HD$HD$H HHL$HD$HD$HT$HhH|$H|$0HGHD$HD$8HHu*HD$HL$H H $HL$@HL$HHHD$HD$PH HHL$ HD$(:HL$H<$LHHD$H $HL$XHD$`HL$ HD$(H HHL$ HD$(HD$ HT$(HhHHD$Ht$HT6@T$@L$L$T$8L$uL$D$ȈD$D$ L$D$D$T$ffT$ffL$fL$fT$fff9L$ufL$fD$ffD$fD$f ffL$fD$fD$fT$D$t$D$t$9L$uL$D$ȉD$D$ L$D$D$T$|$D$D$D$HHD$Ht$HD$Ht$HHH9L$uHL$HD$HHD$HD$H HHL$HD$HD$HT$HH|$LD$HD$HT$Ht$H|$Ht$HT$LD$HD$HHHLH)HL$u8HD$Ht$HL$H|$HT$HHHPHHH@H0HD$H5H=H HHxH0HPHHHD$UHHH`HT$ Ht$(H|$0H|$8H$H$HDŽ$HFH+HwTHD$0HL$ HT$(H=H5H|$@Ht$HH HT$PHL$XHT$PHL$XH$H$HD$(HHD$H$ HD$8H]H|$HHD$ HL$(HT$HHH1HT$HHD$@H HL$PHD$XHL$PHD$XH$H$HD$HHD$H$HL$PHD$XH$ H$(HL$PHD$XH$0H$8H|$Ht$XHHt$HHt$PH$@H$HH|$`H|$0H Ht$`HD$0HHD$Ht$HD$Ht$HHH9L$uHL$HD$HHD$HD$H HHL$HD$HD$HT$H|$HGH|$HGfffL$fD$ffL$fL$L$ufD$fD$fD$f ffL$fD$fD$fT$H8H|$($1Ƀ<$HDHtZ$D$HD$HD$0H|$Ht$HD$HD$HD$ HD$H=Ht$HHHH8HXH<$H|$PH|$Ht$OH4$H|$HXHHH<$Ht$HT$H|$0H|$HD$ HT$(HT$ 1HHDHt*H$Ht$ HT$(Ht$8HT$@H8H@P$D$!H$H8HpHT$HL$$D$D$$HHPXPH=1D$D$ lenM called `Result::unwrap()` on an `Err` valueYU%assertion failed: n < NX assertion failed: 0 < index && index <= NX Kq*S?%Y YF P P a>+o|unsafe precondition(s) violated: slice::split_at_unchecked requires the index to be within the slice This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: slice::split_at_mut_unchecked requires the index to be within the slice This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: Alignment::new_unchecked requires a power of two This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: ptr::offset_from_unsigned requires `self >= origin` This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: Layout::from_size_alignment_unchecked requires that the rounded-up allocation size does not exceed isize::MAX This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: NonNull::new_unchecked requires that the pointer is non-null This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: usize::unchecked_add cannot overflow This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.Y4encode_utf8: need  bytes to encode U+ i but buffer has just unsafe precondition(s) violated: slice::get_unchecked requires that the index is within the slice This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: slice::get_unchecked_mut requires that the index is within the slice This indicates a bug in the program. This Undefined Behavior check is optional, and cannot be relied on for safety.unsafe precondition(s) violated: slice::get_unchecked_mut requires that the range is within the slice This indicates a bug in the program. 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2026-09-01))/root/.cargo/registry/src/index.crates.io-1949cf8c6b5b557f/rand-0.10.3/src/lib.rs/@/rand.732d352979d76d2a-cgu.1/root/.cargo/registry/src/index.crates.io-1949cf8c6b5b557f/rand-0.10.3 as core::fmt::Write>::{vtable}drop_in_place()*const ()sizeusizealign__method3__method4__method5stdiodefault_write_fmtsysstdiounixStderrTinner&mut std::sys::stdio::unix::Stderrerrorcoreresultu64Okrepr__0ptrnon_nullpointerNonNull<()>__1markeru8OskindNotFoundPermissionDeniedConnectionRefusedConnectionResetHostUnreachableNetworkUnreachableConnectionAbortedNotConnectedAddrInUseAddrNotAvailableNetworkDownBrokenPipeAlreadyExistsWouldBlockNotADirectoryIsADirectoryDirectoryNotEmptyReadOnlyFilesystemFilesystemLoopStaleNetworkFileHandleInvalidInputInvalidDataTimedOutWriteZeroStorageFullNotSeekableQuotaExceededFileTooLargeResourceBusyExecutableFileBusyDeadlockCrossesDevicesTooManyLinksInvalidFilenameArgumentListTooLongInterruptedUnsupportedUnexpectedEofOutOfMemoryInProgressTooManyOpenFilesOtherUncategorizedErrorKind(dyn