malachite-float 0.9.2

// 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 core::cmp::Ordering::{self, *};
use malachite_base::num::arithmetic::traits::{LogBase, LogBaseAssign};
use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::basic::traits::{Infinity, NaN, NegativeInfinity, One, Zero};
use malachite_base::num::conversion::traits::{ExactFrom, RoundingFrom};
use malachite_base::num::float::NiceFloat;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_base::rounding_modes::RoundingMode::{self, *};
use malachite_base::rounding_modes::exhaustive::exhaustive_rounding_modes;
use malachite_base::test_util::generators::unsigned_rounding_mode_pair_gen_var_3;
use malachite_float::arithmetic::log_base::primitive_float_log_base;
use malachite_float::arithmetic::log_base_rational_base::primitive_float_log_base_rational_base;
use malachite_float::test_util::arithmetic::log_base_rational_base::{
    rug_log_base_rational_base, rug_log_base_rational_base_prec,
    rug_log_base_rational_base_prec_round, rug_log_base_rational_base_round,
};
use malachite_float::test_util::common::rug_round_try_from_rounding_mode;
use malachite_float::test_util::generators::{
    float_rational_rounding_mode_triple_gen_var_12, float_rational_rounding_mode_triple_gen_var_13,
    float_rational_unsigned_rounding_mode_quadruple_gen_var_11,
    float_rational_unsigned_rounding_mode_quadruple_gen_var_12,
};
use malachite_float::{ComparableFloat, ComparableFloatRef, Float};
use malachite_q::Rational;
use std::panic::catch_unwind;

// Cross-checks the by-value/by-reference/assigning variants, precision, and (unless `extreme`) the
// rug oracle. The oracle is skipped for extreme inputs, whose ln(x)/ln(base) bracketing at large
// working precision (driven by an extreme `x` or a large `base`) is slow. Returns the computed
// `(Float, Ordering)`.
fn check(
    x: &Float,
    base: &Rational,
    prec: u64,
    rm: RoundingMode,
    extreme: bool,
) -> (Float, Ordering) {
    let (log, o) = x.clone().log_base_rational_base_prec_round(base, prec, rm);
    assert!(log.is_valid());

    let (log_alt, o_alt) = x.log_base_rational_base_prec_round_ref(base, prec, rm);
    assert!(log_alt.is_valid());
    assert_eq!(ComparableFloatRef(&log_alt), ComparableFloatRef(&log));
    assert_eq!(o_alt, o);

    let mut x_alt = x.clone();
    let o_alt = x_alt.log_base_rational_base_prec_round_assign(base, prec, rm);
    assert!(x_alt.is_valid());
    assert_eq!(ComparableFloatRef(&x_alt), ComparableFloatRef(&log));
    assert_eq!(o_alt, o);

    if log.is_normal() {
        assert_eq!(log.get_prec(), Some(prec));
    }

    // Also skip the oracle for large bases: its ln(x)/ln(base) bracketing uses a working precision
    // that grows with the base's bit length, so it is slow for big rationals (the common small-base
    // case keeps full oracle coverage).
    if !extreme
        && base.significant_bits() <= 128
        && let Ok(rug_rm) = rug_round_try_from_rounding_mode(rm)
    {
        let (rug_log, rug_o) =
            rug_log_base_rational_base_prec_round(&rug::Float::exact_from(x), base, prec, rug_rm);
        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_log)),
            ComparableFloatRef(&log),
        );
        assert_eq!(rug_o, o);
    }
    (log, o)
}

