malachite-float 0.12.0

// 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::{Cos, CosAssign, PowerOf2};
use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::basic::traits::{
    Infinity, NaN, NegativeInfinity, NegativeZero, One, Zero,
};
use malachite_base::num::comparison::traits::PartialOrdAbs;
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::{
    primitive_float_gen, primitive_float_unsigned_pair_gen_var_1,
    unsigned_rounding_mode_pair_gen_var_3,
};
use malachite_float::float::arithmetic::cos::{
    primitive_float_cos, primitive_float_cos_pi, primitive_float_cos_pi_rational,
    primitive_float_cos_rational, primitive_float_cos_with_period,
    primitive_float_cos_with_period_rational,
};
use malachite_float::test_util::common::{
    assert_rounding_ordering_consistent, parse_hex_string, rug_round_try_from_rounding_mode,
    to_hex_string,
};
use malachite_float::test_util::float::arithmetic::cos::{
    rug_cos, rug_cos_pi_prec_round, rug_cos_pi_rational_prec_round, rug_cos_prec,
    rug_cos_prec_round, rug_cos_rational_prec, rug_cos_rational_prec_round, rug_cos_round,
    rug_cos_with_period_prec, rug_cos_with_period_prec_round, rug_cos_with_period_rational_prec,
    rug_cos_with_period_rational_prec_round,
};
use malachite_float::test_util::generators::{
    float_gen, float_rounding_mode_pair_gen_var_47, float_unsigned_pair_gen_var_1,
    float_unsigned_pair_gen_var_2, float_unsigned_rounding_mode_triple_gen_var_36,
    float_unsigned_rounding_mode_triple_gen_var_37, float_unsigned_rounding_mode_triple_gen_var_38,
    float_unsigned_unsigned_rounding_mode_quadruple_gen_var_15,
    float_unsigned_unsigned_rounding_mode_quadruple_gen_var_16,
    float_unsigned_unsigned_triple_gen_var_1, rational_unsigned_rounding_mode_triple_gen_var_10,
    rational_unsigned_unsigned_rounding_mode_quadruple_gen_var_4,
};
use malachite_float::{ComparableFloat, ComparableFloatRef, Float};
use malachite_q::Rational;
use malachite_q::test_util::generators::{
    rational_gen, rational_unsigned_pair_gen_var_1, rational_unsigned_pair_gen_var_3,
};
use std::panic::catch_unwind;
use std::str::FromStr;

#[test]
fn test_cos_prec_round() {
    let test = |s, s_hex, prec: u64, rm, out: &str, out_hex: &str, o_out: Ordering| {
        let x = parse_hex_string(s_hex);
        assert_eq!(x.to_string(), s);

        let (c, o) = x.clone().cos_prec_round(prec, rm);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, o_out);

        let (c_alt, o_alt) = x.cos_prec_round_ref(prec, rm);
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        let mut c_alt = x.clone();
        let o_alt = c_alt.cos_prec_round_assign(prec, rm);
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        if let Ok(rug_rm) = rug_round_try_from_rounding_mode(rm) {
            let (rug_c, rug_o) = rug_cos_prec_round(&rug::Float::exact_from(&x), prec, rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    };
    test("NaN", "NaN", 1, Nearest, "NaN", "NaN", Equal);
    test("Infinity", "Infinity", 1, Nearest, "NaN", "NaN", Equal);
    test("-Infinity", "-Infinity", 1, Nearest, "NaN", "NaN", Equal);
    test("0.0", "0x0.0", 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("-0.0", "-0x0.0", 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("0.0", "0x0.0", 10, Nearest, "1.0000", "0x1.000#10", Equal);
    test("1.0", "0x1.0#1", 1, Floor, "0.50", "0x0.8#1", Less);
    test("1.0", "0x1.0#1", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("1.0", "0x1.0#1", 1, Nearest, "0.50", "0x0.8#1", Less);
    test("1.0", "0x1.0#1", 10, Floor, "0.54004", "0x0.8a4#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        10,
        Ceiling,
        "0.54102",
        "0x0.8a8#10",
        Greater,
    );
    test("1.0", "0x1.0#1", 10, Nearest, "0.54004", "0x0.8a4#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        100,
        Floor,
        "0.54030230586813971740093660744256",
        "0x0.8a51407da8345c91c2466d976#100",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Ceiling,
        "0.54030230586813971740093660744335",
        "0x0.8a51407da8345c91c2466d977#100",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Nearest,
        "0.54030230586813971740093660744335",
        "0x0.8a51407da8345c91c2466d977#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Nearest,
        "0.54004",
        "0x0.8a4#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        10,
        Nearest,
        "-0.41602",
        "-0x0.6a8#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        10,
        Nearest,
        "-0.99023",
        "-0x0.fd8#10",
        Less,
    );
    test(
        "4.0",
        "0x4.0#1",
        10,
        Nearest,
        "-0.65332",
        "-0x0.a74#10",
        Greater,
    );
    test(
        "4.0",
        "0x4.0#1",
        100,
        Nearest,
        "-0.65364362086361191463916818309786",
        "-0x0.a7553036d926062336d0e16e4#100",
        Less,
    );
    test(
        "100.0",
        "0x64.0#5",
        10,
        Nearest,
        "0.86230",
        "0x0.dcc#10",
        Less,
    );
    test(
        "100.0",
        "0x64.0#5",
        100,
        Floor,
        "0.86231887228768393410193851395020",
        "0x0.dcc0edfb32fefb1fa19b9b30b#100",
        Less,
    );
    test(
        "100.0",
        "0x64.0#5",
        100,
        Ceiling,
        "0.86231887228768393410193851395099",
        "0x0.dcc0edfb32fefb1fa19b9b30c#100",
        Greater,
    );
    test(
        "1.00000e6",
        "0xf.424E+4#14",
        64,
        Nearest,
        "0.936752127533144786917",
        "0x0.efcefcc836996357#64",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        50,
        Nearest,
        "0.87758256189037276",
        "0x0.e0a94032dbea8#50",
        Greater,
    );
    test(
        "0.102",
        "0x0.1a#4",
        50,
        Nearest,
        "0.99484696102354064",
        "0x0.feae4a5a1f000#50",
        Greater,
    );
    test(
        "1.000e-10",
        "0x6.eE-9#7",
        50,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#50",
        Greater,
    );
    test(
        "1.000e-10",
        "0x6.eE-9#7",
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.000e-10",
        "0x6.eE-9#7",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.570796326794896600",
        "0x1.921fb54442d183#57",
        53,
        Nearest,
        "1.9598976533924290e-17",
        "0x1.69898cc51701cE-14#53",
        Greater,
    );
    test(
        "3.14159265358979289",
        "0x3.243f6a8885a2f#54",
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Less,
    );
    test(
        "6.28318530717958579",
        "0x6.487ed5110b45e#54",
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "9.979e99",
        "0x1.24E+83#7",
        53,
        Nearest,
        "-0.42980316367459315",
        "-0x0.6e079483b32060#53",
        Greater,
    );
    test("3.0", "0x3.0#2", 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test("3.0", "0x3.0#2", 1, Floor, "-1.0", "-0x1.0#1", Less);
    test("3.0", "0x3.0#2", 1, Ceiling, "-0.50", "-0x0.8#1", Greater);
    test("3.0", "0x3.0#2", 2, Nearest, "-1.0", "-0x1.0#2", Less);
    // - tiny x: the small-input shortcut rounds 1 - x^2/2 directly
    test("0.25", "0x0.4#1", 1, Down, "0.50", "0x0.8#1", Less);
    // - general path: the first working precision can round
    test("1.0", "0x1.0#1", 1, Down, "0.50", "0x0.8#1", Less);
    // - cancellation: cos(x) is much smaller than 1, so the working precision grows by the lost
    //   bits
    test("2.0", "0x2.0#1", 1, Down, "-0.25", "-0x0.4#1", Greater);
    // - |x| >= 4: argument reduction modulo 2 pi
    test("4.0", "0x4.0#1", 1, Down, "-0.50", "-0x0.8#1", Greater);
    // - the sum rounds to exactly 1 at the working precision, and the error bound alone decides the
    //   rounding
    test(
        "-3.495934488151859089160804055e56",
        "-0xe.41ed086a5791d9e5b2924E+46#87",
        2,
        Down,
        "0.75",
        "0x0.c#2",
        Less,
    );
    // - x equals the working-precision 2 pi, so the reduced argument is zero and the loop retries
    //   at a higher precision
    test(
        "6.28318536",
        "0x6.487ed6#26",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    // - x = pi / 2 rounded to 53 bits: cos(x) is about 2^-54, found after growing the precision
    test(
        "1.5707963267948966",
        "0x1.921fb54442d18#53",
        53,
        Nearest,
        "6.1232339957367660e-17",
        "0x4.69898cc51701cE-14#53",
        Greater,
    );
    test(
        "1.5707963267948966192313216916397514420985846996875529104874722",
        "0x1.921fb54442d18469898cc51701b839a252049c1114cf98e804#200",
        100,
        Floor,
        "5.7099684971243490026437400060191e-62",
        "0x1.77d4c76273644a29410f31c68E-51#100",
        Less,
    );
    test(
        "4.7123889803846898576939650749192543286",
        "0x4.b65f1fccc8748d3c9ca64f450528b0#120",
        120,
        Ceiling,
        "2.3305317247657495256428231620634736190e-36",
        "0x3.1909f22bccc1913547f3b9881a9d8cE-30#120",
        Greater,
    );
    // - x = pi rounded to 64 bits: cos(x) is within 2^-128 of -1
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        64,
        Nearest,
        "-1.00000000000000000000",
        "-0x1.0000000000000000#64",
        Less,
    );
}

#[test]
#[should_panic]
fn cos_prec_round_fail() {
    Float::ONE.cos_prec_round(0, Nearest);
}

#[test]
#[should_panic]
fn cos_prec_round_exact_fail() {
    Float::ONE.cos_prec_round(10, Exact);
}

#[test]
#[should_panic]
fn cos_prec_fail() {
    Float::ONE.cos_prec(0);
}

#[test]
#[should_panic]
fn cos_round_fail() {
    Float::ONE.cos_round(Exact);
}

#[allow(clippy::needless_pass_by_value)]
fn cos_prec_round_properties_helper(x: Float, prec: u64, rm: RoundingMode) {
    let (c, o) = x.clone().cos_prec_round(prec, rm);
    assert!(c.is_valid());
    assert_rounding_ordering_consistent(&c, rm, o);

    let (c_alt, o_alt) = x.cos_prec_round_ref(prec, rm);
    assert!(c_alt.is_valid());
    assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
    assert_eq!(o_alt, o);

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

    if let Ok(rug_rm) = rug_round_try_from_rounding_mode(rm) {
        let (rug_c, rug_o) = rug_cos_prec_round(&rug::Float::exact_from(&x), prec, rug_rm);
        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_c)),
            ComparableFloatRef(&c)
        );
        assert_eq!(rug_o, o);
    }

    // cos is even
    let (c_neg, o_neg) = (-&x).cos_prec_round(prec, rm);
    assert_eq!(ComparableFloatRef(&c_neg), ComparableFloatRef(&c));
    assert_eq!(o_neg, o);

    // |cos x| <= 1
    if c.is_finite() {
        assert!(c.le_abs(&1u32));
    }
    if c.is_normal() {
        assert_eq!(c.get_prec(), Some(prec));
    }

    if o == Equal {
        // cos is exact only for x = 0 (and NaN, and ±inf): the result is rounding-mode-invariant
        for rm2 in exhaustive_rounding_modes() {
            let (c2, o2) = x.cos_prec_round_ref(prec, rm2);
            assert_eq!(
                ComparableFloat(c2.abs_negative_zero_ref()),
                ComparableFloat(c.abs_negative_zero_ref())
            );
            assert_eq!(o2, Equal);
        }
    } else {
        assert_panic!(x.cos_prec_round_ref(prec, Exact));
    }
}

#[test]
fn cos_prec_round_properties() {
    float_unsigned_rounding_mode_triple_gen_var_36().test_properties(|(x, prec, rm)| {
        cos_prec_round_properties_helper(x, prec, rm);
    });

    unsigned_rounding_mode_pair_gen_var_3().test_properties(|(prec, rm)| {
        let (c, o) = Float::NAN.cos_prec_round(prec, rm);
        assert!(c.is_nan());
        assert_eq!(o, Equal);

        let (c, o) = Float::INFINITY.cos_prec_round(prec, rm);
        assert!(c.is_nan());
        assert_eq!(o, Equal);

        let (c, o) = Float::NEGATIVE_INFINITY.cos_prec_round(prec, rm);
        assert!(c.is_nan());
        assert_eq!(o, Equal);

        let (c, o) = Float::ZERO.cos_prec_round(prec, rm);
        assert_eq!(ComparableFloat(c), ComparableFloat(Float::one_prec(prec)));
        assert_eq!(o, Equal);

        let (c, o) = Float::NEGATIVE_ZERO.cos_prec_round(prec, rm);
        assert_eq!(ComparableFloat(c), ComparableFloat(Float::one_prec(prec)));
        assert_eq!(o, Equal);
    });
}

#[test]
fn cos_round_properties() {
    float_rounding_mode_pair_gen_var_47().test_properties(|(x, rm)| {
        let (c, o) = x.clone().cos_round(rm);
        assert!(c.is_valid());
        assert_rounding_ordering_consistent(&c, rm, o);
        let (c_alt, o_alt) = x.cos_round_ref(rm);
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        let mut x_alt = x.clone();
        let o_alt = x_alt.cos_round_assign(rm);
        assert!(x_alt.is_valid());
        assert_eq!(ComparableFloatRef(&x_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        let (c_alt, o_alt) = x.cos_prec_round_ref(x.significant_bits(), rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        if let Ok(rug_rm) = rug_round_try_from_rounding_mode(rm) {
            let (rug_c, rug_o) = rug_cos_round(&rug::Float::exact_from(&x), rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    });
}