core::error::Error + core::marker::Send + core::marker::Sync)vtable__ARRAY_SIZE_TYPE__&[usize; 10]*const (dyn core::error::Error + core::marker::Send + core::marker::Sync)NonNull<(dyn core::error::Error + core::marker::Send + core::marker::Sync)>error_drop*mut (dyn core::error::Error + core::marker::Send + core::marker::Sync)unsafe fn(*mut (dyn core::error::Error + core::marker::Send + core::marker::Sync))outer_drop*mut core::io::error::Customunsafe fn(*mut core::io::error::Custom)Custom*const core::io::error::CustomNonNullCustomOwnerCi32SimpleSimpleMessagemessagedata_ptrlength&str&core::io::error::SimpleMessageErrorDataPhantomData>ReprErrorEErrResult<(), core::io::error::Error>Adapter as core::fmt::Write>::{vtable_type}::{vtable}numEmptyInvalidDigitPosOverflowNegOverflowZeroNotAPowerOfTwoIntErrorKindTryFromIntError::{vtable_type}randrngsthreadTHREAD_RNG_KEY{constant#0}{closure#0}__RUST_STD_INTERNAL_VALthread_localnativelazyallocrccellrand_coreblockchacha20R12RvariantsLegacyVstateu32tokensavx2_cpuidInitTokensse2_cpuid(chacha20::avx2_cpuid::InitToken, chacha20::sse2_cpuid::InitToken)_pd(chacha20::R12, chacha20::variants::Legacy)PhantomData<(chacha20::R12, chacha20::variants::Legacy)>ChaChaCoreReseedingCoreGresultsBlockRngvalueUnsafeCell>GlobalAstrongUnsafeCellCellweakRcInner>>*const alloc::rc::RcInner>>NonNull>>>phantomPhantomData>>>Rc>, alloc::alloc::Global>Dmemmaybe_uninituninitmanually_dropmaybe_danglingPMaybeDangling>, alloc::alloc::Global>>ManuallyDrop>, alloc::alloc::Global>>MaybeUninit>, alloc::alloc::Global>>UnsafeCell>, alloc::alloc::Global>>>UninitializedAliveDestroyedState<()>UnsafeCell>Cell>Storage>, alloc::alloc::Global>, ()>_RNvNCNKNvNtNtCs9T56m8BN4Ao_4rand4rngs6thread14THREAD_RNG_KEY0023___RUST_STD_INTERNAL_VAL{closure#1}!StateUnsafeCell>Cell>Storage>, alloc::alloc::Global>, !>_RNvNCNKNvNtNtCs9T56m8BN4Ao_4rand4rngs6thread14THREAD_RNG_KEY0s_023___RUST_STD_INTERNAL_VAL<&() as core::fmt::Debug>::{vtable}&()<&() as core::fmt::Debug>::{vtable_type}ffi__variant1__variant2c_voidalignment_Align1Shl0_Align1Shl1_Align1Shl2_Align1Shl3_Align1Shl4_Align1Shl5_Align1Shl6_Align1Shl7_Align1Shl8_Align1Shl9_Align1Shl10_Align1Shl11_Align1Shl12_Align1Shl13_Align1Shl14_Align1Shl15_Align1Shl16_Align1Shl17_Align1Shl18_Align1Shl19_Align1Shl20_Align1Shl21_Align1Shl22_Align1Shl23_Align1Shl24_Align1Shl25_Align1Shl26_Align1Shl27_Align1Shl28_Align1Shl29_Align1Shl30_Align1Shl31_Align1Shl32_Align1Shl33_Align1Shl34_Align1Shl35_Align1Shl36_Align1Shl37_Align1Shl38_Align1Shl39_Align1Shl40_Align1Shl41_Align1Shl42_Align1Shl43_Align1Shl44_Align1Shl45_Align1Shl46_Align1Shl47_Align1Shl48_Align1Shl49_Align1Shl50_Align1Shl51_Align1Shl52_Align1Shl53_Align1Shl54_Align1Shl55_Align1Shl56_Align1Shl57_Align1Shl58_Align1Shl59_Align1Shl60_Align1Shl61_Align1Shl62_Align1Shl63AlignmentEnumdistruniformEmptyRangeNonFiniteweightedInvalidWeightInsufficientNonZeroOverflowgetrandombackendslinux_android_with_fallbackfill_innersyncatomic*mut core::ffi::c_voidvprivateAlign8<*mut core::ffi::c_void>UnsafeCell>Atomic<*mut core::ffi::c_void>LazyPtr*const core::ffi::c_voidNonNullfn() -> core::ptr::non_null::NonNullimpl