#[test]
fn test_log_base_rational_base_prec_round() {
    let test = |n: i64, d: u64, bn: u64, bd: u64, prec: u64, rm: RoundingMode, out: &str, o_out| {
        let x = Float::exact_from(Rational::from_signeds(n, i64::exact_from(d)));
        let base = Rational::from_unsigneds(bn, bd);
        let (log, o) = check(&x, &base, prec, rm, false);
        assert_eq!(log.to_string(), out);
        assert_eq!(o, o_out);
    };
    // Exact, integer base.
    test(9, 1, 3, 1, 10, Exact, "2.0", Equal); // log_3(9) = 2
    test(8, 1, 2, 1, 10, Exact, "3.0", Equal); // log_2(8) = 3
    test(27, 1, 3, 1, 10, Exact, "3.0", Equal); // log_3(27) = 3
    // Exact, rational base.
    test(8, 1, 4, 1, 10, Exact, "1.5", Equal); // log_4(8) = 3/2
    test(2, 1, 4, 1, 10, Exact, "0.5", Equal); // log_4(2) = 1/2
    test(9, 4, 3, 2, 10, Exact, "2.0", Equal); // log_{3/2}(9/4) = 2
    test(3, 2, 9, 4, 10, Exact, "0.5", Equal); // log_{9/4}(3/2) = 1/2
    // x < 1 (negative result), base a power of 2.
    test(1, 4, 4, 1, 10, Exact, "-1.0", Equal); // log_4(1/4) = -1
    test(1, 4, 2, 1, 10, Exact, "-2.0", Equal); // log_2(1/4) = -2
    test(1, 8, 2, 1, 10, Exact, "-3.0", Equal); // log_2(1/8) = -3
    // Irrational (cross-checked against the oracle).
    test(2, 1, 3, 1, 20, Floor, "0.630929", Less); // log_3(2)
    test(2, 1, 3, 1, 20, Ceiling, "0.63093", Greater);
    test(2, 1, 3, 1, 20, Nearest, "0.63093", Greater);
    test(2, 1, 3, 2, 20, Nearest, "1.709511", Less); // log_{3/2}(2)
    // x = 1.
    test(1, 1, 3, 1, 10, Exact, "0.0", Equal);
    test(1, 1, 7, 3, 10, Exact, "0.0", Equal);
}

#[test]
fn test_log_base_rational_base_specials() {
    let three = Rational::from(3u32);
    let nearest = |x: Float| x.log_base_rational_base_prec_round(&three, 10, Nearest);

    assert_eq!(nearest(Float::NAN).0.to_string(), "NaN");
    assert_eq!(nearest(Float::INFINITY), (Float::INFINITY, Equal));
    assert_eq!(nearest(Float::NEGATIVE_INFINITY).0.to_string(), "NaN");
    assert_eq!(nearest(Float::ZERO), (Float::NEGATIVE_INFINITY, Equal));
    assert_eq!(nearest(-Float::ZERO), (Float::NEGATIVE_INFINITY, Equal));
    assert_eq!(nearest(Float::ONE), (Float::ZERO, Equal)); // log_3(1) = 0
    assert_eq!(nearest(Float::from(-2)).0.to_string(), "NaN"); // x < 0
}

#[test]
fn test_log_base_rational_base_prec() {
    // The `_prec` methods round to nearest; cross-checked against the rug oracle.
    let test = |n: i64, d: u64, bn: u64, bd: u64, prec: u64, out: &str, o_out| {
        let x = Float::exact_from(Rational::from_signeds(n, i64::exact_from(d)));
        let base = Rational::from_unsigneds(bn, bd);

        let (log, o) = x.clone().log_base_rational_base_prec(&base, prec);
        assert!(log.is_valid());
        assert_eq!(log.to_string(), out);
        assert_eq!(o, o_out);

        let (log_alt, o_alt) = x.log_base_rational_base_prec_ref(&base, prec);
        assert!(log_alt.is_valid());
        assert_eq!(ComparableFloatRef(&log_alt), ComparableFloatRef(&log));
        assert_eq!(o_alt, o);

        let mut x_alt = x.clone();
        let o_alt = x_alt.log_base_rational_base_prec_assign(&base, prec);
        assert!(x_alt.is_valid());
        assert_eq!(ComparableFloatRef(&x_alt), ComparableFloatRef(&log));
        assert_eq!(o_alt, o);

