malachite_float/float/exhaustive/

mod.rs

// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.

use crate::Float;
use crate::InnerFloat::Finite;
use alloc::vec::IntoIter;
use core::iter::{Chain, Once, once};
use core::mem::swap;
use malachite_base::iterators::bit_distributor::BitDistributorOutputType;
use malachite_base::num::arithmetic::traits::{NegModPowerOf2, PowerOf2};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::basic::traits::{Infinity, NaN, NegativeInfinity, NegativeZero, Zero};
use malachite_base::num::exhaustive::{
    ExhaustiveSignedRange, PrimitiveIntIncreasingRange, exhaustive_signed_inclusive_range,
    primitive_int_increasing_inclusive_range,
};
use malachite_base::num::iterators::{BitDistributorSequence, bit_distributor_sequence};
use malachite_base::num::logic::traits::{LowMask, NotAssign};
use malachite_base::tuples::exhaustive::{
    ExhaustiveDependentPairs, ExhaustiveDependentPairsYsGenerator, LexDependentPairs,
    exhaustive_dependent_pairs, lex_dependent_pairs,
};
use malachite_nz::natural::Natural;
use malachite_nz::natural::exhaustive::{
    ExhaustiveNaturalRange, exhaustive_natural_inclusive_range,
};
use malachite_nz::platform::Limb;

/// Generates all finite positive [`Float`]s with a specified `sci_exponent` (one less than the raw
/// exponent) and precision.
///
/// This `struct` is created by [`exhaustive_positive_floats_with_sci_exponent_and_precision`]; see
/// its documentation for more.
#[derive(Clone, Debug)]
pub struct ExhaustivePositiveFloatsWithSciExponentAndPrecision {
    exponent: i32,
    precision: u64,
    shift: u64,
    significands: ExhaustiveNaturalRange,
}

impl Iterator for ExhaustivePositiveFloatsWithSciExponentAndPrecision {
    type Item = Float;

    #[inline]
    fn next(&mut self) -> Option<Float> {
        self.significands.next().map(|s| {
            Float(Finite {
                sign: true,
                exponent: self.exponent,
                precision: self.precision,
                significand: s << self.shift,
            })
        })
    }
}

/// Generates all finite positive [`Float`]s with a specified `sci_exponent` (one less than the raw
/// exponent) and precision.
///
/// Positive and negative zero are both excluded.
///
/// A finite positive [`Float`] may be uniquely expressed as $x = m_s2^e_s$, where $1 \leq m_s < 2$
/// and $e_s$ is an integer; then $e_s$ is the sci-exponent.
///
/// The output length is $2^{p-1}$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `prec`.
///
/// # Panics
/// Panics if the precision is zero.
///
/// # Examples
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::*;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_positive_floats_with_sci_exponent_and_precision(0, 4)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &["1.00#4", "1.12#4", "1.25#4", "1.38#4", "1.50#4", "1.62#4", "1.75#4", "1.88#4"]
/// );
///
/// assert_eq!(
///     exhaustive_positive_floats_with_sci_exponent_and_precision(2, 5)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "4.00#5", "4.25#5", "4.50#5", "4.75#5", "5.00#5", "5.25#5", "5.50#5", "5.75#5",
///         "6.00#5", "6.25#5", "6.50#5", "6.75#5", "7.00#5", "7.25#5", "7.50#5", "7.75#5"
///     ]
/// );
/// ```
pub fn exhaustive_positive_floats_with_sci_exponent_and_precision(
    sci_exponent: i32,
    prec: u64,
) -> ExhaustivePositiveFloatsWithSciExponentAndPrecision {
    assert!(sci_exponent < Float::MAX_EXPONENT);
    assert!(sci_exponent >= Float::MIN_EXPONENT_MINUS_1);
    assert_ne!(prec, 0);
    ExhaustivePositiveFloatsWithSciExponentAndPrecision {
        exponent: sci_exponent + 1,
        precision: prec,
        shift: prec.neg_mod_power_of_2(Limb::LOG_WIDTH),
        significands: exhaustive_natural_inclusive_range(
            Natural::power_of_2(prec - 1),
            Natural::low_mask(prec),
        ),
    }
}