FnOnce() -> NonNull_RINvMNtNvNtNtCs9oodc2A4NLd_9getrandom8backends27linux_android_with_fallback10fill_inner4lazyINtB3_7LazyPtrNtNtCsgxBkk5gSRhY_4core3ffi6c_voidE11unsync_initNvB7_4initECs9T56m8BN4Ao_4randunsync_init core::ptr::non_null::NonNull>&getrandom::backends::linux_android_with_fallback::fill_inner::lazy::LazyPtrconvertInfallible{impl#0}unsync_initinit{closure_env#0} core::ptr::non_null::NonNull>impl FnOnce() -> Result, E>_RINvMNtNvNtNtCs9oodc2A4NLd_9getrandom8backends27linux_android_with_fallback10fill_inner4lazyINtB3_7LazyPtrNtNtCsgxBkk5gSRhY_4core3ffi6c_voidE15try_unsync_initNtNtB1K_7convert10InfallibleNCINvB2_11unsync_initNvB7_4initE0ECs9T56m8BN4Ao_4randtry_unsync_init core::ptr::non_null::NonNull>>Result, core::convert::Infallible>_RINvMNtNvNtNtCs9oodc2A4NLd_9getrandom8backends27linux_android_with_fallback10fill_inner4lazyINtB3_7LazyPtrNtNtCsgxBkk5gSRhY_4core3ffi6c_voidE9cold_initNtNtB1K_7convert10InfallibleNCINvB2_11unsync_initNvB7_4initE0ECs9T56m8BN4Ao_4randcold_init core::ptr::non_null::NonNull>>fmttemplate*const u8NonNullargsrttyPlaceholderformatterResult<(), core::fmt::Error>optionsflagswidthu16precisionFormattingOptionsbufdyn core::fmt::Write&[usize; 6]&mut dyn core::fmt::WriteFormatter&mut core::fmt::Formatterunsafe fn(core::ptr::non_null::NonNull<()>, &mut core::fmt::Formatter) -> core::result::Result<(), core::fmt::Error>_lifetimePhantomData<&()>CountArgumentTypeArgument*const core::fmt::rt::ArgumentNonNullArguments_RINvMs2_NtCsgxBkk5gSRhY_4core3fmtNtB6_9Arguments3newKj1f_Kj1_ECs9T56m8BN4Ao_4randnew<31, 1>&[u8; 31]&[core::fmt::rt::Argument; 1]_RINvMs2_NtCsgxBkk5gSRhY_4core3fmtNtB6_9Arguments3newKj23_Kj1_ECs9T56m8BN4Ao_4randnew<35, 1>&[u8; 35]_RNvMNtCsgxBkk5gSRhY_4core6resultINtB2_6ResultuNtNtNtB4_2io5error5ErrorE5is_okCs9T56m8BN4Ao_4randis_ok<(), core::io::error::Error>bool&core::result::Result<(), core::io::error::Error>self_RNvMNtCsgxBkk5gSRhY_4core6resultINtB2_6ResultuNtNtNtB4_2io5error5ErrorE6is_errCs9T56m8BN4Ao_4randis_err<(), core::io::error::Error>core_archx86i64__m128iMaybeDanglingManuallyDropMaybeUninit_RINvMs1_NtNtCsgxBkk5gSRhY_4core3mem12maybe_uninitINtB6_11MaybeUninitNtNtNtBa_9core_arch3x867___m128iE17array_assume_initKj4_ECs9T56m8BN4Ao_4randarray_assume_initpaniclocationfilename*const strNonNulllinecol_filenamePhantomData<&str>Location&core::panic::location::Locationarray{impl#11}_RNvMs9_NtCsgxBkk5gSRhY_4core3numj13unchecked_addunchecked_addrhsarray_mut&mut [core::mem::maybe_uninit::MaybeUninit]initializedGuard_RNvMsn_NtCsgxBkk5gSRhY_4core5arrayINtB5_5GuardNtNtNtB7_9core_arch3x867___m128iE14push_uncheckedCs9T56m8BN4Ao_4randpush_unchecked&mut core::array::Guarditemopscontrol_flowtry_traitNeverShortCircuitResidualB_RNvXNtNtCsgxBkk5gSRhY_4core3ops12control_flowINtB2_11ControlFlowNtNtB4_9try_trait25NeverShortCircuitResidualNtNtNtB6_9core_arch3x867___m128iENtB12_3Try6branchCs9T56m8BN4Ao_4randbranchContinueBreakControlFlowControlFlow, core::core_arch::x86::__m128i>ControlFlowcbsliceindex{impl#2}_RNvXs0_NtNtCsgxBkk5gSRhY_4core5slice5indexjINtB5_10SliceIndexSINtNtNtB9_3mem12maybe_uninit11MaybeUninitNtNtNtB9_9core_arch3x867___m128iEE17get_unchecked_mutCs9T56m8BN4Ao_4randget_unchecked_mut>*mut core::mem::maybe_uninit::MaybeUninitI_RINvMNtCsgxBkk5gSRhY_4core5sliceSINtNtNtB5_3mem12maybe_uninit11MaybeUninitNtNtNtB5_9core_arch3x867___m128iE17get_unchecked_mutjECs9T56m8BN4Ao_4randget_unchecked_mut, usize>&mut