        let (rug_log, rug_o) =
            rug_log_base_rational_base_prec(&rug::Float::exact_from(&x), &base, prec);
        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_log)),
            ComparableFloatRef(&log),
        );
        assert_eq!(rug_o, o);
    };
    test(9, 1, 3, 1, 10, "2.0", Equal); // log_3(9) = 2
    test(8, 1, 2, 1, 10, "3.0", Equal); // log_2(8) = 3
    test(8, 1, 4, 1, 10, "1.5", Equal); // log_4(8) = 3/2
    test(2, 1, 4, 1, 10, "0.5", Equal); // log_4(2) = 1/2
    test(9, 4, 3, 2, 10, "2.0", Equal); // log_{3/2}(9/4) = 2
    test(3, 2, 9, 4, 10, "0.5", Equal); // log_{9/4}(3/2) = 1/2
    test(1, 4, 4, 1, 10, "-1.0", Equal); // log_4(1/4) = -1
    test(1, 8, 2, 1, 10, "-3.0", Equal); // log_2(1/8) = -3
    test(2, 1, 3, 1, 20, "0.63093", Greater); // log_3(2)
    test(2, 1, 3, 2, 20, "1.709511", Less); // log_{3/2}(2)
    test(1, 1, 3, 1, 10, "0.0", Equal); // log_3(1) = 0
}

#[test]
fn test_log_base_rational_base_round() {
    // The `_round` methods round to the input's precision; cross-checked against the rug oracle.
    let test = |n: i64, d: u64, bn: u64, bd: u64, rm: RoundingMode, out: &str, o_out| {
        let x = Float::exact_from(Rational::from_signeds(n, i64::exact_from(d)));
        let base = Rational::from_unsigneds(bn, bd);

        let (log, o) = x.clone().log_base_rational_base_round(&base, rm);
        assert!(log.is_valid());
        assert_eq!(log.to_string(), out);
        assert_eq!(o, o_out);

        let (log_alt, o_alt) = x.log_base_rational_base_round_ref(&base, rm);
        assert!(log_alt.is_valid());
        assert_eq!(ComparableFloatRef(&log_alt), ComparableFloatRef(&log));
        assert_eq!(o_alt, o);

        if let Ok(rug_rm) = rug_round_try_from_rounding_mode(rm) {
            let (rug_log, rug_o) =
                rug_log_base_rational_base_round(&rug::Float::exact_from(&x), &base, rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_log)),
                ComparableFloatRef(&log),
            );
            assert_eq!(rug_o, o);
        }
    };
    // Exact results that fit in the input's precision (across all rounding modes).
    test(9, 1, 3, 1, Floor, "2.0", Equal); // log_3(9) = 2, x has precision 4
    test(9, 1, 3, 1, Ceiling, "2.0", Equal);
    test(9, 1, 3, 1, Nearest, "2.0", Equal);
    test(9, 1, 3, 1, Down, "2.0", Equal);
    test(9, 1, 3, 1, Up, "2.0", Equal);
    test(9, 1, 3, 1, Exact, "2.0", Equal);
    test(81, 1, 3, 1, Exact, "4.0", Equal); // log_3(81) = 4, x has precision 7
    test(2, 1, 4, 1, Exact, "0.5", Equal); // log_4(2) = 1/2
    test(1, 4, 4, 1, Exact, "-1.0", Equal); // log_4(1/4) = -1
    test(9, 4, 3, 2, Exact, "2.0", Equal); // log_{3/2}(9/4) = 2
    test(3, 2, 9, 4, Exact, "0.5", Equal); // log_{9/4}(3/2) = 1/2
    // Specials (the input's precision is irrelevant).
    test(1, 1, 3, 1, Exact, "0.0", Equal); // log_3(1) = 0
    test(-3, 1, 3, 1, Nearest, "NaN", Equal); // x < 0
}