#[test]
fn cos_prec_properties() {
    float_unsigned_pair_gen_var_1().test_properties(|(x, prec)| {
        let (c, o) = x.clone().cos_prec(prec);
        assert!(c.is_valid());
        let (c_alt, o_alt) = x.cos_prec_ref(prec);
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

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

        let (c_alt, o_alt) = x.cos_prec_round_ref(prec, Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        let (rug_c, rug_o) = rug_cos_prec(&rug::Float::exact_from(&x), prec);
        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_c)),
            ComparableFloatRef(&c)
        );
        assert_eq!(rug_o, o);
    });
}

#[test]
fn cos_properties() {
    float_gen().test_properties(|x| {
        let c = x.clone().cos();
        assert!(c.is_valid());
        let c_alt = (&x).cos();
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));

        let mut x_alt = x.clone();
        x_alt.cos_assign();
        assert!(x_alt.is_valid());
        assert_eq!(ComparableFloatRef(&x_alt), ComparableFloatRef(&c));

        let (c_alt, _) = x.cos_prec_round_ref(x.significant_bits(), Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));

        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_cos(&rug::Float::exact_from(&x)))),
            ComparableFloatRef(&c)
        );

        assert_eq!(ComparableFloatRef(&(-&x).cos()), ComparableFloatRef(&c));
        if c.is_finite() {
            assert!(c.le_abs(&1u32));
        }
    });
}

// n * pi / 2, with pi rounded to the nearest `prec` bits and the product exact
fn odd_multiple_of_half_pi(n: i64, prec: u64) -> Float {
    Float::pi_prec(prec)
        .0
        .mul_prec_round(Float::from(n), prec + 64, Exact)
        .0
        >> 1u32
}

// Inputs close to an odd multiple of pi/2, where the cosine is tiny and takes the near-zero path: n
// * pi / 2 with pi rounded to `prec_x` bits. The rows with `prec_x` at most 100 and a large output
// precision need several terms of the sin(delta) / delta series.
#[test]
fn test_cos_near_zero() {
    let test = |n: i64, prec_x: u64, prec: u64, rm, out: &str, out_hex: &str, o_out: Ordering| {
        let x = odd_multiple_of_half_pi(n, prec_x);
        let (c, o) = x.cos_prec_round_ref(prec, rm);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, o_out);