core::mem::maybe_uninit::MaybeUninit_RNvMs1_NtNtCsgxBkk5gSRhY_4core3mem12maybe_uninitINtB5_11MaybeUninitNtNtNtB9_9core_arch3x867___m128iE5writeCs9T56m8BN4Ao_4randwrite&mut 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4]>]>_RNvMs1_NtNtCsgxBkk5gSRhY_4core3ptr9const_ptrPSINtNtNtB9_3mem12maybe_uninit11MaybeUninitANtNtNtB9_9core_arch3x867___m256ij4_E3lenCs9T56m8BN4Ao_4randlen>_RNvXs0_NtNtCsgxBkk5gSRhY_4core5slice5indexjINtB5_10SliceIndexSINtNtNtB9_3mem12maybe_uninit11MaybeUninitANtNtNtB9_9core_arch3x867___m256ij4_EE13get_uncheckedCs9T56m8BN4Ao_4randget_unchecked>*const core::mem::maybe_uninit::MaybeUninit<[core::core_arch::x86::__m256i; 4]>_RINvMNtCsgxBkk5gSRhY_4core5sliceSINtNtNtB5_3mem12maybe_uninit11MaybeUninitANtNtNtB5_9core_arch3x867___m256ij4_E13get_uncheckedjECs9T56m8BN4Ao_4randget_unchecked, usize>&core::mem::maybe_uninit::MaybeUninit<[core::core_arch::x86::__m256i; 4]>_RNvMs1_NtNtCsgxBkk5gSRhY_4core3mem12maybe_uninitINtB5_11MaybeUninitANtNtNtB9_9core_arch3x867___m256ij4_E6as_ptrCs9T56m8BN4Ao_4randas_ptr<[core::core_arch::x86::__m256i; 4]>*const [core::core_arch::x86::__m256i; 4]_RNvMs1_NtNtCsgxBkk5gSRhY_4core3mem12maybe_uninitINtB5_11MaybeUninitANtNtNtB9_9core_arch3x867___m256ij4_E16assume_init_readCs9T56m8BN4Ao_4randassume_init_read<[core::core_arch::x86::__m256i; 4]>_RINvNtCsgxBkk5gSRhY_4core3ptr4readANtNtNtB4_9core_arch3x867___m256ij4_ECs9T56m8BN4Ao_4randread<[core::core_arch::x86::__m256i; 4]>_RNvMNtNtCsgxBkk5gSRhY_4core3ptr9const_ptrPANtNtNtB6_9core_arch3x867___m256ij4_4readCs9T56m8BN4Ao_4randDATAalivePolymorphicIter<[core::mem::maybe_uninit::MaybeUninit<[core::core_arch::x86::__m256i; 4]>]>_RNvMs8_NtNtNtCsgxBkk5gSRhY_4core5array4iter10iter_innerINtB5_15PolymorphicIterSINtNtNtBb_3mem12maybe_uninit11MaybeUninitANtNtNtBb_9core_arch3x867___m256ij4_EE4nextCs9T56m8BN4Ao_4randnext<[core::core_arch::x86::__m256i; 4]>&mut core::array::iter::iter_inner::PolymorphicIter<[core::mem::maybe_uninit::MaybeUninit<[core::core_arch::x86::__m256i; 4]>]>vecraw_vecunique_markerPhantomDataUniquecapUsizeNoHighBitRawVecInnerPhantomDataRawVecVec_RNvMs_NtCs6i54tJFfzR_5alloc3vecINtB4_3VecmE3lenCs9T56m8BN4Ao_4randlen&alloc::vec::VecPhantomDataRawVecVec_RNvMs_NtCs6i54tJFfzR_5alloc3vecINtB4_3VecyE3lenCs9T56m8BN4Ao_4randlen&alloc::vec::Vec_RNvMs_NtCsgxBkk5gSRhY_4core3nums15overflowing_addi16(i16, bool)_RNvMs_NtNtCs9T56m8BN4Ao_4rand4rngs6threadNtB4_13ReseedingCore13try_to_reseedtry_to_reseed_RNvMs_NtNtCs9T56m8BN4Ao_4rand4rngs6threadNtB4_13ReseedingCore6reseed_RNvMsa_NtCsgxBkk5gSRhY_4core3fmtNtB5_9Formatter9write_fmtCs9T56m8BN4Ao_4randwrite_fmt_RNvXs_NtCs6i54tJFfzR_5alloc5allocNtB4_6GlobalNtNtCsgxBkk5gSRhY_4core5alloc9Allocator8allocateCs9T56m8BN4Ao_4randallocate&alloc::alloc::Global_RNvMNtCs6i54tJFfzR_5alloc5allocNtB2_6Global10alloc_implCs9T56m8BN4Ao_4randalloc_implzeroedboxedcharmethods_RNvNtNtCsgxBkk5gSRhY_4core4char7methods8len_utf8Cs9T56m8BN4Ao_4randlen_utf8code_RNvMNtCsgxBkk5gSRhY_4core5sliceSh10as_mut_ptrCs9T56m8BN4Ao_4randas_mut_ptr_RINvNtNtCsgxBkk5gSRhY_4core5slice3raw18from_raw_parts_muthECs9T56m8BN4Ao_4randfrom_raw_parts_mutencode_utf8_raw_RNvNvNtNtCsgxBkk5gSRhY_4core4char7methods15encode_utf8_raw8do_panicdo_panicdst_len_RNvMNtNtCsgxBkk5gSRhY_4core3ptr7mut_ptrOh3addCs9T56m8BN4Ao_4randother_RNvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x863avx18__mm256_setr_epi64xCs9T56m8BN4Ao_4rand_mm256_setr_epi64xad_RNvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse219__mm_undefined_si128Cs9T56m8BN4Ao_4rand_mm_undefined_si128_RINvNtCsgxBkk5gSRhY_4core3ptr19copy_nonoverlappinghECs9T56m8BN4Ao_4randcopy_nonoverlapping_RINvNtCsgxBkk5gSRhY_4core3ptr15write_unalignedNtNtNtB4_9core_arch3x867___m128iECs9T56m8BN4Ao_4randwrite_unaligned_RNvMNtNtCsgxBkk5gSRhY_4core3ptr7mut_ptrONtNtNtB6_9core_arch3x867___m128i15write_unalignedCs9T56m8BN4Ao_4rand*mut core::core_arch::x86::__m128iPacked_RINvNtCsgxBkk5gSRhY_4core3ptr5writeINtB2_6PackedNtNtNtB4_9core_arch3x867___m128iEECs9T56m8BN4Ao_4randwrite>split_at_uncheckedsplit_at_mut_unchecked_RNvMs9_NtCsgxBkk5gSRhY_4core3numj10count_onescount_ones_RNvMs9_NtCsgxBkk5gSRhY_4core3numj15is_power_of_twois_power_of_twonew_uncheckedoffset_from_unsignedruntime_ptr_ge_RNvNvNvMNtNtCsgxBkk5gSRhY_4core3ptr9const_ptrPp20offset_from_unsigned14runtime_ptr_ge7runtimeCs9T56m8BN4Ao_4rand_RNvNvMNtNtCsgxBkk5gSRhY_4core3ptr9const_ptrPp20offset_from_unsigned14runtime_ptr_geCs9T56m8BN4Ao_4randthisorigin_RNvMNtNtCsgxBkk5gSRhY_4core5alloc6layoutNtB2_6Layout22max_size_for_alignmentmax_size_for_alignment_RNvMNtNtCsgxBkk5gSRhY_4core5alloc6layoutNtB2_6Layout23is_size_alignment_validCs9T56m8BN4Ao_4randis_size_alignment_validfrom_size_alignment_unchecked_RNvMs9_NtCsgxBkk5gSRhY_4core3numj15overflowing_add(usize, bool)_RNvMsW_NtCsgxBkk5gSRhY_4core4cellINtB5_10UnsafeCellINtNtCshlZbxpCh3yF_9rand_core5block8BlockRngNtNtNtCs9T56m8BN4Ao_4rand4rngs6thread13ReseedingCoreEE3newB1B_new>_RINvMs2_NtCsgxBkk5gSRhY_4core3fmtNtB6_9Arguments3newKj47_Kj3_ECs9T56m8BN4Ao_4randnew<71, 3>&[u8; 71]&[core::fmt::rt::Argument; 3]_RINvMNtNtCsgxBkk5gSRhY_4core3fmt2rtNtB3_8Argument11new_displayjECs9T56m8BN4Ao_4randnew_display_RINvMNtNtCsgxBkk5gSRhY_4core3fmt2rtNtB3_8Argument13new_upper_hexmECs9T56m8BN4Ao_4randnew_upper_hex&u32get_uncheckedget_unchecked_mutsys_rng_RINvMs2_NtCs6i54tJFfzR_5alloc7raw_vecNtB6_11RawVecInner8non_nullmECs9T56m8BN4Ao_4randnon_nullNonNull&alloc::raw_vec::RawVecInner_RINvMs2_NtCs6i54tJFfzR_5alloc7raw_vecNtB6_11RawVecInner3ptrmECs9T56m8BN4Ao_4randptr_RNvMs0_NtCs6i54tJFfzR_5alloc7raw_vecINtB5_6RawVecmE3ptrCs9T56m8BN4Ao_4randptr&alloc::raw_vec::RawVec_RNvMs_NtCs6i54tJFfzR_5alloc3vecINtB4_3VecmE6as_ptrCs9T56m8BN4Ao_4randas_ptr_RNvMs_NtCs6i54tJFfzR_5alloc3vecINtB4_3VecmE8as_sliceCs9T56m8BN4Ao_4randas_slice_RNvXs7_NtCs6i54tJFfzR_5alloc3vecINtB5_3VecmENtNtNtCsgxBkk5gSRhY_4core3ops5deref5Deref5derefCs9T56m8BN4Ao_4randderef{impl#14}rangeRangeFull_RNvXsc_NtCs6i54tJFfzR_5alloc3vecINtB5_3VecmEINtNtNtCsgxBkk5gSRhY_4core3ops5index5IndexNtNtBL_5range9RangeFullE5indexCs9T56m8BN4Ao_4randindexcmp_RNvXNtNtCsgxBkk5gSRhY_4core5slice3cmpSmNtNtB6_3cmp9PartialEq2eqCs9T56m8BN4Ao_4randeq*const [u32]partial_eq_RINvMs2_NtCs6i54tJFfzR_5alloc7raw_vecNtB6_11RawVecInner8non_nullyECs9T56m8BN4Ao_4randnon_null*const u64NonNull_RINvMs2_NtCs6i54tJFfzR_5alloc7raw_vecNtB6_11RawVecInner3ptryECs9T56m8BN4Ao_4randptr*mut u64_RNvMs0_NtCs6i54tJFfzR_5alloc7raw_vecINtB5_6RawVecyE3ptrCs9T56m8BN4Ao_4randptr&alloc::raw_vec::RawVec_RNvMs_NtCs6i54tJFfzR_5alloc3vecINtB4_3VecyE6as_ptrCs9T56m8BN4Ao_4randas_ptr_RNvMs_NtCs6i54tJFfzR_5alloc3vecINtB4_3VecyE8as_sliceCs9T56m8BN4Ao_4randas_slice&[u64]_RNvXs7_NtCs6i54tJFfzR_5alloc3vecINtB5_3VecyENtNtNtCsgxBkk5gSRhY_4core3ops5deref5Deref5derefCs9T56m8BN4Ao_4randderef_RNvXsc_NtCs6i54tJFfzR_5alloc3vecINtB5_3VecyEINtNtNtCsgxBkk5gSRhY_4core3ops5index5IndexNtNtBL_5range9RangeFullE5indexCs9T56m8BN4Ao_4randindex_RNvXNtNtCsgxBkk5gSRhY_4core5slice3cmpSyNtNtB6_3cmp9PartialEq2eqCs9T56m8BN4Ao_4randeq*const [u64]bernoulliimplscollectabort_on_dtor_unwind{impl#80}_RINvNtCsgxBkk5gSRhY_4core3cmp3minjECs9T56m8BN4Ao_4randminv1v2adapterszip_RINvMNtCsgxBkk5gSRhY_4core5sliceSh8as_arrayKj4_ECs9T56m8BN4Ao_4randas_array&[u8; 4]Option<&[u8; 4]>*const [u8; 4]me_RNvXs7_NtCsgxBkk5gSRhY_4core5arrayRAhj4_INtNtB7_7convert7TryFromRShE8try_fromCs9T56m8BN4Ao_4randtry_fromTryFromSliceErrorResult<&[u8; 4], core::array::TryFromSliceError>_RINvMNtCsgxBkk5gSRhY_4core6optionINtB3_6OptionRAhj4_E5ok_orNtNtB5_5array17TryFromSliceErrorECs9T56m8BN4Ao_4randok_or<&[u8; 4], core::array::TryFromSliceError>_RNvMs_NtCsgxBkk5gSRhY_4core6resultINtB4_6ResultRAhj4_NtNtB6_5array17TryFromSliceErrorE6copiedCs9T56m8BN4Ao_4randcopied<[u8; 4], core::array::TryFromSliceError>Result<[u8; 4], core::array::TryFromSliceError>_RINvMNtNtCsgxBkk5gSRhY_4core3ptr9const_ptrPh4castAhj4_ECs9T56m8BN4Ao_4randcast_RINvMs2_NtNtCsgxBkk5gSRhY_4core3ptr9const_ptrPh10cast_arrayKj4_ECs9T56m8BN4Ao_4randcast_array_RNvXs7_NtNtCsgxBkk5gSRhY_4core3cmp5implsRuNtB7_9PartialEq2eqCs9T56m8BN4Ao_4randeq<(), ()>&&()_RNvMNtCs6i54tJFfzR_5alloc5allocNtB2_6Global23deallocate_impl_runtimeCs9T56m8BN4Ao_4randdeallocate_impl_runtime_RNvMNtCs6i54tJFfzR_5alloc5allocNtB2_6Global15deallocate_implCs9T56m8BN4Ao_4randdeallocate_impl_RNvNtCs6i54tJFfzR_5alloc5alloc15dealloc_nonnullCs9T56m8BN4Ao_4randdealloc_nonnullPolymorphicIter<[core::mem::maybe_uninit::MaybeUninit<[core::core_arch::x86::__m256i; 4]>; 2]>_RNvMs2_NtNtNtCsgxBkk5gSRhY_4core5array4iter10iter_innerINtB5_15PolymorphicIterAINtNtNtBb_3mem12maybe_uninit11MaybeUninitANtNtNtBb_9core_arch3x867___m256ij4_Ej2_E13new_uncheckedCs9T56m8BN4Ao_4randnew_unchecked<[core::core_arch::x86::__m256i; 4], 2>MaybeDangling; 2]>>_RNvMNtNtCsgxBkk5gSRhY_4core3mem14maybe_danglingINtB2_13MaybeDanglingINtNtNtNtB6_5array4iter10iter_inner15PolymorphicIterAINtNtB4_12maybe_uninit11MaybeUninitANtNtNtB6_9core_arch3x867___m256ij4_Ej2_EE3newCs9T56m8BN4Ao_4randnew; 2]>>ManuallyDrop; 2]>>_RNvMNtNtCsgxBkk5gSRhY_4core3mem13manually_dropINtB2_12ManuallyDropINtNtNtNtB6_5array4iter10iter_inner15PolymorphicIterAINtNtB4_12maybe_uninit11MaybeUninitANtNtNtB6_9core_arch3x867___m256ij4_Ej2_EE3newCs9T56m8BN4Ao_4randWrite{impl#12}{impl#13}NonNull<[core::core_arch::x86::__m256i; 4]>end_or_len*mut [core::core_arch::x86::__m256i; 4]&mut [core::core_arch::x86::__m256i; 4]PhantomData<&mut [core::core_arch::x86::__m256i; 4]>IterMut<[core::core_arch::x86::__m256i; 4]>_RNvMsa_NtNtCsgxBkk5gSRhY_4core5slice4iterINtB5_7IterMutANtNtNtB9_9core_arch3x867___m256ij4_E3newCs9T56m8BN4Ao_4randnew<[core::core_arch::x86::__m256i; 4]>&mut [[core::core_arch::x86::__m256i; 4]]_RNvMNtCsgxBkk5gSRhY_4core5sliceSANtNtNtB4_9core_arch3x867___m256ij4_8iter_mutCs9T56m8BN4Ao_4randiter_mut<[core::core_arch::x86::__m256i; 4]>_RINvNtCsgxBkk5gSRhY_4core3ptr22without_provenance_mutANtNtNtB4_9core_arch3x867___m256ij4_ECs9T56m8BN4Ao_4randwithout_provenance_mut<[core::core_arch::x86::__m256i; 4]>addr_RNvMNtNtCsgxBkk5gSRhY_4core3ptr7mut_ptrOANtNtNtB6_9core_arch3x867___m256ij4_3addCs9T56m8BN4Ao_4randadd<[core::core_arch::x86::__m256i; 