#[test]
fn test_log_base_rational_base() {
    // The `LogBase<Rational>` trait: rounds to the input's precision, to nearest.
    let test = |n: i64, d: u64, bn: u64, bd: u64, out: &str| {
        let x = Float::exact_from(Rational::from_signeds(n, i64::exact_from(d)));
        let base = Rational::from_unsigneds(bn, bd);

        let log = x.clone().log_base(base.clone());
        assert!(log.is_valid());
        assert_eq!(log.to_string(), out);

        let log_alt = (&x).log_base(&base);
        assert_eq!(ComparableFloatRef(&log_alt), ComparableFloatRef(&log));

        let mut x_alt = x.clone();
        x_alt.log_base_assign(&base);
        assert_eq!(ComparableFloatRef(&x_alt), ComparableFloatRef(&log));

        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_log_base_rational_base(
                &rug::Float::exact_from(&x),
                &base
            ))),
            ComparableFloatRef(&log),
        );
    };
    test(9, 1, 3, 1, "2.0"); // log_3(9) = 2
    test(81, 1, 3, 1, "4.0"); // log_3(81) = 4
    test(2, 1, 4, 1, "0.5"); // log_4(2) = 1/2
    test(1, 4, 4, 1, "-1.0"); // log_4(1/4) = -1
}

fn log_base_rational_base_prec_round_properties_helper(
    x: &Float,
    base: &Rational,
    prec: u64,
    rm: RoundingMode,
    extreme: bool,
) {
    let (log, o) = check(x, base, prec, rm, extreme);

    // When the base is a `u64` integer, the result must match the independently-implemented
    // integer-base `log_base` (which computes ln(x) / ln(base) rather than log_2(x) / log_2(base)).
    if let Ok(n) = u64::try_from(base) {
        let (alt, o_alt) = x.log_base_prec_round_ref(n, prec, rm);
        assert_eq!(ComparableFloatRef(&alt), ComparableFloatRef(&log));
        assert_eq!(o_alt, o);
    }

    // The sign of the result follows whether x is on the same side of 1 as the base (> 1): x > 1
    // gives a positive log, 0 < x < 1 gives a negative log.
    if log.is_normal() {
        if *x > 1u32 && o > Less {
            assert!(log > 0u32);
        } else if *x > 0u32 && *x < 1u32 && o < Greater {
            assert!(log < 0u32);
        }
    }

    // An exact result does not depend on the rounding mode; an inexact one cannot be produced with
    // `Exact`.
    if o == Equal {
        for rm in exhaustive_rounding_modes() {
            let (alt, o_alt) = x.log_base_rational_base_prec_round_ref(base, prec, rm);
            assert_eq!(
                ComparableFloat(alt.abs_negative_zero()),
                ComparableFloat(log.abs_negative_zero_ref())
            );
            assert_eq!(o_alt, Equal);
        }
    } else {
        assert_panic!(x.log_base_rational_base_prec_round_ref(base, prec, Exact));
    }
}

#[test]
fn log_base_rational_base_prec_round_properties() {
    float_rational_unsigned_rounding_mode_quadruple_gen_var_11().test_properties_with_limit(
        20,
        |(x, base, prec, rm)| {
            log_base_rational_base_prec_round_properties_helper(&x, &base, prec, rm, false);
        },
    );
    float_rational_unsigned_rounding_mode_quadruple_gen_var_12().test_properties_with_limit(
        20,
        |(x, base, prec, rm)| {
            log_base_rational_base_prec_round_properties_helper(&x, &base, prec, rm, true);
        },
    );

    // The special cases hold for every base > 1, precision, and rounding mode.
    unsigned_rounding_mode_pair_gen_var_3().test_properties(|(prec, rm)| {
        for base in [Rational::from(3u32), Rational::from_unsigneds(3u32, 2)] {
            let f = |x: Float| x.log_base_rational_base_prec_round(&base, prec, rm);
            assert!(f(Float::NAN).0.is_nan());
            assert_eq!(f(Float::INFINITY), (Float::INFINITY, Equal));
            assert!(f(Float::NEGATIVE_INFINITY).0.is_nan());
            assert_eq!(f(Float::ZERO), (Float::NEGATIVE_INFINITY, Equal));
            assert_eq!(f(-Float::ZERO), (Float::NEGATIVE_INFINITY, Equal));
            assert_eq!(f(Float::ONE), (Float::ZERO, Equal));
            assert!(f(Float::from(-2)).0.is_nan());
        }
    });
}