#[derive(Clone, Debug)]
struct FloatsWithSciExponentAndPrecisionGenerator {
    sci_exponent: i32,
}

impl
    ExhaustiveDependentPairsYsGenerator<
        u64,
        Float,
        ExhaustivePositiveFloatsWithSciExponentAndPrecision,
    > for FloatsWithSciExponentAndPrecisionGenerator
{
    #[inline]
    fn get_ys(&self, &prec: &u64) -> ExhaustivePositiveFloatsWithSciExponentAndPrecision {
        exhaustive_positive_floats_with_sci_exponent_and_precision(self.sci_exponent, prec)
    }
}

#[inline]
fn exhaustive_positive_floats_with_sci_exponent_helper(
    sci_exponent: i32,
) -> LexDependentPairs<
    u64,
    Float,
    FloatsWithSciExponentAndPrecisionGenerator,
    PrimitiveIntIncreasingRange<u64>,
    ExhaustivePositiveFloatsWithSciExponentAndPrecision,
> {
    lex_dependent_pairs(
        primitive_int_increasing_inclusive_range(1, u64::MAX),
        FloatsWithSciExponentAndPrecisionGenerator { sci_exponent },
    )
}

/// Generates all finite positive [`Float`]s with a specified `sci_exponent` (one less than the raw
/// exponent).
///
/// This `struct` is created by [`exhaustive_positive_floats_with_sci_exponent`]; see its
/// documentation for more.
#[derive(Clone, Debug)]
pub struct ExhaustivePositiveFloatsWithSciExponent(
    LexDependentPairs<
        u64,
        Float,
        FloatsWithSciExponentAndPrecisionGenerator,
        PrimitiveIntIncreasingRange<u64>,
        ExhaustivePositiveFloatsWithSciExponentAndPrecision,
    >,
);

impl Iterator for ExhaustivePositiveFloatsWithSciExponent {
    type Item = Float;

    #[inline]
    fn next(&mut self) -> Option<Float> {
        self.0.next().map(|p| p.1)
    }
}

/// Generates all finite positive [`Float`]s with a specified `sci_exponent` (one less than the raw
/// exponent).
///
/// Positive and negative zero are both excluded.
///
/// A finite positive [`Float`] may be uniquely expressed as $x = m_s2^e_s$, where $1 \leq m_s < 2$
/// and $e_s$ is an integer; then $e_s$ is the sci-exponent.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// # Panics
/// Panics if the precision is zero.
///
/// # Examples
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_positive_floats_with_sci_exponent;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_positive_floats_with_sci_exponent(0)
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "1.0#1", "1.0#2", "1.5#2", "1.0#3", "1.2#3", "1.5#3", "1.8#3", "1.00#4", "1.12#4",
///         "1.25#4", "1.38#4", "1.50#4", "1.62#4", "1.75#4", "1.88#4", "1.00#5", "1.06#5",
///         "1.12#5", "1.19#5", "1.25#5"
///     ]
/// );
///
/// assert_eq!(
///     exhaustive_positive_floats_with_sci_exponent(2)
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "4.0#1", "4.0#2", "6.0#2", "4.0#3", "5.0#3", "6.0#3", "7.0#3", "4.00#4", "4.50#4",
///         "5.00#4", "5.50#4", "6.00#4", "6.50#4", "7.00#4", "7.50#4", "4.00#5", "4.25#5",
///         "4.50#5", "4.75#5", "5.00#5"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_positive_floats_with_sci_exponent(
    sci_exponent: i32,
) -> ExhaustivePositiveFloatsWithSciExponent {
    assert!(sci_exponent < Float::MAX_EXPONENT);
    assert!(sci_exponent >= Float::MIN_EXPONENT_MINUS_1);
    ExhaustivePositiveFloatsWithSciExponent(exhaustive_positive_floats_with_sci_exponent_helper(
        sci_exponent,
    ))
}

