# rng.rs - source
Source of the Rust file `/home/key/.cargo/registry/src/github.com-1ecc6299db9ec823/rand-0.8.5/src/rng.rs`.
Keywords: rust, rustlang, rust-lang

    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
    79
    80
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    94
    95
    96
    97
    98
    99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124
    125
    126
    127
    128
    129
    130
    131
    132
    133
    134
    135
    136
    137
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    151
    152
    153
    154
    155
    156
    157
    158
    159
    160
    161
    162
    163
    164
    165
    166
    167
    168
    169
    170
    171
    172
    173
    174
    175
    176
    177
    178
    179
    180
    181
    182
    183
    184
    185
    186
    187
    188
    189
    190
    191
    192
    193
    194
    195
    196
    197
    198
    199
    200
    201
    202
    203
    204
    205
    206
    207
    208
    209
    210
    211
    212
    213
    214
    215
    216
    217
    218
    219
    220
    221
    222
    223
    224
    225
    226
    227
    228
    229
    230
    231
    232
    233
    234
    235
    236
    237
    238
    239
    240
    241
    242
    243
    244
    245
    246
    247
    248
    249
    250
    251
    252
    253
    254
    255
    256
    257
    258
    259
    260
    261
    262
    263
    264
    265
    266
    267
    268
    269
    270
    271
    272
    273
    274
    275
    276
    277
    278
    279
    280
    281
    282
    283
    284
    285
    286
    287
    288
    289
    290
    291
    292
    293
    294
    295
    296
    297
    298
    299
    300
    301
    302
    303
    304
    305
    306
    307
    308
    309
    310
    311
    312
    313
    314
    315
    316
    317
    318
    319
    320
    321
    322
    323
    324
    325
    326
    327
    328
    329
    330
    331
    332
    333
    334
    335
    336
    337
    338
    339
    340
    341
    342
    343
    344
    345
    346
    347
    348
    349
    350
    351
    352
    353
    354
    355
    356
    357
    358
    359
    360
    361
    362
    363
    364
    365
    366
    367
    368
    369
    370
    371
    372
    373
    374
    375
    376
    377
    378
    379
    380
    381
    382
    383
    384
    385
    386
    387
    388
    389
    390
    391
    392
    393
    394
    395
    396
    397
    398
    399
    400
    401
    402
    403
    404
    405
    406
    407
    408
    409
    410
    411
    412
    413
    414
    415
    416
    417
    418
    419
    420
    421
    422
    423
    424
    425
    426
    427
    428
    429
    430
    431
    432
    433
    434
    435
    436
    437
    438
    439
    440
    441
    442
    443
    444
    445
    446
    447
    448
    449
    450
    451
    452
    453
    454
    455
    456
    457
    458
    459
    460
    461
    462
    463
    464
    465
    466
    467
    468
    469
    470
    471
    472
    473
    474
    475
    476
    477
    478
    479
    480
    481
    482
    483
    484
    485
    486
    487
    488
    489
    490
    491
    492
    493
    494
    495
    496
    497
    498
    499
    500
    501
    502
    503
    504
    505
    506
    507
    508
    509
    510
    511
    512
    513
    514
    515
    516
    517
    518
    519
    520
    521
    522
    523
    524
    525
    526
    527
    528
    529
    530
    531
    532
    533
    534
    535
    536
    537
    538
    539
    540
    541
    542
    543
    544
    545
    546
    547
    548
    549
    550
    551
    552
    553
    554
    555
    556
    557
    558
    559
    560
    561
    562
    563
    564
    565
    566
    567
    568
    569
    570
    571
    572
    573
    574
    575
    576
    577
    578
    579
    580
    581
    582
    583
    584
    585
    586
    587
    588
    589
    590
    591
    592
    593
    594
    595
    596
    597
    598
    599
    600

    // Copyright 2018 Developers of the Rand project.
    // Copyright 2013-2017 The Rust Project Developers.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.

