| // Copyright 2017 The Rust Project Developers. See the COPYRIGHT |
| // file at the top-level directory of this distribution and at |
| // https://rust-lang.org/COPYRIGHT. |
| // |
| // 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. |
| |
| //! Basic floating-point number distributions |
| |
| use core::mem; |
| use Rng; |
| use distributions::{Distribution, Standard}; |
| |
| /// A distribution to sample floating point numbers uniformly in the half-open |
| /// interval `(0, 1]`, i.e. including 1 but not 0. |
| /// |
| /// All values that can be generated are of the form `n * ε/2`. For `f32` |
| /// the 23 most significant random bits of a `u32` are used and for `f64` the |
| /// 53 most significant bits of a `u64` are used. The conversion uses the |
| /// multiplicative method. |
| /// |
| /// See also: [`Standard`] which samples from `[0, 1)`, [`Open01`] |
| /// which samples from `(0, 1)` and [`Uniform`] which samples from arbitrary |
| /// ranges. |
| /// |
| /// # Example |
| /// ``` |
| /// use rand::{thread_rng, Rng}; |
| /// use rand::distributions::OpenClosed01; |
| /// |
| /// let val: f32 = thread_rng().sample(OpenClosed01); |
| /// println!("f32 from (0, 1): {}", val); |
| /// ``` |
| /// |
| /// [`Standard`]: struct.Standard.html |
| /// [`Open01`]: struct.Open01.html |
| /// [`Uniform`]: uniform/struct.Uniform.html |
| #[derive(Clone, Copy, Debug)] |
| pub struct OpenClosed01; |
| |
| /// A distribution to sample floating point numbers uniformly in the open |
| /// interval `(0, 1)`, i.e. not including either endpoint. |
| /// |
| /// All values that can be generated are of the form `n * ε + ε/2`. For `f32` |
| /// the 22 most significant random bits of an `u32` are used, for `f64` 52 from |
| /// an `u64`. The conversion uses a transmute-based method. |
| /// |
| /// See also: [`Standard`] which samples from `[0, 1)`, [`OpenClosed01`] |
| /// which samples from `(0, 1]` and [`Uniform`] which samples from arbitrary |
| /// ranges. |
| /// |
| /// # Example |
| /// ``` |
| /// use rand::{thread_rng, Rng}; |
| /// use rand::distributions::Open01; |
| /// |
| /// let val: f32 = thread_rng().sample(Open01); |
| /// println!("f32 from (0, 1): {}", val); |
| /// ``` |
| /// |
| /// [`Standard`]: struct.Standard.html |
| /// [`OpenClosed01`]: struct.OpenClosed01.html |
| /// [`Uniform`]: uniform/struct.Uniform.html |
| #[derive(Clone, Copy, Debug)] |
| pub struct Open01; |
| |
| |
| pub(crate) trait IntoFloat { |
| type F; |
| |
| /// Helper method to combine the fraction and a contant exponent into a |
| /// float. |
| /// |
| /// Only the least significant bits of `self` may be set, 23 for `f32` and |
| /// 52 for `f64`. |
| /// The resulting value will fall in a range that depends on the exponent. |
| /// As an example the range with exponent 0 will be |
| /// [2<sup>0</sup>..2<sup>1</sup>), which is [1..2). |
| fn into_float_with_exponent(self, exponent: i32) -> Self::F; |
| } |
| |
| macro_rules! float_impls { |
| ($ty:ty, $uty:ty, $fraction_bits:expr, $exponent_bias:expr) => { |
| impl IntoFloat for $uty { |
| type F = $ty; |
| #[inline(always)] |
| fn into_float_with_exponent(self, exponent: i32) -> $ty { |
| // The exponent is encoded using an offset-binary representation |
| let exponent_bits = |
| (($exponent_bias + exponent) as $uty) << $fraction_bits; |
| unsafe { mem::transmute(self | exponent_bits) } |
| } |
| } |
| |
| impl Distribution<$ty> for Standard { |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty { |
| // Multiply-based method; 24/53 random bits; [0, 1) interval. |
| // We use the most significant bits because for simple RNGs |