#[derive(Clone, Debug)]
struct FloatsWithPrecisionAndSciExponentGenerator {
    precision: u64,
}

impl
    ExhaustiveDependentPairsYsGenerator<
        i32,
        Float,
        ExhaustivePositiveFloatsWithSciExponentAndPrecision,
    > for FloatsWithPrecisionAndSciExponentGenerator
{
    #[inline]
    fn get_ys(&self, &exp: &i32) -> ExhaustivePositiveFloatsWithSciExponentAndPrecision {
        exhaustive_positive_floats_with_sci_exponent_and_precision(exp, self.precision)
    }
}

#[inline]
fn exhaustive_floats_with_precision_helper(
    prec: u64,
) -> ExhaustiveDependentPairs<
    i32,
    Float,
    BitDistributorSequence,
    FloatsWithPrecisionAndSciExponentGenerator,
    ExhaustiveSignedRange<i32>,
    ExhaustivePositiveFloatsWithSciExponentAndPrecision,
> {
    exhaustive_dependent_pairs(
        bit_distributor_sequence(
            BitDistributorOutputType::normal(1),
            BitDistributorOutputType::normal(1),
        ),
        exhaustive_signed_inclusive_range(Float::MIN_EXPONENT, Float::MAX_EXPONENT),
        FloatsWithPrecisionAndSciExponentGenerator { precision: prec },
    )
}

/// Generates all finite positive [`Float`]s with a specified precision.
///
/// This `struct` is created by [`exhaustive_positive_floats_with_precision`]; see its documentation
/// for more.
#[derive(Clone, Debug)]
pub struct ExhaustivePositiveFloatsWithPrecision(
    ExhaustiveDependentPairs<
        i32,
        Float,
        BitDistributorSequence,
        FloatsWithPrecisionAndSciExponentGenerator,
        ExhaustiveSignedRange<i32>,
        ExhaustivePositiveFloatsWithSciExponentAndPrecision,
    >,
);

impl Iterator for ExhaustivePositiveFloatsWithPrecision {
    type Item = Float;

    #[inline]
    fn next(&mut self) -> Option<Float> {
        self.0.next().map(|p| p.1)
    }
}

/// Generates all finite positive [`Float`]s with a specified `precision`.
///
/// Positive and negative zero are both excluded.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// # Panics
/// Panics if the precision is zero.
///
/// # Examples
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_positive_floats_with_precision;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_positive_floats_with_precision(1)
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "1.0#1", "2.0#1", "0.50#1", "4.0#1", "0.25#1", "8.0#1", "0.12#1", "16.0#1", "0.062#1",
///         "32.0#1", "0.031#1", "64.0#1", "0.016#1", "1.3e2#1", "0.0078#1", "2.6e2#1", "0.0039#1",
///         "5.1e2#1", "0.0020#1", "1.0e3#1"
///     ]
/// );
///
/// assert_eq!(
///     exhaustive_positive_floats_with_precision(10)
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "1.0000#10",
///         "2.0000#10",
///         "1.0020#10",
///         "2.0039#10",
///         "0.50000#10",
///         "4.0000#10",
///         "0.50098#10",
///         "4.0078#10",
///         "1.0039#10",
///         "2.0078#10",
///         "1.0059#10",
///         "2.0117#10",
///         "0.50195#10",
///         "4.0156#10",
///         "0.50293#10",
///         "4.0234#10",
///         "0.25000#10",
///         "8.0000#10",
///         "0.25049#10",
///         "8.0156#10"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_positive_floats_with_precision(
    prec: u64,
) -> ExhaustivePositiveFloatsWithPrecision {
    assert_ne!(prec, 0);
    ExhaustivePositiveFloatsWithPrecision(exhaustive_floats_with_precision_helper(prec))
}

/// Generates all [`Float`]s with a specified precision. (Since they have a precision, they are
/// finite and nonzero.)
///
/// This `struct` is created by [`exhaustive_floats_with_precision`]; see its documentation for
/// more.
#[derive(Clone, Debug)]
pub struct ExhaustiveFloatsWithPrecision {
    toggle: bool,
    xs: ExhaustivePositiveFloatsWithPrecision,
    x: Float,
}

impl Iterator for ExhaustiveFloatsWithPrecision {
    type Item = Float;