    //! [`Rng`] trait

    use rand_core::{Error, RngCore};
    use crate::distributions::uniform::{SampleRange, SampleUniform};
    use crate::distributions::{self, Distribution, Standard};
    use core::num::Wrapping;
    use core::{mem, slice};

    /// An automatically-implemented extension trait on [`RngCore`] providing high-level
    /// generic methods for sampling values and other convenience methods.
    ///
    /// This is the primary trait to use when generating random values.
    ///
    /// # Generic usage
    ///
    /// The basic pattern is `fn foo<R: Rng + ?Sized>(rng: &mut R)`. Some
    /// things are worth noting here:
    ///
    /// - Since `Rng: RngCore` and every `RngCore` implements `Rng`, it makes no
    ///   difference whether we use `R: Rng` or `R: RngCore`.
    /// - The `+ ?Sized` un-bounding allows functions to be called directly on
    ///   type-erased references; i.e. `foo(r)` where `r: &mut dyn RngCore`. Without
    ///   this it would be necessary to write `foo(&mut r)`.
    ///
    /// An alternative pattern is possible: `fn foo<R: Rng>(rng: R)`. This has some
    /// trade-offs. It allows the argument to be consumed directly without a `&mut`
    /// (which is how `from_rng(thread_rng())` works); also it still works directly
    /// on references (including type-erased references). Unfortunately within the
    /// function `foo` it is not known whether `rng` is a reference type or not,
    /// hence many uses of `rng` require an extra reference, either explicitly
    /// (`distr.sample(&mut rng)`) or implicitly (`rng.gen()`); one may hope the
    /// optimiser can remove redundant references later.
    ///
    /// Example:
    ///
    /// ```
    /// # use rand::thread_rng;
    /// use rand::Rng;
    ///
    /// fn foo<R: Rng + ?Sized>(rng: &mut R) -> f32 {
    ///     rng.gen()
    /// }
    ///
    /// # let v = foo(&mut thread_rng());
    /// ```
    pub trait Rng: RngCore {
        /// Return a random value supporting the [`Standard`] distribution.
        ///
        /// # Example
        ///
        /// ```
        /// use rand::{thread_rng, Rng};
        ///
        /// let mut rng = thread_rng();
        /// let x: u32 = rng.gen();
        /// println!("{}", x);
        /// println!("{:?}", rng.gen::<(f64, bool)>());
        /// ```
        ///
        /// # Arrays and tuples
        ///
        /// The `rng.gen()` method is able to generate arrays (up to 32 elements)
        /// and tuples (up to 12 elements), so long as all element types can be
        /// generated.
        /// When using `rustc` ≥ 1.51, enable the `min_const_gen` feature to support
        /// arrays larger than 32 elements.
        ///
        /// For arrays of integers, especially for those with small element types
        /// (< 64 bit), it will likely be faster to instead use [`Rng::fill`].
        ///
        /// ```
        /// use rand::{thread_rng, Rng};
        ///
        /// let mut rng = thread_rng();
        /// let tuple: (u8, i32, char) = rng.gen(); // arbitrary tuple support
        ///
        /// let arr1: [f32; 32] = rng.gen();        // array construction
        /// let mut arr2 = [0u8; 128];
        /// rng.fill(&mut arr2);                    // array fill
        /// ```
        ///
        /// [`Standard`]: distributions::Standard
        #[inline]
        fn gen<T>(&mut self) -> T
        where Standard: Distribution<T> {
            Standard.sample(self)
        }