4]>*const [[core::core_arch::x86::__m256i; 4]]NonNull<[[core::core_arch::x86::__m256i; 4]]>_RNvMs1_NtNtCsgxBkk5gSRhY_4core3ptr8non_nullINtB5_7NonNullSANtNtNtB9_9core_arch3x867___m256ij4_E8from_mutCs9T56m8BN4Ao_4randfrom_mut<[[core::core_arch::x86::__m256i; 4]]>r_RINvMs1_NtNtCsgxBkk5gSRhY_4core3ptr8non_nullINtB6_7NonNullSANtNtNtBa_9core_arch3x867___m256ij4_E4castBV_ECs9T56m8BN4Ao_4randcast<[[core::core_arch::x86::__m256i; 4]], [core::core_arch::x86::__m256i; 4]>_RNvMs1_NtNtCsgxBkk5gSRhY_4core3ptr8non_nullINtB5_7NonNullANtNtNtB9_9core_arch3x867___m256ij4_E6as_ptrCs9T56m8BN4Ao_4randIdxRangeFrom_RNvXNtNtCsgxBkk5gSRhY_4core5slice5indexSmINtNtNtB6_3ops5index5IndexINtNtBI_5range9RangeFromjEE5indexCs9T56m8BN4Ao_4randindex>{impl#15}Range_RNvXs_NtNtCsgxBkk5gSRhY_4core5slice5indexSmINtNtNtB8_3ops5index8IndexMutINtNtBK_5range5RangejEE9index_mutCs9T56m8BN4Ao_4randindex_mut>{impl#16}_RNvXs2_NtNtCsgxBkk5gSRhY_4core5slice5indexINtNtNtB9_3ops5range5RangejEINtB5_10SliceIndexSINtNtNtB9_3mem12maybe_uninit11MaybeUninitNtNtNtB9_9core_arch3x867___m128iEE17get_unchecked_mutCs9T56m8BN4Ao_4rand*mut [core::mem::maybe_uninit::MaybeUninit]new_len_RNvXs4_NtNtCsgxBkk5gSRhY_4core5slice5indexINtNtNtB9_3ops5range7RangeTojEINtB5_10SliceIndexSINtNtNtB9_3mem12maybe_uninit11MaybeUninitNtNtNtB9_9core_arch3x867___m128iEE17get_unchecked_mutCs9T56m8BN4Ao_4randRangeTo_RINvMNtCsgxBkk5gSRhY_4core5sliceSINtNtNtB5_3mem12maybe_uninit11MaybeUninitNtNtNtB5_9core_arch3x867___m128iE17get_unchecked_mutINtNtNtB5_3ops5range7RangeTojEECs9T56m8BN4Ao_4randget_unchecked_mut, core::ops::range::RangeTo>_RINvNtNtCsgxBkk5gSRhY_4core5slice5index28get_offset_len_mut_noubcheckINtNtNtB6_3mem12maybe_uninit11MaybeUninitNtNtNtB6_9core_arch3x867___m128iEECs9T56m8BN4Ao_4randget_offset_len_mut_noubcheck>offset_RNvMs2_NtNtCsgxBkk5gSRhY_4core3mem12maybe_uninitSINtB5_11MaybeUninitNtNtNtB9_9core_arch3x867___m128iE16assume_init_dropCs9T56m8BN4Ao_4randassume_init_drop{impl#26}{impl#30}{impl#33}_RNvXs3_NtCsgxBkk5gSRhY_4core7defaulthNtB5_7Default7default{impl#37}_RNvMNtNtCsgxBkk5gSRhY_4core4char7methodsc11encode_utf8Cs9T56m8BN4Ao_4randencode_utf8&mut strfunctionFnOnceGenerator_RINvNtCs9k3SxhrAWiO_3std2io17default_write_fmtNtNtNtNtB4_3sys5stdio4unix6StderrECs9T56m8BN4Ao_4randdefault_write_fmt_RINvNtCsgxBkk5gSRhY_4core3ptr9drop_glueINtNtB4_4cell10UnsafeCellINtNtCshlZbxpCh3yF_9rand_core5block8BlockRngNtNtNtCs9T56m8BN4Ao_4rand4rngs6thread13ReseedingCoreEEEB1O_drop_glue>>_RINvNtCsgxBkk5gSRhY_4core3ptr9drop_glueINtNtB4_5array5GuardNtNtNtB4_9core_arch3x867___m128iEECs9T56m8BN4Ao_4randdrop_glue>_RINvNtCsgxBkk5gSRhY_4core3ptr9drop_glueINtNtB4_6result6ResultuNtNtNtB4_2io5error5ErrorEECs9T56m8BN4Ao_4randdrop_glue>_RINvNtCsgxBkk5gSRhY_4core3ptr9drop_glueINtNtCs6i54tJFfzR_5alloc2rc2RcINtNtB4_4cell10UnsafeCellINtNtCshlZbxpCh3yF_9rand_core5block8BlockRngNtNtNtCs9T56m8BN4Ao_4rand4rngs6thread13ReseedingCoreEEEEB2i_drop_glue>, alloc::alloc::Global>>Weak>, 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2>_RINvNtCsgxBkk5gSRhY_4core3ptr9drop_glueINtNtNtB4_5array4iter8IntoIterANtNtNtB4_9core_arch3x867___m256ij4_Kj2_EECs9T56m8BN4Ao_4randdrop_glue>_RINvNtCsgxBkk5gSRhY_4core3ptr9drop_glueINtNvNtCs9k3SxhrAWiO_3std2io17default_write_fmt7AdapterNtNtNtNtBI_3sys5stdio4unix6StderrEECs9T56m8BN4Ao_4randdrop_glue>DtorUnwindGuard_RINvNtCsgxBkk5gSRhY_4core3ptr9drop_glueNtNvNtNtCs9k3SxhrAWiO_3std3sys12thread_local20abort_on_dtor_unwind15DtorUnwindGuardECs9T56m8BN4Ao_4randdrop_glueNeverShortCircuitnew_ref__state_ptr*const