        let (rug_c, rug_o) = rug_cos_prec_round(
            &rug::Float::exact_from(&x),
            prec,
            rug_round_try_from_rounding_mode(rm).unwrap(),
        );
        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_c)),
            ComparableFloatRef(&c)
        );
        assert_eq!(rug_o, o);
    };
    test(1, 150, 1, Up, "-7.0e-46", "-0x4.0E-38#1", Less);
    test(1, 150, 1, Floor, "-7.0e-46", "-0x4.0E-38#1", Less);
    test(1, 150, 1, Ceiling, "-3.5e-46", "-0x2.0E-38#1", Greater);
    test(1, 150, 1, Nearest, "-7.0e-46", "-0x4.0E-38#1", Less);
    test(1, 150, 10, Down, "-6.8833e-46", "-0x3.eeE-38#10", Greater);
    test(1, 150, 10, Up, "-6.8902e-46", "-0x3.efE-38#10", Less);
    test(1, 150, 10, Floor, "-6.8902e-46", "-0x3.efE-38#10", Less);
    test(
        1,
        150,
        10,
        Ceiling,
        "-6.8833e-46",
        "-0x3.eeE-38#10",
        Greater,
    );
    test(1, 150, 10, Nearest, "-6.8902e-46", "-0x3.efE-38#10", Less);
    test(
        1,
        150,
        53,
        Down,
        "-6.8896173743304411e-46",
        "-0x3.eeeb306717fbeE-38#53",
        Greater,
    );
    test(
        1,
        150,
        53,
        Up,
        "-6.8896173743304419e-46",
        "-0x3.eeeb306717fc0E-38#53",
        Less,
    );
    test(
        1,
        150,
        53,
        Floor,
        "-6.8896173743304419e-46",
        "-0x3.eeeb306717fc0E-38#53",
        Less,
    );
    test(
        1,
        150,
        53,
        Ceiling,
        "-6.8896173743304411e-46",
        "-0x3.eeeb306717fbeE-38#53",
        Greater,
    );
    test(
        1,
        150,
        53,
        Nearest,
        "-6.8896173743304411e-46",
        "-0x3.eeeb306717fbeE-38#53",
        Greater,
    );
    test(
        1,
        150,
        100,
        Nearest,
        "-6.8896173743304413174294781085918e-46",
        "-0x3.eeeb306717fbe882b389d8c9cE-38#100",
        Less,
    );
    test(1, 190, 1, Down, "2.5e-60", "0x4.0E-50#1", Less);
    test(1, 190, 1, Up, "5.0e-60", "0x8.0E-50#1", Greater);
    test(1, 190, 1, Floor, "2.5e-60", "0x4.0E-50#1", Less);
    test(1, 190, 1, Ceiling, "5.0e-60", "0x8.0E-50#1", Greater);
    test(1, 190, 1, Nearest, "2.5e-60", "0x4.0E-50#1", Less);
    test(1, 190, 10, Down, "2.5427e-60", "0x4.16E-50#10", Less);
    test(1, 190, 10, Up, "2.5475e-60", "0x4.18E-50#10", Greater);
    test(1, 190, 10, Floor, "2.5427e-60", "0x4.16E-50#10", Less);
    test(1, 190, 10, Ceiling, "2.5475e-60", "0x4.18E-50#10", Greater);
    test(1, 190, 10, Nearest, "2.5475e-60", "0x4.18E-50#10", Greater);
    test(
        1,
        190,
        53,
        Down,
        "2.5463057961157001e-60",
        "0x4.177d4c7627364E-50#53",
        Less,
    );
    test(
        1,
        190,
        53,
        Up,
        "2.5463057961157007e-60",
        "0x4.177d4c7627368E-50#53",
        Greater,
    );
    test(
        1,
        190,
        53,
        Floor,
        "2.5463057961157001e-60",
        "0x4.177d4c7627364E-50#53",
        Less,
    );
    test(
        1,
        190,
        53,
        Ceiling,
        "2.5463057961157007e-60",
        "0x4.177d4c7627368E-50#53",
        Greater,
    );
    test(
        1,
        190,
        53,
        Nearest,
        "2.5463057961157001e-60",
        "0x4.177d4c7627364E-50#53",
        Less,
    );
    test(
        1,
        190,
        100,
        Nearest,
        "2.5463057961157001728840630215730e-60",
        "0x4.177d4c76273644a29410f31c8E-50#100",
        Greater,
    );
    test(1, 200, 1, Down, "3.9e-62", "0x1.0E-51#1", Less);
    test(1, 200, 1, Up, "7.8e-62", "0x2.0E-51#1", Greater);
    test(1, 200, 1, Floor, "3.9e-62", "0x1.0E-51#1", Less);
    test(1, 200, 1, Ceiling, "7.8e-62", "0x2.0E-51#1", Greater);
    test(1, 200, 1, Nearest, "3.9e-62", "0x1.0E-51#1", Less);
    test(1, 200, 10, Down, "5.7049e-62", "0x1.778E-51#10", Less);
    test(1, 200, 10, Up, "5.7125e-62", "0x1.780E-51#10", Greater);
    test(1, 200, 10, Floor, "5.7049e-62", "0x1.778E-51#10", Less);
    test(1, 200, 10, Ceiling, "5.7125e-62", "0x1.780E-51#10", Greater);
    test(1, 200, 10, Nearest, "5.7125e-62", "0x1.780E-51#10", Greater);
    test(
        1,
        200,
        53,
        Down,
        "5.7099684971243485e-62",
        "0x1.77d4c76273644E-51#53",
        Less,
    );
    test(
        1,
        200,
        53,
        Up,
        "5.7099684971243493e-62",
        "0x1.77d4c76273645E-51#53",
        Greater,
    );
    test(
        1,
        200,
        53,
        Floor,
        "5.7099684971243485e-62",
        "0x1.77d4c76273644E-51#53",
        Less,
    );
    test(
        1,
        200,
        53,
        Ceiling,
        "5.7099684971243493e-62",
        "0x1.77d4c76273645E-51#53",
        Greater,
    );
    test(
        1,
        200,
        53,
        Nearest,
        "5.7099684971243493e-62",
        "0x1.77d4c76273645E-51#53",
        Greater,
    );
    test(
        1,
        200,
        100,
        Nearest,
        "5.7099684971243490026437400060191e-62",
        "0x1.77d4c76273644a29410f31c68E-51#100",
        Less,
    );
    test(3, 200, 1, Down, "-1.6e-61", "-0x4.0E-51#1", Greater);
    test(3, 200, 1, Up, "-3.1e-61", "-0x8.0E-51#1", Less);
    test(3, 200, 1, Floor, "-3.1e-61", "-0x8.0E-51#1", Less);
    test(3, 200, 1, Ceiling, "-1.6e-61", "-0x4.0E-51#1", Greater);
    test(3, 200, 1, Nearest, "-1.6e-61", "-0x4.0E-51#1", Greater);
    test(3, 200, 10, Down, "-1.7107e-61", "-0x4.66E-51#10", Greater);
    test(3, 200, 10, Up, "-1.7138e-61", "-0x4.68E-51#10", Less);
    test(3, 200, 10, Floor, "-1.7138e-61", "-0x4.68E-51#10", Less);
    test(
        3,
        200,
        10,
        Ceiling,
        "-1.7107e-61",
        "-0x4.66E-51#10",
        Greater,
    );
    test(3, 200, 10, Nearest, "-1.7138e-61", "-0x4.68E-51#10", Less);
    test(
        3,
        200,
        53,
        Down,
        "-1.7129905491373045e-61",
        "-0x4.677e56275a2ccE-51#53",
        Greater,
    );
    test(
        3,
        200,
        53,
        Up,
        "-1.7129905491373049e-61",
        "-0x4.677e56275a2d0E-51#53",
        Less,
    );
    test(
        3,
        200,
        53,
        Floor,
        "-1.7129905491373049e-61",
        "-0x4.677e56275a2d0E-51#53",
        Less,
    );
    test(
        3,
        200,
        53,
        Ceiling,
        "-1.7129905491373045e-61",
        "-0x4.677e56275a2ccE-51#53",
        Greater,
    );
    test(
        3,
        200,
        53,
        Nearest,
        "-1.7129905491373045e-61",
        "-0x4.677e56275a2ccE-51#53",
        Greater,
    );
    test(
        3,
        200,
        100,
        Nearest,
        "-1.7129905491373047007931220018057e-61",
        "-0x4.677e56275a2cde7bc32d95538E-51#100",
        Greater,
    );
    test(-1, 200, 1, Down, "3.9e-62", "0x1.0E-51#1", Less);
    test(-1, 200, 1, Up, "7.8e-62", "0x2.0E-51#1", Greater);
    test(-1, 200, 1, Floor, "3.9e-62", "0x1.0E-51#1", Less);
    test(-1, 200, 1, Ceiling, "7.8e-62", "0x2.0E-51#1", Greater);
    test(-1, 200, 1, Nearest, "3.9e-62", "0x1.0E-51#1", Less);
    test(-1, 200, 10, Down, "5.7049e-62", "0x1.778E-51#10", Less);
    test(-1, 200, 10, Up, "5.7125e-62", "0x1.780E-51#10", Greater);
    test(-1, 200, 10, Floor, "5.7049e-62", "0x1.778E-51#10", Less);
    test(
        -1,
        200,
        10,
        Ceiling,
        "5.7125e-62",
        "0x1.780E-51#10",
        Greater,
    );
    test(
        -1,
        200,
        10,
        Nearest,
        "5.7125e-62",
        "0x1.780E-51#10",
        Greater,
    );
    test(
        -1,
        200,
        53,
        Down,
        "5.7099684971243485e-62",
        "0x1.77d4c76273644E-51#53",
        Less,
    );
    test(
        -1,
        200,
        53,
        Up,
        "5.7099684971243493e-62",
        "0x1.77d4c76273645E-51#53",
        Greater,
    );
    test(
        -1,
        200,
        53,
        Floor,
        "5.7099684971243485e-62",
        "0x1.77d4c76273644E-51#53",
        Less,
    );
    test(
        -1,
        200,
        53,
        Ceiling,
        "5.7099684971243493e-62",
        "0x1.77d4c76273645E-51#53",
        Greater,
    );
    test(
        -1,
        200,
        53,
        Nearest,
        "5.7099684971243493e-62",
        "0x1.77d4c76273645E-51#53",
        Greater,
    );
    test(
        -1,
        200,
        100,
        Nearest,
        "5.7099684971243490026437400060191e-62",
        "0x1.77d4c76273644a29410f31c68E-51#100",
        Less,
    );
    test(5, 300, 1, Down, "9.8e-91", "0x2.0E-75#1", Less);
    test(5, 300, 1, Up, "2.0e-90", "0x4.0E-75#1", Greater);
    test(5, 300, 1, Floor, "9.8e-91", "0x2.0E-75#1", Less);
    test(5, 300, 1, Ceiling, "2.0e-90", "0x4.0E-75#1", Greater);
    test(5, 300, 1, Nearest, "9.8e-91", "0x2.0E-75#1", Less);
    test(5, 300, 10, Down, "1.2330e-90", "0x2.83E-75#10", Less);
    test(5, 300, 10, Up, "1.2349e-90", "0x2.84E-75#10", Greater);
    test(5, 300, 10, Floor, "1.2330e-90", "0x2.83E-75#10", Less);
    test(5, 300, 10, Ceiling, "1.2349e-90", "0x2.84E-75#10", Greater);
    test(5, 300, 10, Nearest, "1.2330e-90", "0x2.83E-75#10", Less);
    test(
        5,
        300,
        53,
        Down,
        "1.2331064348210500e-90",
        "0x2.830ab5bd30106E-75#53",
        Less,
    );
    test(
        5,
        300,
        53,
        Up,
        "1.2331064348210502e-90",
        "0x2.830ab5bd30108E-75#53",
        Greater,
    );
    test(
        5,
        300,
        53,
        Floor,
        "1.2331064348210500e-90",
        "0x2.830ab5bd30106E-75#53",
        Less,
    );
    test(
        5,
        300,
        53,
        Ceiling,
        "1.2331064348210502e-90",
        "0x2.830ab5bd30108E-75#53",
        Greater,
    );
    test(
        5,
        300,
        53,
        Nearest,
        "1.2331064348210500e-90",
        "0x2.830ab5bd30106E-75#53",
        Less,
    );
    test(
        5,
        300,
        100,
        Nearest,
        "1.2331064348210500019313688799045e-90",
        "0x2.830ab5bd3010604469f0fe1b0E-75#100",
        Greater,
    );
    test(-3, 300, 1, Down, "-4.9e-91", "-0x1.0E-75#1", Greater);
    test(-3, 300, 1, Up, "-9.8e-91", "-0x2.0E-75#1", Less);
    test(-3, 300, 1, Floor, "-9.8e-91", "-0x2.0E-75#1", Less);
    test(-3, 300, 1, Ceiling, "-4.9e-91", "-0x1.0E-75#1", Greater);
    test(-3, 300, 1, Nearest, "-9.8e-91", "-0x2.0E-75#1", Less);
    test(-3, 300, 10, Down, "-7.3924e-91", "-0x1.818E-75#10", Greater);
    test(-3, 300, 10, Up, "-7.4020e-91", "-0x1.820E-75#10", Less);
    test(-3, 300, 10, Floor, "-7.4020e-91", "-0x1.820E-75#10", Less);
    test(
        -3,
        300,
        10,
        Ceiling,
        "-7.3924e-91",
        "-0x1.818E-75#10",
        Greater,
    );
    test(-3, 300, 10, Nearest, "-7.4020e-91", "-0x1.820E-75#10", Less);
    test(