        /// Generate a random value in the given range.
        ///
        /// This function is optimised for the case that only a single sample is
        /// made from the given range. See also the [`Uniform`] distribution
        /// type which may be faster if sampling from the same range repeatedly.
        ///
        /// Only `gen_range(low..high)` and `gen_range(low..=high)` are supported.
        ///
        /// # Panics
        ///
        /// Panics if the range is empty.
        ///
        /// # Example
        ///
        /// ```
        /// use rand::{thread_rng, Rng};
        ///
        /// let mut rng = thread_rng();
        ///
        /// // Exclusive range
        /// let n: u32 = rng.gen_range(0..10);
        /// println!("{}", n);
        /// let m: f64 = rng.gen_range(-40.0..1.3e5);
        /// println!("{}", m);
        ///
        /// // Inclusive range
        /// let n: u32 = rng.gen_range(0..=10);
        /// println!("{}", n);
        /// ```
        ///
        /// [`Uniform`]: distributions::uniform::Uniform
        fn gen_range<T, R>(&mut self, range: R) -> T
        where
            T: SampleUniform,
            R: SampleRange<T>
        {
            assert!(!range.is_empty(), "cannot sample empty range");
            range.sample_single(self)
        }

        /// Sample a new value, using the given distribution.
        ///
        /// ### Example
        ///
        /// ```
        /// use rand::{thread_rng, Rng};
        /// use rand::distributions::Uniform;
        ///
        /// let mut rng = thread_rng();
        /// let x = rng.sample(Uniform::new(10u32, 15));
        /// // Type annotation requires two types, the type and distribution; the
        /// // distribution can be inferred.
        /// let y = rng.sample::<u16, _>(Uniform::new(10, 15));
        /// ```
        fn sample<T, D: Distribution<T>>(&mut self, distr: D) -> T {
            distr.sample(self)
        }

        /// Create an iterator that generates values using the given distribution.
        ///
        /// Note that this function takes its arguments by value. This works since
        /// `(&mut R): Rng where R: Rng` and
        /// `(&D): Distribution where D: Distribution`,
        /// however borrowing is not automatic hence `rng.sample_iter(...)` may
        /// need to be replaced with `(&mut rng).sample_iter(...)`.
        ///
        /// # Example
        ///
        /// ```
        /// use rand::{thread_rng, Rng};
        /// use rand::distributions::{Alphanumeric, Uniform, Standard};
        ///
        /// let mut rng = thread_rng();
        ///
        /// // Vec of 16 x f32:
        /// let v: Vec<f32> = (&mut rng).sample_iter(Standard).take(16).collect();
        ///
        /// // String:
        /// let s: String = (&mut rng).sample_iter(Alphanumeric)
        ///     .take(7)
        ///     .map(char::from)
        ///     .collect();
        ///
        /// // Combined values
        /// println!("{:?}", (&mut rng).sample_iter(Standard).take(5)
        ///                              .collect::<Vec<(f64, bool)>>());
        ///
        /// // Dice-rolling:
        /// let die_range = Uniform::new_inclusive(1, 6);
        /// let mut roll_die = (&mut rng).sample_iter(die_range);
        /// while roll_die.next().unwrap() != 6 {
        ///     println!("Not a 6; rolling again!");
        /// }
        /// ```
        fn sample_iter<T, D>(self, distr: D) -> distributions::DistIter<D, Self, T>
        where
            D: Distribution<T>,
            Self: Sized,
        {
            distr.sample_iter(self)
        }

        /// Fill any type implementing [`Fill`] with random data
        ///
        /// The distribution is expected to be uniform with portable results, but
        /// this cannot be guaranteed for third-party implementations.
        ///
        /// This is identical to [`try_fill`] except that it panics on error.
        ///
        /// # Example
        ///
        /// ```
        /// use rand::{thread_rng, Rng};
        ///
        /// let mut arr = [0i8; 20];
        /// thread_rng().fill(&mut arr[..]);
        /// ```
        ///
        /// [`fill_bytes`]: RngCore::fill_bytes
        /// [`try_fill`]: Rng::try_fill
        fn fill<T: Fill + ?Sized>(&mut self, dest: &mut T) {
            dest.try_fill(self).unwrap_or_else(|_| panic!("Rng::fill failed"))
        }