    #[inline]
    fn next(&mut self) -> Option<Float> {
        self.toggle.not_assign();
        Some(if self.toggle {
            self.x = self.xs.next().unwrap();
            self.x.clone()
        } else {
            let mut out = Float::NAN;
            swap(&mut out, &mut self.x);
            -out
        })
    }
}

/// Generates all [`Float`]s with a specified precision. (Since they have a precision, they are
/// finite and nonzero.)
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// # Panics
/// Panics if the precision is zero.
///
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_floats_with_precision;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_floats_with_precision(1)
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "1.0#1", "-1.0#1", "2.0#1", "-2.0#1", "0.50#1", "-0.50#1", "4.0#1", "-4.0#1", "0.25#1",
///         "-0.25#1", "8.0#1", "-8.0#1", "0.12#1", "-0.12#1", "16.0#1", "-16.0#1", "0.062#1",
///         "-0.062#1", "32.0#1", "-32.0#1"
///     ]
/// );
///
/// assert_eq!(
///     exhaustive_floats_with_precision(10)
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "1.0000#10",
///         "-1.0000#10",
///         "2.0000#10",
///         "-2.0000#10",
///         "1.0020#10",
///         "-1.0020#10",
///         "2.0039#10",
///         "-2.0039#10",
///         "0.50000#10",
///         "-0.50000#10",
///         "4.0000#10",
///         "-4.0000#10",
///         "0.50098#10",
///         "-0.50098#10",
///         "4.0078#10",
///         "-4.0078#10",
///         "1.0039#10",
///         "-1.0039#10",
///         "2.0078#10",
///         "-2.0078#10"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_floats_with_precision(prec: u64) -> ExhaustiveFloatsWithPrecision {
    ExhaustiveFloatsWithPrecision {
        toggle: false,
        xs: exhaustive_positive_floats_with_precision(prec),
        x: Float::NAN,
    }
}

#[derive(Clone, Debug)]
pub(crate) struct ExhaustivePositiveFiniteFloatsGenerator;

impl ExhaustiveDependentPairsYsGenerator<i32, Float, ExhaustivePositiveFloatsWithSciExponent>
    for ExhaustivePositiveFiniteFloatsGenerator
{
    #[inline]
    fn get_ys(&self, &sci_exponent: &i32) -> ExhaustivePositiveFloatsWithSciExponent {
        exhaustive_positive_floats_with_sci_exponent(sci_exponent)
    }
}

#[inline]
fn exhaustive_positive_finite_floats_helper() -> ExhaustiveDependentPairs<
    i32,
    Float,
    BitDistributorSequence,
    ExhaustivePositiveFiniteFloatsGenerator,
    ExhaustiveSignedRange<i32>,
    ExhaustivePositiveFloatsWithSciExponent,
> {
    exhaustive_dependent_pairs(
        bit_distributor_sequence(
            BitDistributorOutputType::normal(1),
            BitDistributorOutputType::normal(1),
        ),
        exhaustive_signed_inclusive_range(Float::MIN_EXPONENT, Float::MAX_EXPONENT),
        ExhaustivePositiveFiniteFloatsGenerator,
    )
}

/// Generates all positive finite [`Float`]s.
///
/// This `struct` is created by [`exhaustive_positive_finite_floats`]; see its documentation for
/// more.
#[derive(Clone, Debug)]
pub struct ExhaustivePositiveFiniteFloats(
    ExhaustiveDependentPairs<
        i32,
        Float,
        BitDistributorSequence,
        ExhaustivePositiveFiniteFloatsGenerator,
        ExhaustiveSignedRange<i32>,
        ExhaustivePositiveFloatsWithSciExponent,
    >,
);

impl Iterator for ExhaustivePositiveFiniteFloats {
    type Item = Float;

    #[inline]
    fn next(&mut self) -> Option<Float> {
        self.0.next().map(|p| p.1)
    }
}