        -3,
        300,
        53,
        Down,
        "-7.3986386089262991e-91",
        "-0x1.81d339d7e9a36E-75#53",
        Greater,
    );
    test(
        -3,
        300,
        53,
        Up,
        "-7.3986386089263002e-91",
        "-0x1.81d339d7e9a37E-75#53",
        Less,
    );
    test(
        -3,
        300,
        53,
        Floor,
        "-7.3986386089263002e-91",
        "-0x1.81d339d7e9a37E-75#53",
        Less,
    );
    test(
        -3,
        300,
        53,
        Ceiling,
        "-7.3986386089262991e-91",
        "-0x1.81d339d7e9a36E-75#53",
        Greater,
    );
    test(
        -3,
        300,
        53,
        Nearest,
        "-7.3986386089263002e-91",
        "-0x1.81d339d7e9a37E-75#53",
        Less,
    );
    test(
        -3,
        300,
        100,
        Nearest,
        "-7.3986386089263000115882132794221e-91",
        "-0x1.81d339d7e9a36cf5d92a32102E-75#100",
        Greater,
    );
    test(7, 1000, 1, Down, "-3.7e-301", "-0x4.0E-250#1", Greater);
    test(7, 1000, 1, Up, "-7.5e-301", "-0x8.0E-250#1", Less);
    test(7, 1000, 1, Floor, "-7.5e-301", "-0x8.0E-250#1", Less);
    test(7, 1000, 1, Ceiling, "-3.7e-301", "-0x4.0E-250#1", Greater);
    test(7, 1000, 1, Nearest, "-3.7e-301", "-0x4.0E-250#1", Greater);
    test(
        7,
        1000,
        10,
        Down,
        "-4.3747e-301",
        "-0x4.b0E-250#10",
        Greater,
    );
    test(7, 1000, 10, Up, "-4.3820e-301", "-0x4.b2E-250#10", Less);
    test(7, 1000, 10, Floor, "-4.3820e-301", "-0x4.b2E-250#10", Less);
    test(
        7,
        1000,
        10,
        Ceiling,
        "-4.3747e-301",
        "-0x4.b0E-250#10",
        Greater,
    );
    test(
        7,
        1000,
        10,
        Nearest,
        "-4.3820e-301",
        "-0x4.b2E-250#10",
        Less,
    );
    test(
        7,
        1000,
        53,
        Down,
        "-4.3804042091405903e-301",
        "-0x4.b19271bf377b0E-250#53",
        Greater,
    );
    test(
        7,
        1000,
        53,
        Up,
        "-4.3804042091405911e-301",
        "-0x4.b19271bf377b4E-250#53",
        Less,
    );
    test(
        7,
        1000,
        53,
        Floor,
        "-4.3804042091405911e-301",
        "-0x4.b19271bf377b4E-250#53",
        Less,
    );
    test(
        7,
        1000,
        53,
        Ceiling,
        "-4.3804042091405903e-301",
        "-0x4.b19271bf377b0E-250#53",
        Greater,
    );
    test(
        7,
        1000,
        53,
        Nearest,
        "-4.3804042091405911e-301",
        "-0x4.b19271bf377b4E-250#53",
        Less,
    );
    test(
        7,
        1000,
        100,
        Nearest,
        "-4.3804042091405911132891649396465e-301",
        "-0x4.b19271bf377b3dd80357392f8E-250#100",
        Greater,
    );
    test(1, 5000, 1, Down, "-3.5e-1506", "-0x8.0E-1251#1", Greater);
    test(1, 5000, 1, Up, "-7.1e-1506", "-0x1.0E-1250#1", Less);
    test(1, 5000, 1, Floor, "-7.1e-1506", "-0x1.0E-1250#1", Less);
    test(1, 5000, 1, Ceiling, "-3.5e-1506", "-0x8.0E-1251#1", Greater);
    test(1, 5000, 1, Nearest, "-3.5e-1506", "-0x8.0E-1251#1", Greater);
    test(
        1,
        5000,
        10,
        Down,
        "-4.8466e-1506",
        "-0xa.f4E-1251#10",
        Greater,
    );
    test(1, 5000, 10, Up, "-4.8535e-1506", "-0xa.f8E-1251#10", Less);
    test(
        1,
        5000,
        10,
        Floor,
        "-4.8535e-1506",
        "-0xa.f8E-1251#10",
        Less,
    );
    test(
        1,
        5000,
        10,
        Ceiling,
        "-4.8466e-1506",
        "-0xa.f4E-1251#10",
        Greater,
    );
    test(
        1,
        5000,
        10,
        Nearest,
        "-4.8535e-1506",
        "-0xa.f8E-1251#10",
        Less,
    );
    test(
        1,
        5000,
        53,
        Down,
        "-4.8535006557356868e-1506",
        "-0xa.f7f9cdfe9c6c0E-1251#53",
        Greater,
    );
    test(
        1,
        5000,
        53,
        Up,
        "-4.8535006557356876e-1506",
        "-0xa.f7f9cdfe9c6c8E-1251#53",
        Less,
    );
    test(
        1,
        5000,
        53,
        Floor,
        "-4.8535006557356876e-1506",
        "-0xa.f7f9cdfe9c6c8E-1251#53",
        Less,
    );
    test(
        1,
        5000,
        53,
        Ceiling,
        "-4.8535006557356868e-1506",
        "-0xa.f7f9cdfe9c6c0E-1251#53",
        Greater,
    );
    test(
        1,
        5000,
        53,
        Nearest,
        "-4.8535006557356868e-1506",
        "-0xa.f7f9cdfe9c6c0E-1251#53",
        Greater,
    );
    test(
        1,
        5000,
        100,
        Nearest,
        "-4.8535006557356870949617714368251e-1506",
        "-0xa.f7f9cdfe9c6c34c306d00827E-1251#100",
        Greater,
    );
    test(1048577, 1000, 1, Down, "4.9e-296", "0x8.0E-246#1", Less);
    test(1048577, 1000, 1, Up, "9.8e-296", "0x1.0E-245#1", Greater);
    test(1048577, 1000, 1, Floor, "4.9e-296", "0x8.0E-246#1", Less);
    test(
        1048577,
        1000,
        1,
        Ceiling,
        "9.8e-296",
        "0x1.0E-245#1",
        Greater,
    );
    test(1048577, 1000, 1, Nearest, "4.9e-296", "0x8.0E-246#1", Less);
    test(
        1048577,
        1000,
        10,
        Down,
        "6.5558e-296",
        "0xa.b8E-246#10",
        Less,
    );
    test(
        1048577,
        1000,
        10,
        Up,
        "6.5654e-296",
        "0xa.bcE-246#10",
        Greater,
    );
    test(
        1048577,
        1000,
        10,
        Floor,
        "6.5558e-296",
        "0xa.b8E-246#10",
        Less,
    );
    test(
        1048577,
        1000,
        10,
        Ceiling,
        "6.5654e-296",
        "0xa.bcE-246#10",
        Greater,
    );
    test(
        1048577,
        1000,
        10,
        Nearest,
        "6.5654e-296",
        "0xa.bcE-246#10",
        Greater,
    );
    test(
        1048577,
        1000,
        53,
        Down,
        "6.5617015777257331e-296",
        "0xa.ba73f8c9fcc70E-246#53",
        Less,
    );
    test(
        1048577,
        1000,
        53,
        Up,
        "6.5617015777257342e-296",
        "0xa.ba73f8c9fcc78E-246#53",
        Greater,
    );
    test(
        1048577,
        1000,
        53,
        Floor,
        "6.5617015777257331e-296",
        "0xa.ba73f8c9fcc70E-246#53",
        Less,
    );
    test(
        1048577,
        1000,
        53,
        Ceiling,
        "6.5617015777257342e-296",
        "0xa.ba73f8c9fcc78E-246#53",
        Greater,
    );
    test(
        1048577,
        1000,
        53,
        Nearest,
        "6.5617015777257342e-296",
        "0xa.ba73f8c9fcc78E-246#53",
        Greater,
    );
    test(
        1048577,
        1000,
        100,
        Nearest,
        "6.5617015777257337254277324355972e-296",
        "0xa.ba73f8c9fcc74c23ebe63a0bE-246#100",
        Less,
    );
    test(
        1048579,
        2000,
        1,
        Down,
        "-2.3e-597",
        "-0x4.0E-496#1",
        Greater,
    );
    test(1048579, 2000, 1, Up, "-4.6e-597", "-0x8.0E-496#1", Less);
    test(1048579, 2000, 1, Floor, "-4.6e-597", "-0x8.0E-496#1", Less);
    test(
        1048579,
        2000,
        1,
        Ceiling,
        "-2.3e-597",
        "-0x4.0E-496#1",
        Greater,
    );
    test(
        1048579,
        2000,
        1,
        Nearest,
        "-2.3e-597",
        "-0x4.0E-496#1",
        Greater,
    );
    test(
        1048579,
        2000,
        10,
        Down,
        "-2.3992e-597",
        "-0x4.34E-496#10",
        Greater,
    );
    test(
        1048579,
        2000,
        10,
        Up,
        "-2.4036e-597",
        "-0x4.36E-496#10",
        Less,
    );
    test(
        1048579,
        2000,
        10,
        Floor,
        "-2.4036e-597",
        "-0x4.36E-496#10",
        Less,
    );
    test(
        1048579,
        2000,
        10,
        Ceiling,
        "-2.3992e-597",
        "-0x4.34E-496#10",
        Greater,
    );
    test(
        1048579,
        2000,
        10,
        Nearest,
        "-2.4036e-597",
        "-0x4.36E-496#10",
        Less,
    );
    test(
        1048579,
        2000,
        53,
        Down,
        "-2.4024850074608730e-597",
        "-0x4.357cad9e8749cE-496#53",
        Greater,
    );
    test(
        1048579,
        2000,
        53,
        Up,
        "-2.4024850074608735e-597",
        "-0x4.357cad9e874a0E-496#53",
        Less,
    );
    test(
        1048579,
        2000,
        53,
        Floor,
        "-2.4024850074608735e-597",
        "-0x4.357cad9e874a0E-496#53",
        Less,
    );
    test(
        1048579,
        2000,
        53,
        Ceiling,
        "-2.4024850074608730e-597",
        "-0x4.357cad9e8749cE-496#53",
        Greater,
    );
    test(
        1048579,
        2000,
        53,
        Nearest,
        "-2.4024850074608735e-597",
        "-0x4.357cad9e874a0E-496#53",
        Less,
    );
    test(
        1048579,
        2000,
        100,
        Nearest,
        "-2.4024850074608735037918121034245e-597",
        "-0x4.357cad9e8749fdce2e7039980E-496#100",
        Less,
    );
    test(
        1,
        100,
        200,
        Nearest,
        "8.4784276603688996439587014693867018775520284138208363242266186e-32",
        "0x1.b839a252049c1114cf98e804177d4c76273644a29410f31c68E-26#200",
        Less,
    );
    test(
        3,
        70,
        300,
        Nearest,
        "-9.84601062862050162789118856206421377120257443264456283773667580368778297869791669066481\
        56997e-22",
        "-0x4.a64f450528ace6f60dd4333e6ecab80c4667247515c03d71a58ba059e79ebdf97f6caad8630E-18#300",
        Less,
    );
    test(
        -1,
        70,
        600,
        Nearest,
        "3.282003542873500542630396187354737923734191948911604340104315228439512001212817575867967\
        731372313070616956744414466712260078477462741735637350786933057556923781236738926841984996\
        8371e-22",
        "0x1.8cc51701b839a252049c1114cf98e804177cad9cc4d88b22f20ac197d6d5a48d3d31b7c01e756914c1809\
        275c428c08a2d0d186e3b4b633dc034a552759a2dcad5da7752b6a6b5ace917c6E-18#600",
        Greater,
    );
    test(
        1,
        90,
        1000,
        Nearest,
        "2.903855973979360333879556990387591995385154884042586741146238433982103151160615610356893\
        779558205091720450596615978798433445783511684248972731919117289147467475007779984454335221\
        093892643831504338347538685940013443056453075556384505237755060214145095216776145950987187\
        62762754249439112814650591948176017e-28",
        "0x1.701b839a252049c1114cf98e804177d4c76273644a294090580192590e69e98ca6b8d595da3bdb8f1b86c\
        a16b75da5809b6f06368aafa24eb458c65acd365c322501df79534d51ff0b1be994c00ab59e870160af8a68978\
        6d11c4f5de33f2de9ccd39f5e38cf702376a9c68d24864b49903a4060073c54b44eae67107cE-23#1000",
        Less,
    );
}