        /// Fill any type implementing [`Fill`] with random data
        ///
        /// The distribution is expected to be uniform with portable results, but
        /// this cannot be guaranteed for third-party implementations.
        ///
        /// This is identical to [`fill`] except that it forwards errors.
        ///
        /// # Example
        ///
        /// ```
        /// # use rand::Error;
        /// use rand::{thread_rng, Rng};
        ///
        /// # fn try_inner() -> Result<(), Error> {
        /// let mut arr = [0u64; 4];
        /// thread_rng().try_fill(&mut arr[..])?;
        /// # Ok(())
        /// # }
        ///
        /// # try_inner().unwrap()
        /// ```
        ///
        /// [`try_fill_bytes`]: RngCore::try_fill_bytes
        /// [`fill`]: Rng::fill
        fn try_fill<T: Fill + ?Sized>(&mut self, dest: &mut T) -> Result<(), Error> {
            dest.try_fill(self)
        }

        /// Return a bool with a probability `p` of being true.
        ///
        /// See also the [`Bernoulli`] distribution, which may be faster if
        /// sampling from the same probability repeatedly.
        ///
        /// # Example
        ///
        /// ```
        /// use rand::{thread_rng, Rng};
        ///
        /// let mut rng = thread_rng();
        /// println!("{}", rng.gen_bool(1.0 / 3.0));
        /// ```
        ///
        /// # Panics
        ///
        /// If `p < 0` or `p > 1`.
        ///
        /// [`Bernoulli`]: distributions::Bernoulli
        #[inline]
        fn gen_bool(&mut self, p: f64) -> bool {
            let d = distributions::Bernoulli::new(p).unwrap();
            self.sample(d)
        }

        /// Return a bool with a probability of `numerator/denominator` of being
        /// true. I.e. `gen_ratio(2, 3)` has chance of 2 in 3, or about 67%, of
        /// returning true. If `numerator == denominator`, then the returned value
        /// is guaranteed to be `true`. If `numerator == 0`, then the returned
        /// value is guaranteed to be `false`.
        ///
        /// See also the [`Bernoulli`] distribution, which may be faster if
        /// sampling from the same `numerator` and `denominator` repeatedly.
        ///
        /// # Panics
        ///
        /// If `denominator == 0` or `numerator > denominator`.
        ///
        /// # Example
        ///
        /// ```
        /// use rand::{thread_rng, Rng};
        ///
        /// let mut rng = thread_rng();
        /// println!("{}", rng.gen_ratio(2, 3));
        /// ```
        ///
        /// [`Bernoulli`]: distributions::Bernoulli
        #[inline]
        fn gen_ratio(&mut self, numerator: u32, denominator: u32) -> bool {
            let d = distributions::Bernoulli::from_ratio(numerator, denominator).unwrap();
            self.sample(d)
        }
    }

    impl<R: RngCore + ?Sized> Rng for R {}

    /// Types which may be filled with random data
    ///
    /// This trait allows arrays to be efficiently filled with random data.
    ///
    /// Implementations are expected to be portable across machines unless
    /// clearly documented otherwise (see the
    /// [Chapter on Portability](https://rust-random.github.io/book/portability.html)).
    pub trait Fill {
        /// Fill self with random data
        fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error>;
    }

    macro_rules! impl_fill_each {
        () => {};
        ($t:ty) => {
            impl Fill for [$t] {
                fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
                    for elt in self.iter_mut() {
                        *elt = rng.gen();
                    }
                    Ok(())
                }
            }
        };
        ($t:ty, $($tt:ty,)*) => {
            impl_fill_each!($t);
            impl_fill_each!($($tt,)*);
        };
    }

    impl_fill_each!(bool, char, f32, f64,);

    impl Fill for [u8] {
        fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
            rng.try_fill_bytes(self)
        }
    }

    macro_rules! impl_fill {
        () => {};
        ($t:ty) => {
            impl Fill for [$t] {
                #[inline(never)] // in micro benchmarks, this improves performance
                fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
                    if self.len() > 0 {
                        rng.try_fill_bytes(unsafe {
                            slice::from_raw_parts_mut(self.as_mut_ptr()
                                as *mut u8,
                                self.len() * mem::size_of::<$t>()
                            )
                        })?;
                        for x in self {
                            *x = x.to_le();
                        }
                    }
                    Ok(())
                }
            }

