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
// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! Generating numbers between two others.

// this is surprisingly complicated to be both generic & correct

use std::num::Wrapping as w;

use Rng;
use distributions::{Sample, IndependentSample};

/// Sample values uniformly between two bounds.
///
/// This gives a uniform distribution (assuming the RNG used to sample
/// it is itself uniform & the `SampleRange` implementation for the
/// given type is correct), even for edge cases like `low = 0u8`,
/// `high = 170u8`, for which a naive modulo operation would return
/// numbers less than 85 with double the probability to those greater
/// than 85.
///
/// Types should attempt to sample in `[low, high)`, i.e., not
/// including `high`, but this may be very difficult. All the
/// primitive integer types satisfy this property, and the float types
/// normally satisfy it, but rounding may mean `high` can occur.
///
/// # Example
///
/// ```rust
/// use rand::distributions::{IndependentSample, Range};
///
/// fn main() {
///     let between = Range::new(10, 10000);
///     let mut rng = rand::thread_rng();
///     let mut sum = 0;
///     for _ in 0..1000 {
///         sum += between.ind_sample(&mut rng);
///     }
///     println!("{}", sum);
/// }
/// ```
#[derive(Clone, Copy)]
pub struct Range<X> {
    low: X,
    range: X,
    accept_zone: X
}

impl<X: SampleRange + PartialOrd> Range<X> {
    /// Create a new `Range` instance that samples uniformly from
    /// `[low, high)`. Panics if `low >= high`.
    pub fn new(low: X, high: X) -> Range<X> {
        assert!(low < high, "Range::new called with `low >= high`");
        SampleRange::construct_range(low, high)
    }
}

impl<Sup: SampleRange> Sample<Sup> for Range<Sup> {
    #[inline]
    fn sample<R: Rng>(&mut self, rng: &mut R) -> Sup { self.ind_sample(rng) }
}
impl<Sup: SampleRange> IndependentSample<Sup> for Range<Sup> {
    fn ind_sample<R: Rng>(&self, rng: &mut R) -> Sup {
        SampleRange::sample_range(self, rng)
    }
}

/// The helper trait for types that have a sensible way to sample
/// uniformly between two values. This should not be used directly,
/// and is only to facilitate `Range`.
pub trait SampleRange : Sized {
    /// Construct the `Range` object that `sample_range`
    /// requires. This should not ever be called directly, only via
    /// `Range::new`, which will check that `low < high`, so this
    /// function doesn't have to repeat the check.
    fn construct_range(low: Self, high: Self) -> Range<Self>;

    /// Sample a value from the given `Range` with the given `Rng` as
    /// a source of randomness.
    fn sample_range<R: Rng>(r: &Range<Self>, rng: &mut R) -> Self;
}

macro_rules! integer_impl {
    ($ty:ty, $unsigned:ident) => {
        impl SampleRange for $ty {
            // we play free and fast with unsigned vs signed here
            // (when $ty is signed), but that's fine, since the
            // contract of this macro is for $ty and $unsigned to be
            // "bit-equal", so casting between them is a no-op & a
            // bijection.

            fn construct_range(low: $ty, high: $ty) -> Range<$ty> {
                let range = (w(high as $unsigned) - w(low as $unsigned)).0;
                let unsigned_max: $unsigned = ::std::$unsigned::MAX;

                // this is the largest number that fits into $unsigned
                // that `range` divides evenly, so, if we've sampled
                // `n` uniformly from this region, then `n % range` is
                // uniform in [0, range)
                let zone = unsigned_max - unsigned_max % range;

                Range {
                    low: low,
                    range: range as $ty,
                    accept_zone: zone as $ty
                }
            }
            #[inline]
            fn sample_range<R: Rng>(r: &Range<$ty>, rng: &mut R) -> $ty {
                loop {
                    // rejection sample
                    let v = rng.gen::<$unsigned>();
                    // until we find something that fits into the
                    // region which r.range evenly divides (this will
                    // be uniformly distributed)
                    if v < r.accept_zone as $unsigned {
                        // and return it, with some adjustments
                        return (w(r.low) + w((v % r.range as $unsigned) as $ty)).0;
                    }
                }
            }
        }
    }
}

integer_impl! { i8, u8 }
integer_impl! { i16, u16 }
integer_impl! { i32, u32 }
integer_impl! { i64, u64 }
integer_impl! { isize, usize }
integer_impl! { u8, u8 }
integer_impl! { u16, u16 }
integer_impl! { u32, u32 }
integer_impl! { u64, u64 }
integer_impl! { usize, usize }

macro_rules! float_impl {
    ($ty:ty) => {
        impl SampleRange for $ty {
            fn construct_range(low: $ty, high: $ty) -> Range<$ty> {
                Range {
                    low: low,
                    range: high - low,
                    accept_zone: 0.0 // unused
                }
            }
            fn sample_range<R: Rng>(r: &Range<$ty>, rng: &mut R) -> $ty {
                r.low + r.range * rng.gen::<$ty>()
            }
        }
    }
}

float_impl! { f32 }
float_impl! { f64 }

#[cfg(test)]
mod tests {
    use distributions::{Sample, IndependentSample};
    use super::Range as Range;

    #[should_panic]
    #[cfg_attr(target_env = "msvc", ignore)]
    #[test]
    fn test_range_bad_limits_equal() {
        Range::new(10, 10);
    }
    #[should_panic]
    #[cfg_attr(target_env = "msvc", ignore)]
    #[test]
    fn test_range_bad_limits_flipped() {
        Range::new(10, 5);
    }

    #[test]
    fn test_integers() {
        let mut rng = ::test::rng();
        macro_rules! t {
            ($($ty:ident),*) => {{
                $(
                   let v: &[($ty, $ty)] = &[(0, 10),
                                            (10, 127),
                                            (::std::$ty::MIN, ::std::$ty::MAX)];
                   for &(low, high) in v.iter() {
                        let mut sampler: Range<$ty> = Range::new(low, high);
                        for _ in 0..1000 {
                            let v = sampler.sample(&mut rng);
                            assert!(low <= v && v < high);
                            let v = sampler.ind_sample(&mut rng);
                            assert!(low <= v && v < high);
                        }
                    }
                 )*
            }}
        }
        t!(i8, i16, i32, i64, isize,
           u8, u16, u32, u64, usize)
    }

    #[test]
    fn test_floats() {
        let mut rng = ::test::rng();
        macro_rules! t {
            ($($ty:ty),*) => {{
                $(
                   let v: &[($ty, $ty)] = &[(0.0, 100.0),
                                            (-1e35, -1e25),
                                            (1e-35, 1e-25),
                                            (-1e35, 1e35)];
                   for &(low, high) in v.iter() {
                        let mut sampler: Range<$ty> = Range::new(low, high);
                        for _ in 0..1000 {
                            let v = sampler.sample(&mut rng);
                            assert!(low <= v && v < high);
                            let v = sampler.ind_sample(&mut rng);
                            assert!(low <= v && v < high);
                        }
                    }
                 )*
            }}
        }

        t!(f32, f64)
    }

}