core::core_arch::x86::__m128i&*const core::core_arch::x86::__m128i{closure_env#0}{closure_env#0}>_RINvNtCsgxBkk5gSRhY_4core5array11try_from_fnINtNtNtB4_3ops9try_trait17NeverShortCircuitNtNtNtB4_9core_arch3x867___m128iEKj4_NCINvMBJ_BG_10wrap_mut_1jNCNvMNtNtCs31D8PfpPePt_8chacha208backends4sse2INtB2s_7BackendNtB2w_3R12NtNtB2w_8variants6LegacyE3new0E0ECs9T56m8BN4Ao_4randtry_from_fn, 4, 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core::io::error::repr::{impl#2}::data::{closure_env#0}>ErrorData<&core::io::error::Custom>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x863avx20__mm256_extract_epi32Kl0_ECs9T56m8BN4Ao_4rand_mm256_extract_epi32<0>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x863avx20__mm256_extract_epi32Kl1_ECs9T56m8BN4Ao_4rand_mm256_extract_epi32<1>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse214__mm_slli_epi32Kl10_ECs9T56m8BN4Ao_4rand_mm_slli_epi32<16>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse214__mm_slli_epi32Kl7_ECs9T56m8BN4Ao_4rand_mm_slli_epi32<7>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse214__mm_slli_epi32Kl8_ECs9T56m8BN4Ao_4rand_mm_slli_epi32<8>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse214__mm_slli_epi32Klc_ECs9T56m8BN4Ao_4rand_mm_slli_epi32<12>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse214__mm_srli_epi32Kl10_ECs9T56m8BN4Ao_4rand_mm_srli_epi32<16>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse214__mm_srli_epi32Kl14_ECs9T56m8BN4Ao_4rand_mm_srli_epi32<20>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse214__mm_srli_epi32Kl18_ECs9T56m8BN4Ao_4rand_mm_srli_epi32<24>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse214__mm_srli_epi32Kl19_ECs9T56m8BN4Ao_4rand_mm_srli_epi32<25>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse217__mm_shuffle_epi32Kl39_ECs9T56m8BN4Ao_4rand_mm_shuffle_epi32<57>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse217__mm_shuffle_epi32Kl4e_ECs9T56m8BN4Ao_4rand_mm_shuffle_epi32<78>_RINvNtNtNtCsgxBkk5gSRhY_4core9core_arch3x864sse217__mm_shuffle_epi32Kl93_ECs9T56m8BN4Ao_4rand_mm_shuffle_epi32<147>PhantomData<&u32>Iter&u64PhantomData<&u64>IterZip, 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core::slice::iter::Iter>{closure_env#1}_RINvYINtNtNtNtCsgxBkk5gSRhY_4core4iter8adapters3zip3ZipINtNtNtBc_5slice4iter4IteryEIBS_mEENtNtNtBa_6traits8iterator8Iterator3allNCNvXs0_NtNtCs9T56m8BN4Ao_4rand3seq6index_NtB2a_8IndexVecNtNtBc_3cmp9PartialEq2eqs_0EB2e_all, core::slice::iter::Iter>, rand::seq::index_::{impl#2}::eq::{closure_env#1}>{closure_env#0}<(&u64, &u32), rand::seq::index_::{impl#2}::eq::{closure_env#1}>_RINvYINtNtNtNtCsgxBkk5gSRhY_4core4iter8adapters3zip3ZipINtNtNtBc_5slice4iter4IteryEIBS_mEENtNtNtBa_6traits8iterator8Iterator8try_folduNCINvNvB1q_3all5checkTRyRmENCNvXs0_NtNtCs9T56m8BN4Ao_4rand3seq6index_NtB2H_8IndexVecNtNtBc_3cmp9PartialEq2eqs_0E0INtNtNtBc_3ops12control_flow11ControlFlowuEEB2L_try_fold, core::slice::iter::Iter>, (), core::iter::traits::iterator::Iterator::all::check::{closure_env#0}<(&u64, &u32), rand::seq::index_::{impl#2}::eq::{closure_env#1}>, core::ops::control_flow::ControlFlow<(), 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