            impl Fill for [Wrapping<$t>] {
                #[inline(never)]
                fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
                    if self.len() > 0 {
                        rng.try_fill_bytes(unsafe {
                            slice::from_raw_parts_mut(self.as_mut_ptr()
                                as *mut u8,
                                self.len() * mem::size_of::<$t>()
                            )
                        })?;
                        for x in self {
                        *x = Wrapping(x.0.to_le());
                        }
                    }
                    Ok(())
                }
            }
        };
        ($t:ty, $($tt:ty,)*) => {
            impl_fill!($t);
            // TODO: this could replace above impl once Rust #32463 is fixed
            // impl_fill!(Wrapping<$t>);
            impl_fill!($($tt,)*);
        }
    }

    impl_fill!(u16, u32, u64, usize, u128,);
    impl_fill!(i8, i16, i32, i64, isize, i128,);

    #[cfg_attr(doc_cfg, doc(cfg(feature = "min_const_gen")))]
    #[cfg(feature = "min_const_gen")]
    impl<T, const N: usize> Fill for [T; N]
    where [T]: Fill
    {
        fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
            self[..].try_fill(rng)
        }
    }

    #[cfg(not(feature = "min_const_gen"))]
    macro_rules! impl_fill_arrays {
        ($n:expr,) => {};
        ($n:expr, $N:ident) => {
            impl<T> Fill for [T; $n] where [T]: Fill {
                fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
                    self[..].try_fill(rng)
                }
            }
        };
        ($n:expr, $N:ident, $($NN:ident,)*) => {
            impl_fill_arrays!($n, $N);
            impl_fill_arrays!($n - 1, $($NN,)*);
        };
        (!div $n:expr,) => {};
        (!div $n:expr, $N:ident, $($NN:ident,)*) => {
            impl_fill_arrays!($n, $N);
            impl_fill_arrays!(!div $n / 2, $($NN,)*);
        };
    }
    #[cfg(not(feature = "min_const_gen"))]
    #[rustfmt::skip]
    impl_fill_arrays!(32, N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,);
    #[cfg(not(feature = "min_const_gen"))]
    impl_fill_arrays!(!div 4096, N,N,N,N,N,N,N,);

    #[cfg(test)]
    mod test {
        use super::*;
        use crate::test::rng;
        use crate::rngs::mock::StepRng;
        #[cfg(feature = "alloc")] use alloc::boxed::Box;

        #[test]
        fn test_fill_bytes_default() {
            let mut r = StepRng::new(0x11_22_33_44_55_66_77_88, 0);

            // check every remainder mod 8, both in small and big vectors.
            let lengths = [0, 1, 2, 3, 4, 5, 6, 7, 80, 81, 82, 83, 84, 85, 86, 87];
            for &n in lengths.iter() {
                let mut buffer = [0u8; 87];
                let v = &mut buffer[0..n];
                r.fill_bytes(v);

                // use this to get nicer error messages.
                for (i, &byte) in v.iter().enumerate() {
                    if byte == 0 {
                        panic!("byte {} of {} is zero", i, n)
                    }
                }
            }
        }

        #[test]
        fn test_fill() {
            let x = 9041086907909331047; // a random u64
            let mut rng = StepRng::new(x, 0);

            // Convert to byte sequence and back to u64; byte-swap twice if BE.
            let mut array = [0u64; 2];
            rng.fill(&mut array[..]);
            assert_eq!(array, [x, x]);
            assert_eq!(rng.next_u64(), x);

            // Convert to bytes then u32 in LE order
            let mut array = [0u32; 2];
            rng.fill(&mut array[..]);
            assert_eq!(array, [x as u32, (x >> 32) as u32]);
            assert_eq!(rng.next_u32(), x as u32);

            // Check equivalence using wrapped arrays
            let mut warray = [Wrapping(0u32); 2];
            rng.fill(&mut warray[..]);
            assert_eq!(array[0], warray[0].0);
            assert_eq!(array[1], warray[1].0);