#[test]
fn log_base_rational_base_prec_properties() {
    let f = |x: Float, base: Rational, prec: u64, extreme: bool| {
        let (log, o) = x.clone().log_base_rational_base_prec(&base, prec);
        assert!(log.is_valid());
        let (log_ref, o_ref) = x.log_base_rational_base_prec_ref(&base, prec);
        assert_eq!(ComparableFloatRef(&log_ref), ComparableFloatRef(&log));
        assert_eq!(o_ref, o);
        let (expected, eo) = check(&x, &base, prec, Nearest, extreme);
        assert_eq!(ComparableFloatRef(&log), ComparableFloatRef(&expected));
        assert_eq!(o, eo);
    };
    float_rational_unsigned_rounding_mode_quadruple_gen_var_11()
        .test_properties_with_limit(20, |(x, base, prec, _rm)| f(x, base, prec, false));
    float_rational_unsigned_rounding_mode_quadruple_gen_var_12()
        .test_properties_with_limit(20, |(x, base, prec, _rm)| f(x, base, prec, true));
}

#[test]
fn log_base_rational_base_round_properties() {
    let f = |x: Float, base: Rational, rm: RoundingMode, extreme: bool| {
        let (log, o) = x.clone().log_base_rational_base_round(&base, rm);
        assert!(log.is_valid());
        let (log_ref, o_ref) = x.log_base_rational_base_round_ref(&base, rm);
        assert_eq!(ComparableFloatRef(&log_ref), ComparableFloatRef(&log));
        assert_eq!(o_ref, o);
        let (expected, eo) = check(&x, &base, x.significant_bits(), rm, extreme);
        assert_eq!(ComparableFloatRef(&log), ComparableFloatRef(&expected));
        assert_eq!(o, eo);
    };
    float_rational_rounding_mode_triple_gen_var_12()
        .test_properties_with_limit(20, |(x, base, rm)| f(x, base, rm, false));
    float_rational_rounding_mode_triple_gen_var_13()
        .test_properties_with_limit(20, |(x, base, rm)| f(x, base, rm, true));
}

#[test]
fn log_base_rational_base_properties() {
    let f = |x: Float, base: Rational, extreme: bool| {
        let (expected, _) = check(&x, &base, x.significant_bits(), Nearest, extreme);
        let log = x.clone().log_base(base.clone());
        assert!(log.is_valid());
        assert_eq!(ComparableFloatRef(&log), ComparableFloatRef(&expected));
        let log_ref = (&x).log_base(&base);
        assert_eq!(ComparableFloatRef(&log_ref), ComparableFloatRef(&log));
        let mut x_alt = x.clone();
        x_alt.log_base_assign(&base);
        assert_eq!(ComparableFloatRef(&x_alt), ComparableFloatRef(&log));
    };
    float_rational_rounding_mode_triple_gen_var_12()
        .test_properties_with_limit(20, |(x, base, _rm)| f(x, base, false));
    float_rational_rounding_mode_triple_gen_var_13()
        .test_properties_with_limit(20, |(x, base, _rm)| f(x, base, true));
}

#[test]
fn log_base_rational_base_fail() {
    // Precision must be nonzero.
    assert_panic!(Float::from(8).log_base_rational_base_prec_round(
        &Rational::from(3u32),
        0,
        Nearest
    ));
    // Base must be greater than 1.
    assert_panic!(Float::from(8).log_base_rational_base_prec_round(&Rational::ONE, 10, Nearest));
    assert_panic!(Float::from(8).log_base_rational_base_prec_round(
        &Rational::from_unsigneds(1u32, 2),
        10,
        Nearest
    ));
    // Exact is not allowed when the result is not exactly representable.
    assert_panic!(Float::from(2).log_base_rational_base_prec_round(
        &Rational::from(3u32),
        10,
        Exact
    ));
}