// Inputs within 2^(-2^30) of an odd multiple of pi/2, whose cosines underflow. Constructing an
// input and each call computes pi to about 2^30 bits (~6 minutes each), so this test is slow even
// in release mode; the two calls cover both signs, rounding to zero and rounding away from it, and
// `Nearest` and a directed mode. Slow enough to dominate a test run, and its result does not depend
// on the limb width, so it runs only in the 64-bit-limb configuration.
#[cfg(not(feature = "32_bit_limbs"))]
#[test]
fn test_cos_underflow() {
    let p = (1u64 << 30) + 64;
    // 2^(-2^30), the smallest positive `Float`, at the output precision
    let min_positive = Float::one_prec(10) >> (1u64 << 30);
    assert_eq!(min_positive.get_exponent(), Some(Float::MIN_EXPONENT));
    // pi rounded down: x_lo < pi/2, so cos(x_lo) is positive, and at most half an ulp of x_lo,
    // 2^(-2^30 - 64), in magnitude
    let mut pi = Float::pi_prec_round(p, Floor).0;
    let x_lo = &pi >> 1u32;
    let (c, o) = x_lo.cos_prec_round_ref(10, Ceiling);
    assert_eq!(ComparableFloatRef(&c), ComparableFloatRef(&min_positive));
    assert_eq!(o, Greater);
    // pi rounded up: x_hi > pi/2, so cos(x_hi) is negative
    pi.increment();
    let x_hi = pi >> 1u32;
    let (c, o) = x_hi.cos_prec_round_ref(10, Nearest);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::NEGATIVE_ZERO));
    assert_eq!(o, Greater);
}

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_cos() {
    fn test<T: PrimitiveFloat>(x: T, out: T)
    where
        Float: From<T> + PartialOrd<T>,
        for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
    {
        assert_eq!(NiceFloat(primitive_float_cos(x)), NiceFloat(out));
    }
    test::<f32>(f32::NAN, f32::NAN);
    test::<f32>(f32::INFINITY, f32::NAN);
    test::<f32>(f32::NEGATIVE_INFINITY, f32::NAN);
    test::<f32>(0.0, 1.0);
    test::<f32>(-0.0, 1.0);
    test::<f32>(1.0, 0.5403023);
    test::<f32>(-1.0, 0.5403023);
    test::<f32>(0.5, 0.87758255);
    test::<f32>(-0.5, 0.87758255);
    test::<f32>(2.0, -0.41614684);
    test::<f32>(-2.0, -0.41614684);
    test::<f32>(core::f32::consts::PI, -1.0);
    test::<f32>(core::f32::consts::FRAC_PI_2, -4.371139e-8);
    test::<f32>(core::f32::consts::E, -0.91173387);
    test::<f32>(100.0, 0.8623189);
    test::<f32>(1.0e10, 0.87311965);
    test::<f32>(1.0e30, -0.6116048);
    test::<f32>(3.4028235e38, 0.853021);
    test::<f32>(1.1754944e-38, 1.0);

    test::<f64>(f64::NAN, f64::NAN);
    test::<f64>(f64::INFINITY, f64::NAN);
    test::<f64>(f64::NEGATIVE_INFINITY, f64::NAN);
    test::<f64>(0.0, 1.0);
    test::<f64>(-0.0, 1.0);
    test::<f64>(1.0, 0.5403023058681398);
    test::<f64>(-1.0, 0.5403023058681398);
    test::<f64>(0.5, 0.8775825618903728);
    test::<f64>(-0.5, 0.8775825618903728);
    test::<f64>(2.0, -0.4161468365471424);
    test::<f64>(-2.0, -0.4161468365471424);
    test::<f64>(core::f64::consts::PI, -1.0);
    test::<f64>(core::f64::consts::FRAC_PI_2, 6.123233995736766e-17);
    test::<f64>(core::f64::consts::E, -0.9117339147869651);
    test::<f64>(100.0, 0.8623188722876839);
    test::<f64>(1.0e10, 0.873119622676856);
    test::<f64>(1.0e100, 0.9247242387519338);
    test::<f64>(1.0e300, -0.5753861119575491);
    test::<f64>(1.7976931348623157e308, -0.9999876894265599);
    test::<f64>(2.2250738585072014e-308, 1.0);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_cos_properties_helper<T: PrimitiveFloat>()
where
    Float: From<T> + PartialOrd<T>,
    for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
{
    primitive_float_gen::<T>().test_properties(|x| {
        let c = primitive_float_cos(x);
        // cos is NaN exactly for NaN and infinite inputs, and otherwise lies in [-1, 1].
        assert_eq!(c.is_nan(), !x.is_finite());
        if x.is_finite() {
            assert!(c >= T::NEGATIVE_ONE && c <= T::ONE);
            // cos is even
            assert_eq!(NiceFloat(primitive_float_cos(-x)), NiceFloat(c));
            // the result is the correctly rounded cosine, as computed by MPFR at the same precision
            let rug_x = rug::Float::with_val(
                u32::exact_from(T::MANTISSA_WIDTH + 1),
                &rug::Float::exact_from(&Float::from(x)),
            );
            let rug_c: T = T::exact_from(&<Float as From<&rug::Float>>::from(&rug_x.cos()));
            assert_eq!(NiceFloat(rug_c), NiceFloat(c));
        }
    });
}

#[test]
fn primitive_float_cos_properties() {
    apply_fn_to_primitive_floats!(primitive_float_cos_properties_helper);
}

#[test]
fn test_cos_rational_prec() {
    let test = |s, prec, out: &str, out_hex: &str, out_o| {
        let x = Rational::from_str(s).unwrap();

        let (c, o) = Float::cos_rational_prec(x.clone(), prec);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, out_o);

        let (c, o) = Float::cos_rational_prec_ref(&x, prec);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, out_o);
    };
    test("0", 1, "1.0", "0x1.0#1", Equal);
    test("0", 5, "1.00", "0x1.0#5", Equal);
    test("0", 10, "1.0000", "0x1.000#10", Equal);
    test("0", 20, "1.0000000", "0x1.00000#20", Equal);
    test("0", 53, "1.0000000000000000", "0x1.0000000000000#53", Equal);
    test(
        "0",
        100,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Equal,
    );
    test("1", 1, "0.50", "0x0.8#1", Less);
    test("1", 5, "0.531", "0x0.88#5", Less);
    test("1", 10, "0.54004", "0x0.8a4#10", Less);
    test("1", 20, "0.54030228", "0x0.8a514#20", Less);
    test(
        "1",
        53,
        "0.54030230586813977",
        "0x0.8a51407da83460#53",
        Greater,
    );
    test(
        "1",
        100,
        "0.54030230586813971740093660744335",
        "0x0.8a51407da8345c91c2466d977#100",
        Greater,
    );
    test("-1", 1, "0.50", "0x0.8#1", Less);
    test("-1", 5, "0.531", "0x0.88#5", Less);
    test("-1", 10, "0.54004", "0x0.8a4#10", Less);
    test("-1", 20, "0.54030228", "0x0.8a514#20", Less);
    test(
        "-1",
        53,
        "0.54030230586813977",
        "0x0.8a51407da83460#53",
        Greater,
    );
    test(
        "-1",
        100,
        "0.54030230586813971740093660744335",
        "0x0.8a51407da8345c91c2466d977#100",
        Greater,
    );
    test("1/2", 1, "1.0", "0x1.0#1", Greater);
    test("1/2", 5, "0.875", "0x0.e0#5", Less);
    test("1/2", 10, "0.87793", "0x0.e0c#10", Greater);
    test("1/2", 20, "0.87758255", "0x0.e0a94#20", Less);
    test(
        "1/2",
        53,
        "0.87758256189037276",
        "0x0.e0a94032dbea80#53",
        Greater,
    );
    test(
        "1/2",
        100,
        "0.87758256189037271611628158260408",
        "0x0.e0a94032dbea7cedbddd9da30#100",
        Greater,
    );
    test("1/3", 1, "1.0", "0x1.0#1", Greater);
    test("1/3", 5, "0.938", "0x0.f0#5", Less);
    test("1/3", 10, "0.94531", "0x0.f20#10", Greater);
    test("1/3", 20, "0.94495678", "0x0.f1e8b#20", Less);
    test(
        "1/3",
        53,
        "0.94495694631473770",
        "0x0.f1e8b2cc8cc168#53",
        Greater,
    );
    test(
        "1/3",
        100,
        "0.94495694631473766438828400767583",
        "0x0.f1e8b2cc8cc1656b6998d964d#100",
        Less,
    );
    test("-1/3", 1, "1.0", "0x1.0#1", Greater);
    test("-1/3", 5, "0.938", "0x0.f0#5", Less);
    test("-1/3", 10, "0.94531", "0x0.f20#10", Greater);
    test("-1/3", 20, "0.94495678", "0x0.f1e8b#20", Less);
    test(
        "-1/3",
        53,
        "0.94495694631473770",
        "0x0.f1e8b2cc8cc168#53",
        Greater,
    );
    test(
        "-1/3",
        100,
        "0.94495694631473766438828400767583",
        "0x0.f1e8b2cc8cc1656b6998d964d#100",
        Less,
    );
    test("3/5", 1, "1.0", "0x1.0#1", Greater);
    test("3/5", 10, "0.82520", "0x0.d34#10", Less);
    test(
        "3/5",
        53,
        "0.82533561490967833",
        "0x0.d34931e242d8a8#53",
        Greater,
    );
    test(
        "3/5",
        100,
        "0.82533561490967829724095249895546",
        "0x0.d34931e242d8a5cb448dccbdf#100",
        Greater,
    );
    test("22/7", 1, "-1.0", "-0x1.0#1", Less);
    test("22/7", 5, "-1.00", "-0x1.0#5", Less);
    test("22/7", 10, "-1.0000", "-0x1.000#10", Less);
    test("22/7", 20, "-0.99999905", "-0x0.fffff#20", Greater);
    test(
        "22/7",
        53,
        "-0.99999920053355296",
        "-0x0.fffff296515870#53",
        Less,
    );
    test(
        "22/7",
        100,
        "-0.99999920053355290326833573965634",
        "-0x0.fffff29651586c28bc01f9fb2#100",
        Greater,
    );
    test("-22/7", 1, "-1.0", "-0x1.0#1", Less);
    test("-22/7", 5, "-1.00", "-0x1.0#5", Less);
    test("-22/7", 10, "-1.0000", "-0x1.000#10", Less);
    test("-22/7", 20, "-0.99999905", "-0x0.fffff#20", Greater);
    test(
        "-22/7",
        53,
        "-0.99999920053355296",
        "-0x0.fffff296515870#53",
        Less,
    );
    test(
        "-22/7",
        100,
        "-0.99999920053355290326833573965634",
        "-0x0.fffff29651586c28bc01f9fb2#100",
        Greater,
    );
    test("355/113", 1, "-1.0", "-0x1.0#1", Less);
    test("355/113", 5, "-1.00", "-0x1.0#5", Less);
    test("355/113", 10, "-1.0000", "-0x1.000#10", Less);
    test("355/113", 20, "-1.0000000", "-0x1.00000#20", Less);
    test(
        "355/113",
        53,
        "-0.99999999999996447",
        "-0x0.fffffffffff600#53",
        Less,
    );
    test(
        "355/113",
        100,
        "-0.99999999999996441843371693431264",
        "-0x0.fffffffffff5fc13f3fa12934#100",
        Greater,
    );
    test("3", 1, "-1.0", "-0x1.0#1", Less);
    test("3", 5, "-1.00", "-0x1.0#5", Less);
    test("3", 10, "-0.99023", "-0x0.fd8#10", Less);
    test("3", 20, "-0.98999214", "-0x0.fd702#20", Greater);
    test(
        "3",
        53,
        "-0.98999249660044542",
        "-0x0.fd7025f42f2e90#53",
        Greater,
    );
    test(
        "3",
        100,
        "-0.98999249660044545727157279473154",
        "-0x0.fd7025f42f2e9307dff82fdf7#100",
        Less,
    );
    test("100", 1, "1.0", "0x1.0#1", Greater);
    test("100", 5, "0.875", "0x0.e0#5", Greater);
    test("100", 10, "0.86230", "0x0.dcc#10", Less);
    test("100", 20, "0.86231899", "0x0.dcc0f#20", Greater);
    test(
        "100",
        53,
        "0.86231887228768389",
        "0x0.dcc0edfb32fef8#53",
        Less,
    );
    test(
        "100",
        100,
        "0.86231887228768393410193851395099",
        "0x0.dcc0edfb32fefb1fa19b9b30c#100",
        Greater,
    );
    test("1000000", 1, "1.0", "0x1.0#1", Greater);
    test("1000000", 5, "0.938", "0x0.f0#5", Greater);
    test("1000000", 10, "0.93652", "0x0.efc#10", Less);
    test("1000000", 20, "0.93675232", "0x0.efcf0#20", Greater);
    test(
        "1000000",
        53,
        "0.93675212753314474",
        "0x0.efcefcc8369960#53",
        Less,
    );
    test(
        "1000000",
        100,
        "0.93675212753314478693853253507492",
        "0x0.efcefcc836996357644d418cd#100",
        Greater,
    );
    test("1/1000000", 1, "1.0", "0x1.0#1", Greater);
    test("1/1000000", 5, "1.00", "0x1.0#5", Greater);
    test("1/1000000", 10, "1.0000", "0x1.000#10", Greater);
    test("1/1000000", 20, "1.0000000", "0x1.00000#20", Greater);
    test(
        "1/1000000",
        53,
        "0.99999999999949996",
        "0x0.ffffffffff7340#53",
        Less,
    );
    test(
        "1/1000000",
        100,
        "0.99999999999950000000000004166665",
        "0x0.ffffffffff734333f690bc5c6#100",
        Less,
    );
    test("-1/1000000", 1, "1.0", "0x1.0#1", Greater);
    test("-1/1000000", 5, "1.00", "0x1.0#5", Greater);
    test("-1/1000000", 10, "1.0000", "0x1.000#10", Greater);
    test("-1/1000000", 20, "1.0000000", "0x1.00000#20", Greater);
    test(
        "-1/1000000",
        53,
        "0.99999999999949996",
        "0x0.ffffffffff7340#53",
        Less,
    );
    test(
        "-1/1000000",
        100,
        "0.99999999999950000000000004166665",
        "0x0.ffffffffff734333f690bc5c6#100",
        Less,
    );
    test("1/1000000000000000000000000", 1, "1.0", "0x1.0#1", Greater);
    test("1/1000000000000000000000000", 5, "1.00", "0x1.0#5", Greater);
    test(
        "1/1000000000000000000000000",
        10,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        20,
        "1.0000000",
        "0x1.00000#20",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        53,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        100,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        1,
        "9.9e-32",
        "0x2.0E-26#1",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        5,
        "8.63e-32",
        "0x1.cE-26#5",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        10,
        "8.4741e-32",
        "0x1.b80E-26#10",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        20,
        "8.4784270e-32",
        "0x1.b839aE-26#20",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        53,
        "8.4784276603688996e-32",
        "0x1.b839a252049c1E-26#53",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        100,
        "8.4784276603688996439587014693888e-32",
        "0x1.b839a252049c1114cf98e8042E-26#100",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        1,
        "-2.0e-31",
        "-0x4.0E-26#1",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        5,
        "-2.59e-31",
        "-0x5.4E-26#5",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        10,
        "-2.5422e-31",
        "-0x5.28E-26#10",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        20,
        "-2.5435290e-31",
        "-0x5.28ad0E-26#20",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        53,
        "-2.5435282981106700e-31",
        "-0x5.28ace6f60dd44E-26#53",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        100,
        "-2.5435282981106698931876104408174e-31",
        "-0x5.28ace6f60dd4333e6ecab80c8E-26#100",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        1,
        "-1.0",
        "-0x1.0#1",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        5,
        "-1.00",
        "-0x1.0#5",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        10,
        "-1.0000",
        "-0x1.000#10",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        20,
        "-1.0000000",
        "-0x1.00000#20",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        53,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        100,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        1,
        "9.9e-32",
        "0x2.0E-26#1",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        5,
        "8.63e-32",
        "0x1.cE-26#5",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        10,
        "8.4741e-32",
        "0x1.b80E-26#10",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        20,
        "8.4784270e-32",
        "0x1.b839aE-26#20",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        53,
        "8.4784276603688996e-32",
        "0x1.b839a252049c1E-26#53",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        100,
        "8.4784276603688996439587014693888e-32",
        "0x1.b839a252049c1114cf98e8042E-26#100",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        1,
        "0.50",
        "0x0.8#1",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        5,
        "0.484",
        "0x0.7c#5",
        Less,
    );
    test(
        "1267650600228229401496703205376",
        10,
        "0.48926",
        "0x0.7d4#10",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        20,
        "0.48917866",
        "0x0.7d3ad0#20",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        53,
        "0.48917865697472146",
        "0x0.7d3acffd9b8db4#53",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        100,
        "0.48917865697472144990578930875139",
        "0x0.7d3acffd9b8db34b71d86c7ff0#100",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        1,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        5,
        "1.00",
        "0x1.0#5",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        20,
        "1.0000000",
        "0x1.00000#20",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        53,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        100,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
}