            // Check equivalence for generated floats
            let mut array = [0f32; 2];
            rng.fill(&mut array);
            let gen: [f32; 2] = rng.gen();
            assert_eq!(array, gen);
        }

        #[test]
        fn test_fill_empty() {
            let mut array = [0u32; 0];
            let mut rng = StepRng::new(0, 1);
            rng.fill(&mut array);
            rng.fill(&mut array[..]);
        }

        #[test]
        fn test_gen_range_int() {
            let mut r = rng(101);
            for _ in 0..1000 {
                let a = r.gen_range(-4711..17);
                assert!((-4711..17).contains(&a));
                let a: i8 = r.gen_range(-3..42);
                assert!((-3..42).contains(&a));
                let a: u16 = r.gen_range(10..99);
                assert!((10..99).contains(&a));
                let a: i32 = r.gen_range(-100..2000);
                assert!((-100..2000).contains(&a));
                let a: u32 = r.gen_range(12..=24);
                assert!((12..=24).contains(&a));

                assert_eq!(r.gen_range(0u32..1), 0u32);
                assert_eq!(r.gen_range(-12i64..-11), -12i64);
                assert_eq!(r.gen_range(3_000_000..3_000_001), 3_000_000);
            }
        }

        #[test]
        fn test_gen_range_float() {
            let mut r = rng(101);
            for _ in 0..1000 {
                let a = r.gen_range(-4.5..1.7);
                assert!((-4.5..1.7).contains(&a));
                let a = r.gen_range(-1.1..=-0.3);
                assert!((-1.1..=-0.3).contains(&a));

                assert_eq!(r.gen_range(0.0f32..=0.0), 0.);
                assert_eq!(r.gen_range(-11.0..=-11.0), -11.);
                assert_eq!(r.gen_range(3_000_000.0..=3_000_000.0), 3_000_000.);
            }
        }

        #[test]
        #[should_panic]
        fn test_gen_range_panic_int() {
            #![allow(clippy::reversed_empty_ranges)]
            let mut r = rng(102);
            r.gen_range(5..-2);
        }

        #[test]
        #[should_panic]
        fn test_gen_range_panic_usize() {
            #![allow(clippy::reversed_empty_ranges)]
            let mut r = rng(103);
            r.gen_range(5..2);
        }

        #[test]
        fn test_gen_bool() {
            #![allow(clippy::bool_assert_comparison)]

            let mut r = rng(105);
            for _ in 0..5 {
                assert_eq!(r.gen_bool(0.0), false);
                assert_eq!(r.gen_bool(1.0), true);
            }
        }

        #[test]
        fn test_rng_trait_object() {
            use crate::distributions::{Distribution, Standard};
            let mut rng = rng(109);
            let mut r = &mut rng as &mut dyn RngCore;
            r.next_u32();
            r.gen::<i32>();
            assert_eq!(r.gen_range(0..1), 0);
            let _c: u8 = Standard.sample(&mut r);
        }

        #[test]
        #[cfg(feature = "alloc")]
        fn test_rng_boxed_trait() {
            use crate::distributions::{Distribution, Standard};
            let rng = rng(110);
            let mut r = Box::new(rng) as Box<dyn RngCore>;
            r.next_u32();
            r.gen::<i32>();
            assert_eq!(r.gen_range(0..1), 0);
            let _c: u8 = Standard.sample(&mut r);
        }

        #[test]
        #[cfg_attr(miri, ignore)] // Miri is too slow
        fn test_gen_ratio_average() {
            const NUM: u32 = 3;
            const DENOM: u32 = 10;
            const N: u32 = 100_000;

            let mut sum: u32 = 0;
            let mut rng = rng(111);
            for _ in 0..N {
                if rng.gen_ratio(NUM, DENOM) {
                    sum += 1;
                }
            }
            // Have Binomial(N, NUM/DENOM) distribution
            let expected = (NUM * N) / DENOM; // exact integer
            assert!(((sum - expected) as i32).abs() < 500);
        }
    }