rand_distr/
utils.rs

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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.

//! Math helper functions

use crate::ziggurat_tables;
#[allow(unused_imports)]
use num_traits::Float; // Used for `no_std` to get `f64::abs()` working before `rustc 1.84`
use rand::distr::hidden_export::IntoFloat;
use rand::Rng;

/// Sample a random number using the Ziggurat method (specifically the
/// ZIGNOR variant from Doornik 2005). Most of the arguments are
/// directly from the paper:
///
/// * `rng`: source of randomness
/// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
/// * `X`: the $x_i$ abscissae.
/// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
/// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
/// * `pdf`: the probability density function
/// * `zero_case`: manual sampling from the tail when we chose the
///    bottom box (i.e. i == 0)
#[inline(always)] // Forced inlining improves the perf by 25-50%
pub(crate) fn ziggurat<R: Rng + ?Sized, P, Z>(
    rng: &mut R,
    symmetric: bool,
    x_tab: ziggurat_tables::ZigTable,
    f_tab: ziggurat_tables::ZigTable,
    mut pdf: P,
    mut zero_case: Z,
) -> f64
where
    P: FnMut(f64) -> f64,
    Z: FnMut(&mut R, f64) -> f64,
{
    loop {
        // As an optimisation we re-implement the conversion to a f64.
        // From the remaining 12 most significant bits we use 8 to construct `i`.
        // This saves us generating a whole extra random number, while the added
        // precision of using 64 bits for f64 does not buy us much.
        let bits = rng.next_u64();
        let i = bits as usize & 0xff;

        let u = if symmetric {
            // Convert to a value in the range [2,4) and subtract to get [-1,1)
            // We can't convert to an open range directly, that would require
            // subtracting `3.0 - EPSILON`, which is not representable.
            // It is possible with an extra step, but an open range does not
            // seem necessary for the ziggurat algorithm anyway.
            (bits >> 12).into_float_with_exponent(1) - 3.0
        } else {
            // Convert to a value in the range [1,2) and subtract to get (0,1)
            (bits >> 12).into_float_with_exponent(0) - (1.0 - f64::EPSILON / 2.0)
        };
        let x = u * x_tab[i];

        let test_x = if symmetric { x.abs() } else { x };

        // algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
        if test_x < x_tab[i + 1] {
            return x;
        }
        if i == 0 {
            return zero_case(rng, u);
        }
        // algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
        if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.random::<f64>() < pdf(x) {
            return x;
        }
    }
}