// The inputs include dyadic approximations of pi/2, 3pi/2, and pi (from `Float::pi_prec(100)`),
// which take the near-zero path, as well as 2^100, which is reduced modulo 2 pi, and values small
// enough to round to 1.
#[test]
fn test_cos_rational_prec_round() {
    let test = |s, prec, rm, out: &str, out_hex: &str, out_o| {
        let x = Rational::from_str(s).unwrap();

        let (c, o) = Float::cos_rational_prec_round(x.clone(), prec, rm);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, out_o);

        let (c, o) = Float::cos_rational_prec_round_ref(&x, prec, rm);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, out_o);
    };
    test("0", 1, Down, "1.0", "0x1.0#1", Equal);
    test("0", 1, Up, "1.0", "0x1.0#1", Equal);
    test("0", 1, Floor, "1.0", "0x1.0#1", Equal);
    test("0", 1, Ceiling, "1.0", "0x1.0#1", Equal);
    test("0", 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("0", 1, Exact, "1.0", "0x1.0#1", Equal);
    test("0", 5, Nearest, "1.00", "0x1.0#5", Equal);
    test("0", 10, Down, "1.0000", "0x1.000#10", Equal);
    test("0", 10, Up, "1.0000", "0x1.000#10", Equal);
    test("0", 10, Floor, "1.0000", "0x1.000#10", Equal);
    test("0", 10, Ceiling, "1.0000", "0x1.000#10", Equal);
    test("0", 10, Nearest, "1.0000", "0x1.000#10", Equal);
    test("0", 10, Exact, "1.0000", "0x1.000#10", Equal);
    test("0", 20, Nearest, "1.0000000", "0x1.00000#20", Equal);
    test(
        "0",
        53,
        Down,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "0",
        53,
        Up,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "0",
        53,
        Floor,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "0",
        53,
        Ceiling,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "0",
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "0",
        53,
        Exact,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "0",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Equal,
    );
    test("1", 1, Down, "0.50", "0x0.8#1", Less);
    test("1", 1, Up, "1.0", "0x1.0#1", Greater);
    test("1", 1, Floor, "0.50", "0x0.8#1", Less);
    test("1", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("1", 1, Nearest, "0.50", "0x0.8#1", Less);
    test("1", 5, Nearest, "0.531", "0x0.88#5", Less);
    test("1", 10, Down, "0.54004", "0x0.8a4#10", Less);
    test("1", 10, Up, "0.54102", "0x0.8a8#10", Greater);
    test("1", 10, Floor, "0.54004", "0x0.8a4#10", Less);
    test("1", 10, Ceiling, "0.54102", "0x0.8a8#10", Greater);
    test("1", 10, Nearest, "0.54004", "0x0.8a4#10", Less);
    test("1", 20, Nearest, "0.54030228", "0x0.8a514#20", Less);
    test(
        "1",
        53,
        Down,
        "0.54030230586813965",
        "0x0.8a51407da83458#53",
        Less,
    );
    test(
        "1",
        53,
        Up,
        "0.54030230586813977",
        "0x0.8a51407da83460#53",
        Greater,
    );
    test(
        "1",
        53,
        Floor,
        "0.54030230586813965",
        "0x0.8a51407da83458#53",
        Less,
    );
    test(
        "1",
        53,
        Ceiling,
        "0.54030230586813977",
        "0x0.8a51407da83460#53",
        Greater,
    );
    test(
        "1",
        53,
        Nearest,
        "0.54030230586813977",
        "0x0.8a51407da83460#53",
        Greater,
    );
    test(
        "1",
        100,
        Nearest,
        "0.54030230586813971740093660744335",
        "0x0.8a51407da8345c91c2466d977#100",
        Greater,
    );
    test("-1", 1, Down, "0.50", "0x0.8#1", Less);
    test("-1", 1, Up, "1.0", "0x1.0#1", Greater);
    test("-1", 1, Floor, "0.50", "0x0.8#1", Less);
    test("-1", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("-1", 1, Nearest, "0.50", "0x0.8#1", Less);
    test("-1", 5, Nearest, "0.531", "0x0.88#5", Less);
    test("-1", 10, Down, "0.54004", "0x0.8a4#10", Less);
    test("-1", 10, Up, "0.54102", "0x0.8a8#10", Greater);
    test("-1", 10, Floor, "0.54004", "0x0.8a4#10", Less);
    test("-1", 10, Ceiling, "0.54102", "0x0.8a8#10", Greater);
    test("-1", 10, Nearest, "0.54004", "0x0.8a4#10", Less);
    test("-1", 20, Nearest, "0.54030228", "0x0.8a514#20", Less);
    test(
        "-1",
        53,
        Down,
        "0.54030230586813965",
        "0x0.8a51407da83458#53",
        Less,
    );
    test(
        "-1",
        53,
        Up,
        "0.54030230586813977",
        "0x0.8a51407da83460#53",
        Greater,
    );
    test(
        "-1",
        53,
        Floor,
        "0.54030230586813965",
        "0x0.8a51407da83458#53",
        Less,
    );
    test(
        "-1",
        53,
        Ceiling,
        "0.54030230586813977",
        "0x0.8a51407da83460#53",
        Greater,
    );
    test(
        "-1",
        53,
        Nearest,
        "0.54030230586813977",
        "0x0.8a51407da83460#53",
        Greater,
    );
    test(
        "-1",
        100,
        Nearest,
        "0.54030230586813971740093660744335",
        "0x0.8a51407da8345c91c2466d977#100",
        Greater,
    );
    test("1/2", 1, Down, "0.50", "0x0.8#1", Less);
    test("1/2", 1, Up, "1.0", "0x1.0#1", Greater);
    test("1/2", 1, Floor, "0.50", "0x0.8#1", Less);
    test("1/2", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("1/2", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1/2", 5, Nearest, "0.875", "0x0.e0#5", Less);
    test("1/2", 10, Down, "0.87695", "0x0.e08#10", Less);
    test("1/2", 10, Up, "0.87793", "0x0.e0c#10", Greater);
    test("1/2", 10, Floor, "0.87695", "0x0.e08#10", Less);
    test("1/2", 10, Ceiling, "0.87793", "0x0.e0c#10", Greater);
    test("1/2", 10, Nearest, "0.87793", "0x0.e0c#10", Greater);
    test("1/2", 20, Nearest, "0.87758255", "0x0.e0a94#20", Less);
    test(
        "1/2",
        53,
        Down,
        "0.87758256189037265",
        "0x0.e0a94032dbea78#53",
        Less,
    );
    test(
        "1/2",
        53,
        Up,
        "0.87758256189037276",
        "0x0.e0a94032dbea80#53",
        Greater,
    );
    test(
        "1/2",
        53,
        Floor,
        "0.87758256189037265",
        "0x0.e0a94032dbea78#53",
        Less,
    );
    test(
        "1/2",
        53,
        Ceiling,
        "0.87758256189037276",
        "0x0.e0a94032dbea80#53",
        Greater,
    );
    test(
        "1/2",
        53,
        Nearest,
        "0.87758256189037276",
        "0x0.e0a94032dbea80#53",
        Greater,
    );
    test(
        "1/2",
        100,
        Nearest,
        "0.87758256189037271611628158260408",
        "0x0.e0a94032dbea7cedbddd9da30#100",
        Greater,
    );
    test("1/3", 1, Down, "0.50", "0x0.8#1", Less);
    test("1/3", 1, Up, "1.0", "0x1.0#1", Greater);
    test("1/3", 1, Floor, "0.50", "0x0.8#1", Less);
    test("1/3", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("1/3", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1/3", 5, Nearest, "0.938", "0x0.f0#5", Less);
    test("1/3", 10, Down, "0.94434", "0x0.f1c#10", Less);
    test("1/3", 10, Up, "0.94531", "0x0.f20#10", Greater);
    test("1/3", 10, Floor, "0.94434", "0x0.f1c#10", Less);
    test("1/3", 10, Ceiling, "0.94531", "0x0.f20#10", Greater);
    test("1/3", 10, Nearest, "0.94531", "0x0.f20#10", Greater);
    test("1/3", 20, Nearest, "0.94495678", "0x0.f1e8b#20", Less);
    test(
        "1/3",
        53,
        Down,
        "0.94495694631473759",
        "0x0.f1e8b2cc8cc160#53",
        Less,
    );
    test(
        "1/3",
        53,
        Up,
        "0.94495694631473770",
        "0x0.f1e8b2cc8cc168#53",
        Greater,
    );
    test(
        "1/3",
        53,
        Floor,
        "0.94495694631473759",
        "0x0.f1e8b2cc8cc160#53",
        Less,
    );
    test(
        "1/3",
        53,
        Ceiling,
        "0.94495694631473770",
        "0x0.f1e8b2cc8cc168#53",
        Greater,
    );
    test(
        "1/3",
        53,
        Nearest,
        "0.94495694631473770",
        "0x0.f1e8b2cc8cc168#53",
        Greater,
    );
    test(
        "1/3",
        100,
        Nearest,
        "0.94495694631473766438828400767583",
        "0x0.f1e8b2cc8cc1656b6998d964d#100",
        Less,
    );
    test("-1/3", 1, Down, "0.50", "0x0.8#1", Less);
    test("-1/3", 1, Up, "1.0", "0x1.0#1", Greater);
    test("-1/3", 1, Floor, "0.50", "0x0.8#1", Less);
    test("-1/3", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("-1/3", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("-1/3", 5, Nearest, "0.938", "0x0.f0#5", Less);
    test("-1/3", 10, Down, "0.94434", "0x0.f1c#10", Less);
    test("-1/3", 10, Up, "0.94531", "0x0.f20#10", Greater);
    test("-1/3", 10, Floor, "0.94434", "0x0.f1c#10", Less);
    test("-1/3", 10, Ceiling, "0.94531", "0x0.f20#10", Greater);
    test("-1/3", 10, Nearest, "0.94531", "0x0.f20#10", Greater);
    test("-1/3", 20, Nearest, "0.94495678", "0x0.f1e8b#20", Less);
    test(
        "-1/3",
        53,
        Down,
        "0.94495694631473759",
        "0x0.f1e8b2cc8cc160#53",
        Less,
    );
    test(
        "-1/3",
        53,
        Up,
        "0.94495694631473770",
        "0x0.f1e8b2cc8cc168#53",
        Greater,
    );
    test(
        "-1/3",
        53,
        Floor,
        "0.94495694631473759",
        "0x0.f1e8b2cc8cc160#53",
        Less,
    );
    test(
        "-1/3",
        53,
        Ceiling,
        "0.94495694631473770",
        "0x0.f1e8b2cc8cc168#53",
        Greater,
    );
    test(
        "-1/3",
        53,
        Nearest,
        "0.94495694631473770",
        "0x0.f1e8b2cc8cc168#53",
        Greater,
    );
    test(
        "-1/3",
        100,
        Nearest,
        "0.94495694631473766438828400767583",
        "0x0.f1e8b2cc8cc1656b6998d964d#100",
        Less,
    );
    test("3/5", 1, Down, "0.50", "0x0.8#1", Less);
    test("3/5", 1, Up, "1.0", "0x1.0#1", Greater);
    test("3/5", 1, Floor, "0.50", "0x0.8#1", Less);
    test("3/5", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("3/5", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("3/5", 10, Down, "0.82520", "0x0.d34#10", Less);
    test("3/5", 10, Up, "0.82617", "0x0.d38#10", Greater);
    test("3/5", 10, Floor, "0.82520", "0x0.d34#10", Less);
    test("3/5", 10, Ceiling, "0.82617", "0x0.d38#10", Greater);
    test("3/5", 10, Nearest, "0.82520", "0x0.d34#10", Less);
    test(
        "3/5",
        53,
        Down,
        "0.82533561490967822",
        "0x0.d34931e242d8a0#53",
        Less,
    );
    test(
        "3/5",
        53,
        Up,
        "0.82533561490967833",
        "0x0.d34931e242d8a8#53",
        Greater,
    );
    test(
        "3/5",
        53,
        Floor,
        "0.82533561490967822",
        "0x0.d34931e242d8a0#53",
        Less,
    );
    test(
        "3/5",
        53,
        Ceiling,
        "0.82533561490967833",
        "0x0.d34931e242d8a8#53",
        Greater,
    );
    test(
        "3/5",
        53,
        Nearest,
        "0.82533561490967833",
        "0x0.d34931e242d8a8#53",
        Greater,
    );
    test(
        "3/5",
        100,
        Nearest,
        "0.82533561490967829724095249895546",
        "0x0.d34931e242d8a5cb448dccbdf#100",
        Greater,
    );
    test("22/7", 1, Down, "-0.50", "-0x0.8#1", Greater);
    test("22/7", 1, Up, "-1.0", "-0x1.0#1", Less);
    test("22/7", 1, Floor, "-1.0", "-0x1.0#1", Less);
    test("22/7", 1, Ceiling, "-0.50", "-0x0.8#1", Greater);
    test("22/7", 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test("22/7", 5, Nearest, "-1.00", "-0x1.0#5", Less);
    test("22/7", 10, Down, "-0.99902", "-0x0.ffc#10", Greater);
    test("22/7", 10, Up, "-1.0000", "-0x1.000#10", Less);
    test("22/7", 10, Floor, "-1.0000", "-0x1.000#10", Less);
    test("22/7", 10, Ceiling, "-0.99902", "-0x0.ffc#10", Greater);
    test("22/7", 10, Nearest, "-1.0000", "-0x1.000#10", Less);
    test("22/7", 20, Nearest, "-0.99999905", "-0x0.fffff#20", Greater);
    test(
        "22/7",
        53,
        Down,
        "-0.99999920053355285",
        "-0x0.fffff296515868#53",
        Greater,
    );
    test(
        "22/7",
        53,
        Up,
        "-0.99999920053355296",
        "-0x0.fffff296515870#53",
        Less,
    );
    test(
        "22/7",
        53,
        Floor,
        "-0.99999920053355296",
        "-0x0.fffff296515870#53",
        Less,
    );
    test(
        "22/7",
        53,
        Ceiling,
        "-0.99999920053355285",
        "-0x0.fffff296515868#53",
        Greater,
    );
    test(
        "22/7",
        53,
        Nearest,
        "-0.99999920053355296",
        "-0x0.fffff296515870#53",
        Less,
    );
    test(
        "22/7",
        100,
        Nearest,
        "-0.99999920053355290326833573965634",
        "-0x0.fffff29651586c28bc01f9fb2#100",
        Greater,
    );
    test("-22/7", 1, Down, "-0.50", "-0x0.8#1", Greater);
    test("-22/7", 1, Up, "-1.0", "-0x1.0#1", Less);
    test("-22/7", 1, Floor, "-1.0", "-0x1.0#1", Less);
    test("-22/7", 1, Ceiling, "-0.50", "-0x0.8#1", Greater);
    test("-22/7", 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test("-22/7", 5, Nearest, "-1.00", "-0x1.0#5", Less);
    test("-22/7", 10, Down, "-0.99902", "-0x0.ffc#10", Greater);
    test("-22/7", 10, Up, "-1.0000", "-0x1.000#10", Less);
    test("-22/7", 10, Floor, "-1.0000", "-0x1.000#10", Less);
    test("-22/7", 10, Ceiling, "-0.99902", "-0x0.ffc#10", Greater);
    test("-22/7", 10, Nearest, "-1.0000", "-0x1.000#10", Less);
    test(
        "-22/7",
        20,
        Nearest,
        "-0.99999905",
        "-0x0.fffff#20",
        Greater,
    );
    test(
        "-22/7",
        53,
        Down,
        "-0.99999920053355285",
        "-0x0.fffff296515868#53",
        Greater,
    );
    test(
        "-22/7",
        53,
        Up,
        "-0.99999920053355296",
        "-0x0.fffff296515870#53",
        Less,
    );
    test(
        "-22/7",
        53,
        Floor,
        "-0.99999920053355296",
        "-0x0.fffff296515870#53",
        Less,
    );
    test(
        "-22/7",
        53,
        Ceiling,
        "-0.99999920053355285",
        "-0x0.fffff296515868#53",
        Greater,
    );
    test(
        "-22/7",
        53,
        Nearest,
        "-0.99999920053355296",
        "-0x0.fffff296515870#53",
        Less,
    );
    test(
        "-22/7",
        100,
        Nearest,
        "-0.99999920053355290326833573965634",
        "-0x0.fffff29651586c28bc01f9fb2#100",
        Greater,
    );
    test("355/113", 1, Down, "-0.50", "-0x0.8#1", Greater);
    test("355/113", 1, Up, "-1.0", "-0x1.0#1", Less);
    test("355/113", 1, Floor, "-1.0", "-0x1.0#1", Less);
    test("355/113", 1, Ceiling, "-0.50", "-0x0.8#1", Greater);
    test("355/113", 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test("355/113", 5, Nearest, "-1.00", "-0x1.0#5", Less);
    test("355/113", 10, Down, "-0.99902", "-0x0.ffc#10", Greater);
    test("355/113", 10, Up, "-1.0000", "-0x1.000#10", Less);
    test("355/113", 10, Floor, "-1.0000", "-0x1.000#10", Less);
    test("355/113", 10, Ceiling, "-0.99902", "-0x0.ffc#10", Greater);
    test("355/113", 10, Nearest, "-1.0000", "-0x1.000#10", Less);
    test("355/113", 20, Nearest, "-1.0000000", "-0x1.00000#20", Less);
    test(
        "355/113",
        53,
        Down,
        "-0.99999999999996436",
        "-0x0.fffffffffff5f8#53",
        Greater,
    );
    test(
        "355/113",
        53,
        Up,
        "-0.99999999999996447",
        "-0x0.fffffffffff600#53",
        Less,
    );
    test(
        "355/113",
        53,
        Floor,
        "-0.99999999999996447",
        "-0x0.fffffffffff600#53",
        Less,
    );
    test(
        "355/113",
        53,
        Ceiling,
        "-0.99999999999996436",
        "-0x0.fffffffffff5f8#53",
        Greater,
    );
    test(
        "355/113",
        53,
        Nearest,
        "-0.99999999999996447",
        "-0x0.fffffffffff600#53",
        Less,
    );
    test(
        "355/113",
        100,
        Nearest,
        "-0.99999999999996441843371693431264",
        "-0x0.fffffffffff5fc13f3fa12934#100",
        Greater,
    );
    test("3", 1, Down, "-0.50", "-0x0.8#1", Greater);
    test("3", 1, Up, "-1.0", "-0x1.0#1", Less);
    test("3", 1, Floor, "-1.0", "-0x1.0#1", Less);
    test("3", 1, Ceiling, "-0.50", "-0x0.8#1", Greater);
    test("3", 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test("3", 5, Nearest, "-1.00", "-0x1.0#5", Less);
    test("3", 10, Down, "-0.98926", "-0x0.fd4#10", Greater);
    test("3", 10, Up, "-0.99023", "-0x0.fd8#10", Less);
    test("3", 10, Floor, "-0.99023", "-0x0.fd8#10", Less);
    test("3", 10, Ceiling, "-0.98926", "-0x0.fd4#10", Greater);
    test("3", 10, Nearest, "-0.99023", "-0x0.fd8#10", Less);
    test("3", 20, Nearest, "-0.98999214", "-0x0.fd702#20", Greater);
    test(
        "3",
        53,
        Down,
        "-0.98999249660044542",
        "-0x0.fd7025f42f2e90#53",
        Greater,
    );
    test(
        "3",
        53,
        Up,
        "-0.98999249660044553",
        "-0x0.fd7025f42f2e98#53",
        Less,
    );
    test(
        "3",
        53,
        Floor,
        "-0.98999249660044553",
        "-0x0.fd7025f42f2e98#53",
        Less,
    );
    test(
        "3",
        53,
        Ceiling,
        "-0.98999249660044542",
        "-0x0.fd7025f42f2e90#53",
        Greater,
    );
    test(
        "3",
        53,
        Nearest,
        "-0.98999249660044542",
        "-0x0.fd7025f42f2e90#53",
        Greater,
    );
    test(
        "3",
        100,
        Nearest,
        "-0.98999249660044545727157279473154",
        "-0x0.fd7025f42f2e9307dff82fdf7#100",
        Less,
    );
    test("100", 1, Down, "0.50", "0x0.8#1", Less);
    test("100", 1, Up, "1.0", "0x1.0#1", Greater);
    test("100", 1, Floor, "0.50", "0x0.8#1", Less);
    test("100", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("100", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("100", 5, Nearest, "0.875", "0x0.e0#5", Greater);
    test("100", 10, Down, "0.86230", "0x0.dcc#10", Less);
    test("100", 10, Up, "0.86328", "0x0.dd0#10", Greater);
    test("100", 10, Floor, "0.86230", "0x0.dcc#10", Less);
    test("100", 10, Ceiling, "0.86328", "0x0.dd0#10", Greater);
    test("100", 10, Nearest, "0.86230", "0x0.dcc#10", Less);
    test("100", 20, Nearest, "0.86231899", "0x0.dcc0f#20", Greater);
    test(
        "100",
        53,
        Down,
        "0.86231887228768389",
        "0x0.dcc0edfb32fef8#53",
        Less,
    );
    test(
        "100",
        53,
        Up,
        "0.86231887228768400",
        "0x0.dcc0edfb32ff00#53",
        Greater,
    );
    test(
        "100",
        53,
        Floor,
        "0.86231887228768389",
        "0x0.dcc0edfb32fef8#53",
        Less,
    );
    test(
        "100",
        53,
        Ceiling,
        "0.86231887228768400",
        "0x0.dcc0edfb32ff00#53",
        Greater,
    );
    test(
        "100",
        53,
        Nearest,
        "0.86231887228768389",
        "0x0.dcc0edfb32fef8#53",
        Less,
    );
    test(
        "100",
        100,
        Nearest,
        "0.86231887228768393410193851395099",
        "0x0.dcc0edfb32fefb1fa19b9b30c#100",
        Greater,
    );
    test("1000000", 1, Down, "0.50", "0x0.8#1", Less);
    test("1000000", 1, Up, "1.0", "0x1.0#1", Greater);
    test("1000000", 1, Floor, "0.50", "0x0.8#1", Less);
    test("1000000", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("1000000", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1000000", 5, Nearest, "0.938", "0x0.f0#5", Greater);
