// Copyright 2018 Developers of the Rand project.

//

// 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 crate::distributions::utils::FloatSIMDUtils;

use crate::distributions::{Distribution, Standard};

use crate::Rng;

use core::mem;

#[cfg(feature = "serde1")]

use serde::{Serialize, Deserialize};

/// 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 24 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`]: crate::distributions::Standard

/// [`Open01`]: crate::distributions::Open01

/// [`Uniform`]: crate::distributions::uniform::Uniform

#[derive(Clone, Copy, Debug)]

#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]

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 23 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`]: crate::distributions::Standard

/// [`OpenClosed01`]: crate::distributions::OpenClosed01

/// [`Uniform`]: crate::distributions::uniform::Uniform

#[derive(Clone, Copy, Debug)]

#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]

pub struct Open01;

// This trait is needed by both this lib and rand_distr hence is a hidden export

#[doc(hidden)]

pub trait IntoFloat {

    type F;

    /// Helper method to combine the fraction and a constant 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:ident, $uty:ident, $f_scalar:ident, $u_scalar: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: $u_scalar =

                    (($exponent_bias + exponent) as $u_scalar) << $fraction_bits;

                $ty::from_bits(self | exponent_bits)

            }

Unexecuted instantiation: <u32 as rand::distributions::float::IntoFloat>::into_float_with_exponent

Unexecuted instantiation: <u64 as rand::distributions::float::IntoFloat>::into_float_with_exponent

        }

        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::<$f_scalar>() as u32 * 8;

                let precision = $fraction_bits + 1;

                let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);

                let value: $uty = rng.gen();

                let value = value >> (float_size - precision);

                scale * $ty::cast_from_int(value)

            }

Unexecuted instantiation: <rand::distributions::Standard as rand::distributions::distribution::Distribution<f32>>::sample::<_>

Unexecuted instantiation: <rand::distributions::Standard as rand::distributions::distribution::Distribution<f64>>::sample::<_>

        }

        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::<$f_scalar>() as u32 * 8;

                let precision = $fraction_bits + 1;

                let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);

                let value: $uty = rng.gen();

                let value = value >> (float_size - precision);

                // Add 1 to shift up; will not overflow because of right-shift:

                scale * $ty::cast_from_int(value + 1)

            }

Unexecuted instantiation: <rand::distributions::float::OpenClosed01 as rand::distributions::distribution::Distribution<f32>>::sample::<_>

Unexecuted instantiation: <rand::distributions::float::OpenClosed01 as rand::distributions::distribution::Distribution<f64>>::sample::<_>

        }

        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.

                use core::$f_scalar::EPSILON;

                let float_size = mem::size_of::<$f_scalar>() as u32 * 8;

                let value: $uty = rng.gen();

                let fraction = value >> (float_size - $fraction_bits);

                fraction.into_float_with_exponent(0) - (1.0 - EPSILON / 2.0)

            }

Unexecuted instantiation: <rand::distributions::float::Open01 as rand::distributions::distribution::Distribution<f32>>::sample::<_>

Unexecuted instantiation: <rand::distributions::float::Open01 as rand::distributions::distribution::Distribution<f64>>::sample::<_>

        }

    }

}

float_impls! { f32, u32, f32, u32, 23, 127 }

float_impls! { f64, u64, f64, u64, 52, 1023 }

#[cfg(test)]

mod tests {

    use super::*;

    use crate::rngs::mock::StepRng;

    const EPSILON32: f32 = ::core::f32::EPSILON;

    const EPSILON64: f64 = ::core::f64::EPSILON;

    macro_rules! test_f32 {

        ($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {

            #[test]

            fn $fnn() {

                // Standard

                let mut zeros = StepRng::new(0, 0);

                assert_eq!(zeros.gen::<$ty>(), $ZERO);

                let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);

                assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);

                let mut max = StepRng::new(!0, 0);

                assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);

                // OpenClosed01

                let mut zeros = StepRng::new(0, 0);

                assert_eq!(zeros.sample::<$ty, _>(OpenClosed01), 0.0 + $EPSILON / 2.0);

                let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);

                assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);

                let mut max = StepRng::new(!0, 0);

                assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);

                // Open01

                let mut zeros = StepRng::new(0, 0);

                assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);

                let mut one = StepRng::new(1 << 9 | 1 << (9 + 32), 0);

                assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);

                let mut max = StepRng::new(!0, 0);

                assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);

            }

        };

    }

    test_f32! { f32_edge_cases, f32, 0.0, EPSILON32 }

    macro_rules! test_f64 {

        ($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {

            #[test]

            fn $fnn() {

                // Standard

                let mut zeros = StepRng::new(0, 0);

                assert_eq!(zeros.gen::<$ty>(), $ZERO);

                let mut one = StepRng::new(1 << 11, 0);

                assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);

                let mut max = StepRng::new(!0, 0);

                assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);

                // OpenClosed01

                let mut zeros = StepRng::new(0, 0);

                assert_eq!(zeros.sample::<$ty, _>(OpenClosed01), 0.0 + $EPSILON / 2.0);

                let mut one = StepRng::new(1 << 11, 0);

                assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);

                let mut max = StepRng::new(!0, 0);

                assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);

                // Open01

                let mut zeros = StepRng::new(0, 0);

                assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);

                let mut one = StepRng::new(1 << 12, 0);

                assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);

                let mut max = StepRng::new(!0, 0);

                assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);

            }

        };

    }

    test_f64! { f64_edge_cases, f64, 0.0, EPSILON64 }

    #[test]

    fn value_stability() {

        fn test_samples<T: Copy + core::fmt::Debug + PartialEq, D: Distribution<T>>(

            distr: &D, zero: T, expected: &[T],

        ) {

            let mut rng = crate::test::rng(0x6f44f5646c2a7334);

            let mut buf = [zero; 3];

            for x in &mut buf {

                *x = rng.sample(&distr);

            }

            assert_eq!(&buf, expected);

        }

        test_samples(&Standard, 0f32, &[0.0035963655, 0.7346052, 0.09778172]);

        test_samples(&Standard, 0f64, &[

            0.7346051961657583,

            0.20298547462974248,

            0.8166436635290655,

        ]);

        test_samples(&OpenClosed01, 0f32, &[0.003596425, 0.73460525, 0.09778178]);

        test_samples(&OpenClosed01, 0f64, &[

            0.7346051961657584,

            0.2029854746297426,

            0.8166436635290656,

        ]);

        test_samples(&Open01, 0f32, &[0.0035963655, 0.73460525, 0.09778172]);

        test_samples(&Open01, 0f64, &[

            0.7346051961657584,

            0.20298547462974248,

            0.8166436635290656,

        ]);

    }

}