| // those are usually more random. |
| let float_size = mem::size_of::<$ty>() * 8; |
| let precision = $fraction_bits + 1; |
| let scale = 1.0 / ((1 as $uty << precision) as $ty); |
| |
| let value: $uty = rng.gen(); |
| scale * (value >> (float_size - precision)) as $ty |
| } |
| } |
| |
| impl Distribution<$ty> for OpenClosed01 { |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty { |
| // Multiply-based method; 24/53 random bits; (0, 1] interval. |
| // We use the most significant bits because for simple RNGs |
| // those are usually more random. |
| let float_size = mem::size_of::<$ty>() * 8; |
| let precision = $fraction_bits + 1; |
| let scale = 1.0 / ((1 as $uty << precision) as $ty); |
| |
| let value: $uty = rng.gen(); |
| let value = value >> (float_size - precision); |
| // Add 1 to shift up; will not overflow because of right-shift: |
| scale * (value + 1) as $ty |
| } |
| } |
| |
| impl Distribution<$ty> for Open01 { |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty { |
| // Transmute-based method; 23/52 random bits; (0, 1) interval. |
| // We use the most significant bits because for simple RNGs |
| // those are usually more random. |
| const EPSILON: $ty = 1.0 / (1u64 << $fraction_bits) as $ty; |
| let float_size = mem::size_of::<$ty>() * 8; |
| |
| let value: $uty = rng.gen(); |
| let fraction = value >> (float_size - $fraction_bits); |
| fraction.into_float_with_exponent(0) - (1.0 - EPSILON / 2.0) |
| } |
| } |
| } |
| } |
| float_impls! { f32, u32, 23, 127 } |
| float_impls! { f64, u64, 52, 1023 } |
| |
| |
| #[cfg(test)] |
| mod tests { |
| use Rng; |
| use distributions::{Open01, OpenClosed01}; |
| use rngs::mock::StepRng; |
| |
| const EPSILON32: f32 = ::core::f32::EPSILON; |
| const EPSILON64: f64 = ::core::f64::EPSILON; |
| |
| #[test] |
| fn standard_fp_edge_cases() { |
| let mut zeros = StepRng::new(0, 0); |
| assert_eq!(zeros.gen::<f32>(), 0.0); |
| assert_eq!(zeros.gen::<f64>(), 0.0); |
| |
| let mut one32 = StepRng::new(1 << 8, 0); |
| assert_eq!(one32.gen::<f32>(), EPSILON32 / 2.0); |
| |
| let mut one64 = StepRng::new(1 << 11, 0); |
| assert_eq!(one64.gen::<f64>(), EPSILON64 / 2.0); |
| |
| let mut max = StepRng::new(!0, 0); |
| assert_eq!(max.gen::<f32>(), 1.0 - EPSILON32 / 2.0); |
| assert_eq!(max.gen::<f64>(), 1.0 - EPSILON64 / 2.0); |
| } |
| |
| #[test] |
| fn openclosed01_edge_cases() { |
| let mut zeros = StepRng::new(0, 0); |
| assert_eq!(zeros.sample::<f32, _>(OpenClosed01), 0.0 + EPSILON32 / 2.0); |
| assert_eq!(zeros.sample::<f64, _>(OpenClosed01), 0.0 + EPSILON64 / 2.0); |
| |
| let mut one32 = StepRng::new(1 << 8, 0); |
| assert_eq!(one32.sample::<f32, _>(OpenClosed01), EPSILON32); |
| |
| let mut one64 = StepRng::new(1 << 11, 0); |
| assert_eq!(one64.sample::<f64, _>(OpenClosed01), EPSILON64); |
| |
| let mut max = StepRng::new(!0, 0); |
| assert_eq!(max.sample::<f32, _>(OpenClosed01), 1.0); |
| assert_eq!(max.sample::<f64, _>(OpenClosed01), 1.0); |
| } |
| |
| #[test] |
| fn open01_edge_cases() { |
| let mut zeros = StepRng::new(0, 0); |
| assert_eq!(zeros.sample::<f32, _>(Open01), 0.0 + EPSILON32 / 2.0); |
| assert_eq!(zeros.sample::<f64, _>(Open01), 0.0 + EPSILON64 / 2.0); |
| |
| let mut one32 = StepRng::new(1 << 9, 0); |
| assert_eq!(one32.sample::<f32, _>(Open01), EPSILON32 / 2.0 * 3.0); |
| |
| let mut one64 = StepRng::new(1 << 12, 0); |
| assert_eq!(one64.sample::<f64, _>(Open01), EPSILON64 / 2.0 * 3.0); |
| |
| let mut max = StepRng::new(!0, 0); |
| assert_eq!(max.sample::<f32, _>(Open01), 1.0 - EPSILON32 / 2.0); |
| assert_eq!(max.sample::<f64, _>(Open01), 1.0 - EPSILON64 / 2.0); |
| } |
| } |