/// Generates all positive finite [`Float`]s.
///
/// Positive and negative zero are both excluded.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_positive_finite_floats;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_positive_finite_floats()
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "1.0#1", "2.0#1", "1.0#2", "2.0#2", "0.50#1", "4.0#1", "0.50#2", "4.0#2", "1.5#2",
///         "3.0#2", "1.0#3", "2.0#3", "0.75#2", "6.0#2", "0.50#3", "4.0#3", "0.25#1", "8.0#1",
///         "0.25#2", "8.0#2"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_positive_finite_floats() -> ExhaustivePositiveFiniteFloats {
    ExhaustivePositiveFiniteFloats(exhaustive_positive_finite_floats_helper())
}

/// Generates all negative finite [`Float`]s.
///
/// This `struct` is created by [`exhaustive_negative_finite_floats`]; see its documentation for
/// more.
#[derive(Clone, Debug)]
pub struct ExhaustiveNegativeFiniteFloats(ExhaustivePositiveFiniteFloats);

impl Iterator for ExhaustiveNegativeFiniteFloats {
    type Item = Float;

    #[inline]
    fn next(&mut self) -> Option<Float> {
        self.0.next().map(|f| -f)
    }
}

/// Generates all negative finite [`Float`]s.
///
/// Positive and negative zero are both excluded.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_negative_finite_floats;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_negative_finite_floats()
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "-1.0#1", "-2.0#1", "-1.0#2", "-2.0#2", "-0.50#1", "-4.0#1", "-0.50#2", "-4.0#2",
///         "-1.5#2", "-3.0#2", "-1.0#3", "-2.0#3", "-0.75#2", "-6.0#2", "-0.50#3", "-4.0#3",
///         "-0.25#1", "-8.0#1", "-0.25#2", "-8.0#2"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_negative_finite_floats() -> ExhaustiveNegativeFiniteFloats {
    ExhaustiveNegativeFiniteFloats(exhaustive_positive_finite_floats())
}

/// Generates all nonzero finite [`Float`]s.
///
/// This `struct` is created by [`exhaustive_nonzero_finite_floats`]; see its documentation for
/// more.
#[derive(Clone, Debug)]
pub struct ExhaustiveNonzeroFiniteFloats {
    toggle: bool,
    xs: ExhaustivePositiveFiniteFloats,
    x: Float,
}

impl Iterator for ExhaustiveNonzeroFiniteFloats {
    type Item = Float;

    #[inline]
    fn next(&mut self) -> Option<Float> {
        self.toggle.not_assign();
        Some(if self.toggle {
            self.x = self.xs.next().unwrap();
            self.x.clone()
        } else {
            let mut out = Float::NAN;
            swap(&mut out, &mut self.x);
            -out
        })
    }
}

/// Generates all nonzero finite [`Float`]s.
///
/// Positive and negative zero are both excluded.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_nonzero_finite_floats;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_nonzero_finite_floats()
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "1.0#1", "-1.0#1", "2.0#1", "-2.0#1", "1.0#2", "-1.0#2", "2.0#2", "-2.0#2", "0.50#1",
///         "-0.50#1", "4.0#1", "-4.0#1", "0.50#2", "-0.50#2", "4.0#2", "-4.0#2", "1.5#2",
///         "-1.5#2", "3.0#2", "-3.0#2"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_nonzero_finite_floats() -> ExhaustiveNonzeroFiniteFloats {
    ExhaustiveNonzeroFiniteFloats {
        toggle: false,
        xs: exhaustive_positive_finite_floats(),
        x: Float::NAN,
    }
}

type ExhaustiveNonNegativeFiniteFloats = Chain<Once<Float>, ExhaustivePositiveFiniteFloats>;

/// Generates all non-negative finite [`Float`]s.
///
/// Positive zero is included, but negative zero is not.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_non_negative_finite_floats;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_non_negative_finite_floats()
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "0.0", "1.0#1", "2.0#1", "1.0#2", "2.0#2", "0.50#1", "4.0#1", "0.50#2", "4.0#2",
///         "1.5#2", "3.0#2", "1.0#3", "2.0#3", "0.75#2", "6.0#2", "0.50#3", "4.0#3", "0.25#1",
///         "8.0#1", "0.25#2"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_non_negative_finite_floats() -> ExhaustiveNonNegativeFiniteFloats {
    once(Float::ZERO).chain(exhaustive_positive_finite_floats())
}

type ExhaustiveNonPositiveFiniteFloats = Chain<Once<Float>, ExhaustiveNegativeFiniteFloats>;