    test("1000000", 10, Down, "0.93652", "0x0.efc#10", Less);
    test("1000000", 10, Up, "0.93750", "0x0.f00#10", Greater);
    test("1000000", 10, Floor, "0.93652", "0x0.efc#10", Less);
    test("1000000", 10, Ceiling, "0.93750", "0x0.f00#10", Greater);
    test("1000000", 10, Nearest, "0.93652", "0x0.efc#10", Less);
    test(
        "1000000",
        20,
        Nearest,
        "0.93675232",
        "0x0.efcf0#20",
        Greater,
    );
    test(
        "1000000",
        53,
        Down,
        "0.93675212753314474",
        "0x0.efcefcc8369960#53",
        Less,
    );
    test(
        "1000000",
        53,
        Up,
        "0.93675212753314485",
        "0x0.efcefcc8369968#53",
        Greater,
    );
    test(
        "1000000",
        53,
        Floor,
        "0.93675212753314474",
        "0x0.efcefcc8369960#53",
        Less,
    );
    test(
        "1000000",
        53,
        Ceiling,
        "0.93675212753314485",
        "0x0.efcefcc8369968#53",
        Greater,
    );
    test(
        "1000000",
        53,
        Nearest,
        "0.93675212753314474",
        "0x0.efcefcc8369960#53",
        Less,
    );
    test(
        "1000000",
        100,
        Nearest,
        "0.93675212753314478693853253507492",
        "0x0.efcefcc836996357644d418cd#100",
        Greater,
    );
    test("1/1000000", 1, Down, "0.50", "0x0.8#1", Less);
    test("1/1000000", 1, Up, "1.0", "0x1.0#1", Greater);
    test("1/1000000", 1, Floor, "0.50", "0x0.8#1", Less);
    test("1/1000000", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("1/1000000", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1/1000000", 5, Nearest, "1.00", "0x1.0#5", Greater);
    test("1/1000000", 10, Down, "0.99902", "0x0.ffc#10", Less);
    test("1/1000000", 10, Up, "1.0000", "0x1.000#10", Greater);
    test("1/1000000", 10, Floor, "0.99902", "0x0.ffc#10", Less);
    test("1/1000000", 10, Ceiling, "1.0000", "0x1.000#10", Greater);
    test("1/1000000", 10, Nearest, "1.0000", "0x1.000#10", Greater);
    test(
        "1/1000000",
        20,
        Nearest,
        "1.0000000",
        "0x1.00000#20",
        Greater,
    );
    test(
        "1/1000000",
        53,
        Down,
        "0.99999999999949996",
        "0x0.ffffffffff7340#53",
        Less,
    );
    test(
        "1/1000000",
        53,
        Up,
        "0.99999999999950007",
        "0x0.ffffffffff7348#53",
        Greater,
    );
    test(
        "1/1000000",
        53,
        Floor,
        "0.99999999999949996",
        "0x0.ffffffffff7340#53",
        Less,
    );
    test(
        "1/1000000",
        53,
        Ceiling,
        "0.99999999999950007",
        "0x0.ffffffffff7348#53",
        Greater,
    );
    test(
        "1/1000000",
        53,
        Nearest,
        "0.99999999999949996",
        "0x0.ffffffffff7340#53",
        Less,
    );
    test(
        "1/1000000",
        100,
        Nearest,
        "0.99999999999950000000000004166665",
        "0x0.ffffffffff734333f690bc5c6#100",
        Less,
    );
    test("-1/1000000", 1, Down, "0.50", "0x0.8#1", Less);
    test("-1/1000000", 1, Up, "1.0", "0x1.0#1", Greater);
    test("-1/1000000", 1, Floor, "0.50", "0x0.8#1", Less);
    test("-1/1000000", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("-1/1000000", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("-1/1000000", 5, Nearest, "1.00", "0x1.0#5", Greater);
    test("-1/1000000", 10, Down, "0.99902", "0x0.ffc#10", Less);
    test("-1/1000000", 10, Up, "1.0000", "0x1.000#10", Greater);
    test("-1/1000000", 10, Floor, "0.99902", "0x0.ffc#10", Less);
    test("-1/1000000", 10, Ceiling, "1.0000", "0x1.000#10", Greater);
    test("-1/1000000", 10, Nearest, "1.0000", "0x1.000#10", Greater);
    test(
        "-1/1000000",
        20,
        Nearest,
        "1.0000000",
        "0x1.00000#20",
        Greater,
    );
    test(
        "-1/1000000",
        53,
        Down,
        "0.99999999999949996",
        "0x0.ffffffffff7340#53",
        Less,
    );
    test(
        "-1/1000000",
        53,
        Up,
        "0.99999999999950007",
        "0x0.ffffffffff7348#53",
        Greater,
    );
    test(
        "-1/1000000",
        53,
        Floor,
        "0.99999999999949996",
        "0x0.ffffffffff7340#53",
        Less,
    );
    test(
        "-1/1000000",
        53,
        Ceiling,
        "0.99999999999950007",
        "0x0.ffffffffff7348#53",
        Greater,
    );
    test(
        "-1/1000000",
        53,
        Nearest,
        "0.99999999999949996",
        "0x0.ffffffffff7340#53",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Nearest,
        "0.99999999999950000000000004166665",
        "0x0.ffffffffff734333f690bc5c6#100",
        Less,
    );
    test(
        "1/1000000000000000000000000",
        1,
        Down,
        "0.50",
        "0x0.8#1",
        Less,
    );
    test(
        "1/1000000000000000000000000",
        1,
        Up,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        1,
        Floor,
        "0.50",
        "0x0.8#1",
        Less,
    );
    test(
        "1/1000000000000000000000000",
        1,
        Ceiling,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        1,
        Nearest,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        5,
        Nearest,
        "1.00",
        "0x1.0#5",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        10,
        Down,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1/1000000000000000000000000",
        10,
        Up,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1/1000000000000000000000000",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        20,
        Nearest,
        "1.0000000",
        "0x1.00000#20",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        53,
        Down,
        "0.99999999999999989",
        "0x0.fffffffffffff8#53",
        Less,
    );
    test(
        "1/1000000000000000000000000",
        53,
        Up,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        53,
        Floor,
        "0.99999999999999989",
        "0x0.fffffffffffff8#53",
        Less,
    );
    test(
        "1/1000000000000000000000000",
        53,
        Ceiling,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1/1000000000000000000000000",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        1,
        Down,
        "4.9e-32",
        "0x1.0E-26#1",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        1,
        Up,
        "9.9e-32",
        "0x2.0E-26#1",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        1,
        Floor,
        "4.9e-32",
        "0x1.0E-26#1",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        1,
        Ceiling,
        "9.9e-32",
        "0x2.0E-26#1",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        1,
        Nearest,
        "9.9e-32",
        "0x2.0E-26#1",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        5,
        Nearest,
        "8.63e-32",
        "0x1.cE-26#5",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        10,
        Down,
        "8.4741e-32",
        "0x1.b80E-26#10",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        10,
        Up,
        "8.4837e-32",
        "0x1.b88E-26#10",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        10,
        Floor,
        "8.4741e-32",
        "0x1.b80E-26#10",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        10,
        Ceiling,
        "8.4837e-32",
        "0x1.b88E-26#10",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        10,
        Nearest,
        "8.4741e-32",
        "0x1.b80E-26#10",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        20,
        Nearest,
        "8.4784270e-32",
        "0x1.b839aE-26#20",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        53,
        Down,
        "8.4784276603688996e-32",
        "0x1.b839a252049c1E-26#53",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        53,
        Up,
        "8.4784276603689007e-32",
        "0x1.b839a252049c2E-26#53",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        53,
        Floor,
        "8.4784276603688996e-32",
        "0x1.b839a252049c1E-26#53",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        53,
        Ceiling,
        "8.4784276603689007e-32",
        "0x1.b839a252049c2E-26#53",
        Greater,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        53,
        Nearest,
        "8.4784276603688996e-32",
        "0x1.b839a252049c1E-26#53",
        Less,
    );
    test(
        "124451306656115542615260972311/79228162514264337593543950336",
        100,
        Nearest,
        "8.4784276603688996439587014693888e-32",
        "0x1.b839a252049c1114cf98e8042E-26#100",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        1,
        Down,
        "-2.0e-31",
        "-0x4.0E-26#1",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        1,
        Up,
        "-3.9e-31",
        "-0x8.0E-26#1",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        1,
        Floor,
        "-3.9e-31",
        "-0x8.0E-26#1",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        1,
        Ceiling,
        "-2.0e-31",
        "-0x4.0E-26#1",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        1,
        Nearest,
        "-2.0e-31",
        "-0x4.0E-26#1",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        5,
        Nearest,
        "-2.59e-31",
        "-0x5.4E-26#5",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        10,
        Down,
        "-2.5422e-31",
        "-0x5.28E-26#10",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        10,
        Up,
        "-2.5461e-31",
        "-0x5.2aE-26#10",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        10,
        Floor,
        "-2.5461e-31",
        "-0x5.2aE-26#10",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        10,
        Ceiling,
        "-2.5422e-31",
        "-0x5.28E-26#10",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        10,
        Nearest,
        "-2.5422e-31",
        "-0x5.28E-26#10",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        20,
        Nearest,
        "-2.5435290e-31",
        "-0x5.28ad0E-26#20",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        53,
        Down,
        "-2.5435282981106695e-31",
        "-0x5.28ace6f60dd40E-26#53",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        53,
        Up,
        "-2.5435282981106700e-31",
        "-0x5.28ace6f60dd44E-26#53",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        53,
        Floor,
        "-2.5435282981106700e-31",
        "-0x5.28ace6f60dd44E-26#53",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        53,
        Ceiling,
        "-2.5435282981106695e-31",
        "-0x5.28ace6f60dd40E-26#53",
        Greater,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        53,
        Nearest,
        "-2.5435282981106700e-31",
        "-0x5.28ace6f60dd44E-26#53",
        Less,
    );
    test(
        "373353919968346627845782916933/79228162514264337593543950336",
        100,
        Nearest,
        "-2.5435282981106698931876104408174e-31",
        "-0x5.28ace6f60dd4333e6ecab80c8E-26#100",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        1,
        Down,
        "-0.50",
        "-0x0.8#1",
        Greater,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        1,
        Up,
        "-1.0",
        "-0x1.0#1",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        1,
        Floor,
        "-1.0",
        "-0x1.0#1",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        1,
        Ceiling,
        "-0.50",
        "-0x0.8#1",
        Greater,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        1,
        Nearest,
        "-1.0",
        "-0x1.0#1",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        5,
        Nearest,
        "-1.00",
        "-0x1.0#5",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        10,
        Down,
        "-0.99902",
        "-0x0.ffc#10",
        Greater,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        10,
        Up,
        "-1.0000",
        "-0x1.000#10",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        10,
        Ceiling,
        "-0.99902",
        "-0x0.ffc#10",
        Greater,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        20,
        Nearest,
        "-1.0000000",
        "-0x1.00000#20",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        53,
        Down,
        "-0.99999999999999989",
        "-0x0.fffffffffffff8#53",
        Greater,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        53,
        Up,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        53,
        Floor,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        53,
        Ceiling,
        "-0.99999999999999989",
        "-0x0.fffffffffffff8#53",
        Greater,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Less,
    );
    test(
        "124451306656115542615260972311/39614081257132168796771975168",
        100,
        Nearest,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        1,
        Down,
        "4.9e-32",
        "0x1.0E-26#1",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        1,
        Up,
        "9.9e-32",
        "0x2.0E-26#1",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        1,
        Floor,
        "4.9e-32",
        "0x1.0E-26#1",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        1,
        Ceiling,
        "9.9e-32",
        "0x2.0E-26#1",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        1,
        Nearest,
        "9.9e-32",
        "0x2.0E-26#1",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        5,
        Nearest,
        "8.63e-32",
        "0x1.cE-26#5",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        10,
        Down,
        "8.4741e-32",
        "0x1.b80E-26#10",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        10,
        Up,
        "8.4837e-32",
        "0x1.b88E-26#10",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        10,
        Floor,
        "8.4741e-32",
        "0x1.b80E-26#10",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        10,
        Ceiling,
        "8.4837e-32",
        "0x1.b88E-26#10",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        10,
        Nearest,
        "8.4741e-32",
        "0x1.b80E-26#10",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        20,
        Nearest,
        "8.4784270e-32",
        "0x1.b839aE-26#20",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        53,
        Down,
        "8.4784276603688996e-32",
        "0x1.b839a252049c1E-26#53",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        53,
        Up,
        "8.4784276603689007e-32",
        "0x1.b839a252049c2E-26#53",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        53,
        Floor,
        "8.4784276603688996e-32",
        "0x1.b839a252049c1E-26#53",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        53,
        Ceiling,
        "8.4784276603689007e-32",
        "0x1.b839a252049c2E-26#53",
        Greater,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        53,
        Nearest,
        "8.4784276603688996e-32",
        "0x1.b839a252049c1E-26#53",
        Less,
    );
    test(
        "-124451306656115542615260972311/79228162514264337593543950336",
        100,
        Nearest,
        "8.4784276603688996439587014693888e-32",
        "0x1.b839a252049c1114cf98e8042E-26#100",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        1,
        Down,
        "0.25",
        "0x0.4#1",
        Less,
    );
    test(
        "1267650600228229401496703205376",
        1,
        Up,
        "0.50",
        "0x0.8#1",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        1,
        Floor,
        "0.25",
        "0x0.4#1",
        Less,
    );
    test(
        "1267650600228229401496703205376",
        1,
        Ceiling,
        "0.50",
        "0x0.8#1",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        1,
        Nearest,
        "0.50",
        "0x0.8#1",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        5,
        Nearest,
        "0.484",
        "0x0.7c#5",
        Less,
    );
    test(
        "1267650600228229401496703205376",
        10,
        Down,
        "0.48877",
        "0x0.7d2#10",
        Less,
    );
    test(
        "1267650600228229401496703205376",
        10,
        Up,
        "0.48926",
        "0x0.7d4#10",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        10,
        Floor,
        "0.48877",
        "0x0.7d2#10",
        Less,
    );
    test(
        "1267650600228229401496703205376",
        10,
        Ceiling,
        "0.48926",
        "0x0.7d4#10",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        10,
        Nearest,
        "0.48926",
        "0x0.7d4#10",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        20,
        Nearest,
        "0.48917866",
        "0x0.7d3ad0#20",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        53,
        Down,
        "0.48917865697472140",
        "0x0.7d3acffd9b8db0#53",
        Less,
    );
    test(
        "1267650600228229401496703205376",
        53,
        Up,
        "0.48917865697472146",
        "0x0.7d3acffd9b8db4#53",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        53,
        Floor,
        "0.48917865697472140",
        "0x0.7d3acffd9b8db0#53",
        Less,
    );
    test(
        "1267650600228229401496703205376",
        53,
        Ceiling,
        "0.48917865697472146",
        "0x0.7d3acffd9b8db4#53",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        53,
        Nearest,
        "0.48917865697472146",
        "0x0.7d3acffd9b8db4#53",
        Greater,
    );
    test(
        "1267650600228229401496703205376",
        100,
        Nearest,
        "0.48917865697472144990578930875139",
        "0x0.7d3acffd9b8db34b71d86c7ff0#100",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        1,
        Down,
        "0.50",
        "0x0.8#1",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        1,
        Up,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        1,
        Floor,
        "0.50",
        "0x0.8#1",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        1,
        Ceiling,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        1,
        Nearest,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        5,
        Nearest,
        "1.00",
        "0x1.0#5",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Down,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Up,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        20,
        Nearest,
        "1.0000000",
        "0x1.00000#20",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        53,
        Down,
        "0.99999999999999989",
        "0x0.fffffffffffff8#53",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        53,
        Up,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        53,
        Floor,
        "0.99999999999999989",
        "0x0.fffffffffffff8#53",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        53,
        Ceiling,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
}

