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

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    // 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 = "simd_support")] use packed_simd::*;

    #[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)
                }
            }

            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)
                }
            }

            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)
                }
            }

            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)
                }
            }
        }
    }

    float_impls! { f32, u32, f32, u32, 23, 127 }
    float_impls! { f64, u64, f64, u64, 52, 1023 }

    #[cfg(feature = "simd_support")]
    float_impls! { f32x2, u32x2, f32, u32, 23, 127 }
    #[cfg(feature = "simd_support")]
    float_impls! { f32x4, u32x4, f32, u32, 23, 127 }
    #[cfg(feature = "simd_support")]
    float_impls! { f32x8, u32x8, f32, u32, 23, 127 }
    #[cfg(feature = "simd_support")]
    float_impls! { f32x16, u32x16, f32, u32, 23, 127 }

    #[cfg(feature = "simd_support")]
    float_impls! { f64x2, u64x2, f64, u64, 52, 1023 }
    #[cfg(feature = "simd_support")]
    float_impls! { f64x4, u64x4, f64, u64, 52, 1023 }
    #[cfg(feature = "simd_support")]
    float_impls! { f64x8, u64x8, 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 }
        #[cfg(feature = "simd_support")]
        test_f32! { f32x2_edge_cases, f32x2, f32x2::splat(0.0), f32x2::splat(EPSILON32) }
        #[cfg(feature = "simd_support")]
        test_f32! { f32x4_edge_cases, f32x4, f32x4::splat(0.0), f32x4::splat(EPSILON32) }
        #[cfg(feature = "simd_support")]
        test_f32! { f32x8_edge_cases, f32x8, f32x8::splat(0.0), f32x8::splat(EPSILON32) }
        #[cfg(feature = "simd_support")]
        test_f32! { f32x16_edge_cases, f32x16, f32x16::splat(0.0), f32x16::splat(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 }
        #[cfg(feature = "simd_support")]
        test_f64! { f64x2_edge_cases, f64x2, f64x2::splat(0.0), f64x2::splat(EPSILON64) }
        #[cfg(feature = "simd_support")]
        test_f64! { f64x4_edge_cases, f64x4, f64x4::splat(0.0), f64x4::splat(EPSILON64) }
        #[cfg(feature = "simd_support")]
        test_f64! { f64x8_edge_cases, f64x8, f64x8::splat(0.0), f64x8::splat(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,
            ]);

            #[cfg(feature = "simd_support")]
            {
                // We only test a sub-set of types here. Values are identical to
                // non-SIMD types; we assume this pattern continues across all
                // SIMD types.

                test_samples(&Standard, f32x2::new(0.0, 0.0), &[
                    f32x2::new(0.0035963655, 0.7346052),
                    f32x2::new(0.09778172, 0.20298547),
                    f32x2::new(0.34296435, 0.81664366),
                ]);

                test_samples(&Standard, f64x2::new(0.0, 0.0), &[
                    f64x2::new(0.7346051961657583, 0.20298547462974248),
                    f64x2::new(0.8166436635290655, 0.7423708925400552),
                    f64x2::new(0.16387782224016323, 0.9087068770169618),
                ]);
            }
        }
    }