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_log_base_rational_base() {
    fn test<T: PrimitiveFloat>(x: T, base: &Rational, out: T)
    where
        Float: From<T> + PartialOrd<T>,
        for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
    {
        assert_eq!(
            NiceFloat(primitive_float_log_base_rational_base(x, base)),
            NiceFloat(out)
        );
    }
    test::<f32>(f32::NAN, &Rational::from(10), f32::NAN);
    test::<f32>(f32::INFINITY, &Rational::from(10), f32::INFINITY);
    test::<f32>(f32::NEGATIVE_INFINITY, &Rational::from(10), f32::NAN);
    test::<f32>(0.0, &Rational::from(10), f32::NEGATIVE_INFINITY);
    test::<f32>(-0.0, &Rational::from(10), f32::NEGATIVE_INFINITY);
    test::<f32>(1.0, &Rational::from(10), 0.0);
    test::<f32>(8.0, &Rational::from(4), 1.5); // log_4(8)
    test::<f32>(9.0, &Rational::from(3), 2.0); // log_3(9)
    test::<f32>(1000.0, &Rational::from(10), 3.0); // log_10(1000)
    test::<f32>(2.25, &Rational::from_unsigneds(3u8, 2), 2.0); // log_(3/2)(2.25)
    test::<f32>(2.0, &Rational::from_unsigneds(3u8, 2), 1.7095113); // log_(3/2)(2)
    test::<f32>(50.0, &Rational::from(10), 1.6989699602127075); // log_10(50)
    test::<f32>(-1.0, &Rational::from(10), f32::NAN);

    test::<f64>(f64::NAN, &Rational::from(10), f64::NAN);
    test::<f64>(f64::INFINITY, &Rational::from(10), f64::INFINITY);
    test::<f64>(f64::NEGATIVE_INFINITY, &Rational::from(10), f64::NAN);
    test::<f64>(0.0, &Rational::from(10), f64::NEGATIVE_INFINITY);
    test::<f64>(-0.0, &Rational::from(10), f64::NEGATIVE_INFINITY);
    test::<f64>(1.0, &Rational::from(10), 0.0);
    test::<f64>(8.0, &Rational::from(4), 1.5); // log_4(8)
    test::<f64>(9.0, &Rational::from(3), 2.0); // log_3(9)
    test::<f64>(1000.0, &Rational::from(10), 3.0); // log_10(1000)
    test::<f64>(2.25, &Rational::from_unsigneds(3u8, 2), 2.0); // log_(3/2)(2.25)
    test::<f64>(2.0, &Rational::from_unsigneds(3u8, 2), 1.7095112913514547); // log_(3/2)(2)
    test::<f64>(50.0, &Rational::from(10), 1.6989700043360187); // log_10(50)
    test::<f64>(-1.0, &Rational::from(10), f64::NAN);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_log_base_rational_base_properties_helper<T: PrimitiveFloat>()
where
    Float: From<T> + PartialOrd<T>,
    for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
{
    float_rational_rounding_mode_triple_gen_var_12().test_properties(|(_, base, _)| {
        // The generator yields a `Rational` base greater than 1 (and an unrelated `Float`/rounding
        // mode); test the primitive function over a few fixed primitive-float inputs.
        for x in [T::ZERO, T::ONE, T::TWO, T::NEGATIVE_ONE] {
            let y = primitive_float_log_base_rational_base(x, &base);
            // When the base is a positive integer, the result matches log_base.
            if let Ok(b) = u64::try_from(&base) {
                assert_eq!(NiceFloat(y), NiceFloat(primitive_float_log_base(x, b)));
            }
        }
    });
}

#[test]
fn primitive_float_log_base_rational_base_properties() {
    apply_fn_to_primitive_floats!(primitive_float_log_base_rational_base_properties_helper);
}