/// Generates all non-positive finite [`Float`]s.
///
/// Negative zero is included, but positive zero is not.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_non_positive_finite_floats;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_non_positive_finite_floats()
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "-0.0", "-1.0#1", "-2.0#1", "-1.0#2", "-2.0#2", "-0.50#1", "-4.0#1", "-0.50#2",
///         "-4.0#2", "-1.5#2", "-3.0#2", "-1.0#3", "-2.0#3", "-0.75#2", "-6.0#2", "-0.50#3",
///         "-4.0#3", "-0.25#1", "-8.0#1", "-0.25#2"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_non_positive_finite_floats() -> ExhaustiveNonPositiveFiniteFloats {
    once(Float::NEGATIVE_ZERO).chain(exhaustive_negative_finite_floats())
}

type ExhaustiveFloats = Chain<IntoIter<Float>, ExhaustiveNonzeroFiniteFloats>;

/// Generates all finite [`Float`]s.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_finite_floats;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_finite_floats()
///         .take(20)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "0.0", "-0.0", "1.0#1", "-1.0#1", "2.0#1", "-2.0#1", "1.0#2", "-1.0#2", "2.0#2",
///         "-2.0#2", "0.50#1", "-0.50#1", "4.0#1", "-4.0#1", "0.50#2", "-0.50#2", "4.0#2",
///         "-4.0#2", "1.5#2", "-1.5#2"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_finite_floats() -> ExhaustiveFloats {
    alloc::vec![Float::ZERO, Float::NEGATIVE_ZERO]
        .into_iter()
        .chain(exhaustive_nonzero_finite_floats())
}

/// Generates all [`Float`]s.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(\log i)$
///
/// $M(i) = O(\log i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// ```
/// use itertools::Itertools;
/// use malachite_float::float::exhaustive::exhaustive_floats;
/// use malachite_float::ComparableFloat;
///
/// // The number after the '#' is the precision.
/// assert_eq!(
///     exhaustive_floats()
///         .take(50)
///         .map(|f| ComparableFloat(f).to_string())
///         .collect_vec()
///         .as_slice(),
///     &[
///         "NaN",
///         "Infinity",
///         "-Infinity",
///         "0.0",
///         "-0.0",
///         "1.0#1",
///         "-1.0#1",
///         "2.0#1",
///         "-2.0#1",
///         "1.0#2",
///         "-1.0#2",
///         "2.0#2",
///         "-2.0#2",
///         "0.50#1",
///         "-0.50#1",
///         "4.0#1",
///         "-4.0#1",
///         "0.50#2",
///         "-0.50#2",
///         "4.0#2",
///         "-4.0#2",
///         "1.5#2",
///         "-1.5#2",
///         "3.0#2",
///         "-3.0#2",
///         "1.0#3",
///         "-1.0#3",
///         "2.0#3",
///         "-2.0#3",
///         "0.75#2",
///         "-0.75#2",
///         "6.0#2",
///         "-6.0#2",
///         "0.50#3",
///         "-0.50#3",
///         "4.0#3",
///         "-4.0#3",
///         "0.25#1",
///         "-0.25#1",
///         "8.0#1",
///         "-8.0#1",
///         "0.25#2",
///         "-0.25#2",
///         "8.0#2",
///         "-8.0#2",
///         "0.12#1",
///         "-0.12#1",
///         "16.0#1",
///         "-16.0#1",
///         "0.12#2"
///     ]
/// );
/// ```
#[inline]
pub fn exhaustive_floats() -> ExhaustiveFloats {
    alloc::vec![
        Float::NAN,
        Float::INFINITY,
        Float::NEGATIVE_INFINITY,
        Float::ZERO,
        Float::NEGATIVE_ZERO
    ]
    .into_iter()
    .chain(exhaustive_nonzero_finite_floats())
}