#[test]
#[should_panic]
fn cos_rational_prec_fail() {
    Float::cos_rational_prec(Rational::ONE, 0);
}

#[test]
#[should_panic]
fn cos_rational_prec_ref_fail() {
    Float::cos_rational_prec_ref(&Rational::ONE, 0);
}

#[test]
#[should_panic]
fn cos_rational_prec_round_fail_1() {
    Float::cos_rational_prec_round(Rational::ONE, 0, Floor);
}

#[test]
#[should_panic]
fn cos_rational_prec_round_fail_2() {
    Float::cos_rational_prec_round(Rational::ONE, 10, Exact);
}

#[test]
#[should_panic]
fn cos_rational_prec_round_ref_fail() {
    Float::cos_rational_prec_round_ref(&Rational::ONE, 10, Exact);
}

#[allow(clippy::needless_pass_by_value)]
fn cos_rational_prec_round_properties_helper(x: Rational, prec: u64, rm: RoundingMode) {
    let (c, o) = Float::cos_rational_prec_round(x.clone(), prec, rm);
    assert!(c.is_valid());
    assert_rounding_ordering_consistent(&c, rm, o);

    let (c_alt, o_alt) = Float::cos_rational_prec_round_ref(&x, prec, rm);
    assert!(c_alt.is_valid());
    assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
    assert_eq!(o_alt, o);

    // |cos x| <= 1, and cos is even
    assert!(c.le_abs(&1u32));
    let (c_neg, o_neg) = Float::cos_rational_prec_round(-&x, prec, rm);
    assert_eq!(ComparableFloatRef(&c_neg), ComparableFloatRef(&c));
    assert_eq!(o_neg, o);

    if let Ok(rrm) = rug_round_try_from_rounding_mode(rm) {
        let (rug_c, rug_o) = rug_cos_rational_prec_round(&x, prec, rrm);
        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_c)),
            ComparableFloatRef(&c)
        );
        assert_eq!(rug_o, o);
    }

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

    if o == Equal {
        for rm in exhaustive_rounding_modes() {
            let (s, oo) = Float::cos_rational_prec_round_ref(&x, prec, rm);
            assert_eq!(ComparableFloatRef(&s), ComparableFloatRef(&c));
            assert_eq!(oo, Equal);
        }
    } else {
        assert_panic!(Float::cos_rational_prec_round_ref(&x, prec, Exact));
    }
}

#[test]
fn cos_rational_prec_round_properties() {
    rational_unsigned_rounding_mode_triple_gen_var_10().test_properties(|(x, prec, rm)| {
        cos_rational_prec_round_properties_helper(x, prec, rm);
    });

    unsigned_rounding_mode_pair_gen_var_3().test_properties(|(prec, rm)| {
        let (c, o) = Float::cos_rational_prec_round(Rational::ZERO, prec, rm);
        assert_eq!(ComparableFloat(c), ComparableFloat(Float::one_prec(prec)));
        assert_eq!(o, Equal);
    });
}

#[allow(clippy::needless_pass_by_value)]
fn cos_rational_prec_properties_helper(x: Rational, prec: u64) {
    let (c, o) = Float::cos_rational_prec(x.clone(), prec);
    assert!(c.is_valid());

    let (c_alt, o_alt) = Float::cos_rational_prec_ref(&x, prec);
    assert!(c_alt.is_valid());
    assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
    assert_eq!(o_alt, o);

    let (c_alt, o_alt) = Float::cos_rational_prec_round_ref(&x, prec, Nearest);
    assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
    assert_eq!(o_alt, o);

    assert!(c.le_abs(&1u32));

    let (rug_c, rug_o) = rug_cos_rational_prec(&x, prec);
    assert_eq!(
        ComparableFloatRef(&Float::from(&rug_c)),
        ComparableFloatRef(&c)
    );
    assert_eq!(rug_o, o);

    // the cosine of an exactly representable rational is the Float cosine
    if let Ok(f) = Float::try_from(&x) {
        let (c_alt, o_alt) = f.cos_prec(prec);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
    }
}

#[test]
fn cos_rational_prec_properties() {
    rational_unsigned_pair_gen_var_3().test_properties(|(x, prec)| {
        cos_rational_prec_properties_helper(x, prec);
    });
}

// An input too large to be a `Float`, reduced modulo 2 pi in `Rational` arithmetic with pi to about
// 2^30 bits (~14 minutes in release mode; MPFR cannot serve as an oracle here, so the value was
// cross-checked by temporarily routing moderate inputs through the same reduction). Slow enough to
// dominate a test run, and its result does not depend on the limb width, so it runs only in the
// 64-bit-limb configuration.
#[cfg(not(feature = "32_bit_limbs"))]
#[test]
fn test_cos_rational_huge() {
    let x = Rational::power_of_2(1i64 << 30);
    let (c, o) = Float::cos_rational_prec_round_ref(&x, 10, Nearest);
    assert_eq!(c.to_string(), "-0.77832");
    assert_eq!(to_hex_string(&c), "-0x0.c74#10");
    assert_eq!(o, Greater);
}

// Dyadic rationals within 2^(-2^30) of pi/2, whose cosines underflow: the near-zero path computes
// the distance to pi/2 exactly and rounds the bracket in `Rational` arithmetic, so the underflow
// decision and the `Ordering` are exact. Constructing the inputs and each call computes pi to about
// 2^30 bits (~6 minutes each), so this test is slow even in release mode. Slow enough to dominate a
// test run, and its result does not depend on the limb width, so it runs only in the 64-bit-limb
// configuration.
#[cfg(not(feature = "32_bit_limbs"))]
#[test]
fn test_cos_rational_underflow() {
    let p = (1u64 << 30) + 64;
    // 2^(-2^30), the smallest positive `Float`, at the output precision
    let min_positive = Float::one_prec(10) >> (1u64 << 30);
    // pi rounded down: x_lo < pi/2, so cos(x_lo) is positive, and at most half an ulp of x_lo,
    // 2^(-2^30 - 64), in magnitude
    let mut pi = Float::pi_prec_round(p, Floor).0;
    let x_lo = Rational::exact_from(&(&pi >> 1u32));
    let (c, o) = Float::cos_rational_prec_round_ref(&x_lo, 10, Ceiling);
    assert_eq!(ComparableFloatRef(&c), ComparableFloatRef(&min_positive));
    assert_eq!(o, Greater);
    // pi rounded up: x_hi > pi/2, so cos(x_hi) is negative
    pi.increment();
    let x_hi = Rational::exact_from(&(pi >> 1u32));
    let (c, o) = Float::cos_rational_prec_round_ref(&x_hi, 10, Nearest);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::NEGATIVE_ZERO));
    assert_eq!(o, Greater);
}

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_cos_rational() {
    fn test<T: PrimitiveFloat>(s: &str, out: T)
    where
        Float: From<T> + PartialOrd<T>,
        for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
    {
        let x = Rational::from_str(s).unwrap();
        assert_eq!(
            NiceFloat(primitive_float_cos_rational::<T>(&x)),
            NiceFloat(out)
        );
    }
    test::<f32>("0", 1.0);
    test::<f32>("1", 0.5403023);
    test::<f32>("1/2", 0.87758255);
    test::<f32>("1/3", 0.94495696);
    test::<f32>("3/5", 0.8253356);
    test::<f32>("22/7", -0.9999992);
    test::<f32>("355/113", -1.0);
    test::<f32>("1000000", 0.93675214);
    test::<f32>("1/1000000", 1.0);
    test::<f32>("1/1000000000000000000000000", 1.0);
    test::<f32>("-1", 0.5403023);
    test::<f32>("-1/2", 0.87758255);
    test::<f32>("-1/3", 0.94495696);
    test::<f32>("-22/7", -0.9999992);
    test::<f32>("-1000000", 0.93675214);
    test::<f32>("10000", -0.95215535);

    test::<f64>("0", 1.0);
    test::<f64>("1", 0.5403023058681398);
    test::<f64>("1/2", 0.8775825618903728);
    test::<f64>("1/3", 0.9449569463147377);
    test::<f64>("3/5", 0.8253356149096783);
    test::<f64>("22/7", -0.999999200533553);
    test::<f64>("355/113", -0.9999999999999645);
    test::<f64>("1000000", 0.9367521275331447);
    test::<f64>("1/1000000", 0.9999999999995);
    test::<f64>("1/1000000000000000000000000", 1.0);
    test::<f64>("-1", 0.5403023058681398);
    test::<f64>("-1/2", 0.8775825618903728);
    test::<f64>("-1/3", 0.9449569463147377);
    test::<f64>("-22/7", -0.999999200533553);
    test::<f64>("-1000000", 0.9367521275331447);
    test::<f64>("10000", -0.9521553682590148);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_cos_rational_properties_helper<T: PrimitiveFloat>()
where
    Float: From<T> + PartialOrd<T>,
    Rational: ExactFrom<T>,
    for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
{
    rational_gen().test_properties(|x| {
        let c = primitive_float_cos_rational::<T>(&x);
        // the cosine of a rational is never NaN, and lies in [-1, 1]
        assert!(c >= T::NEGATIVE_ONE && c <= T::ONE);
        // cos is even
        assert_eq!(
            NiceFloat(primitive_float_cos_rational::<T>(&-&x)),
            NiceFloat(c)
        );
        // the result is the correctly rounded cosine, as computed by MPFR at the same precision
        let rug_c = rug_cos_rational_prec(&x, T::MANTISSA_WIDTH + 1).0;
        let rug_c: T = T::exact_from(&<Float as From<&rug::Float>>::from(&rug_c));
        assert_eq!(NiceFloat(rug_c), NiceFloat(c));
    });

    primitive_float_gen::<T>().test_properties(|x| {
        // The cosine of a finite primitive float, taken through the `Rational` path, matches the
        // direct primitive-float cosine.
        if x.is_finite() {
            assert_eq!(
                NiceFloat(primitive_float_cos_rational::<T>(&Rational::exact_from(x))),
                NiceFloat(primitive_float_cos(x))
            );
        }
    });
}

#[test]
fn primitive_float_cos_rational_properties() {
    apply_fn_to_primitive_floats!(primitive_float_cos_rational_properties_helper);
}

#[test]
fn test_cos_with_period_prec_round() {
    let test = |s, s_hex, u: u64, prec: u64, rm, out: &str, out_hex: &str, o_out: Ordering| {
        let x = parse_hex_string(s_hex);
        assert_eq!(x.to_string(), s);

        let (c, o) = x.clone().cos_with_period_prec_round(u, prec, rm);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, o_out);

        let (c_alt, o_alt) = x.cos_with_period_prec_round_ref(u, prec, rm);
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        let mut c_alt = x.clone();
        let o_alt = c_alt.cos_with_period_prec_round_assign(u, prec, rm);
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        if let Ok(rug_rm) = rug_round_try_from_rounding_mode(rm)
            && u32::try_from(u).is_ok()
        {
            let (rug_c, rug_o) =
                rug_cos_with_period_prec_round(&rug::Float::exact_from(&x), u, prec, rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    };
    test("NaN", "NaN", 4, 10, Nearest, "NaN", "NaN", Equal);
    test("Infinity", "Infinity", 4, 10, Nearest, "NaN", "NaN", Equal);
    test(
        "-Infinity",
        "-Infinity",
        4,
        10,
        Nearest,
        "NaN",
        "NaN",
        Equal,
    );
    test(
        "0.0",
        "0x0.0",
        4,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "-0.0",
        "-0x0.0",
        4,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test("1.0", "0x1.0#1", 0, 10, Nearest, "NaN", "NaN", Equal);
    test("NaN", "NaN", 0, 10, Nearest, "NaN", "NaN", Equal);
    test("0.0", "0x0.0", 0, 10, Nearest, "NaN", "NaN", Equal);
    test(
        "0.0",
        "0x0.0",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "0.0",
        "0x0.0",
        360,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "0.0",
        "0x0.0",
        360,
        10,
        Exact,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    // - exact case (a): a quarter turn, +0
    test("90.0", "0x5a.0#6", 360, 10, Nearest, "0.0", "0x0.0", Equal);
    test("90.0", "0x5a.0#6", 360, 10, Floor, "0.0", "0x0.0", Equal);
    test("90.0", "0x5a.0#6", 360, 10, Exact, "0.0", "0x0.0", Equal);
    // - exact case (a): a half turn, -1
    test(
        "180.0",
        "0xb4.0#6",
        360,
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "180.0",
        "0xb4.0#6",
        360,
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "180.0",
        "0xb4.0#6",
        360,
        10,
        Exact,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    // - exact case (a): three quarter turns, +0
    test(
        "270.0",
        "0x10e.0#8",
        360,
        10,
        Nearest,
        "0.0",
        "0x0.0",
        Equal,
    );
    test("270.0", "0x10e.0#8", 360, 10, Floor, "0.0", "0x0.0", Equal);
    test("270.0", "0x10e.0#8", 360, 10, Exact, "0.0", "0x0.0", Equal);
    // - exact case (a): a full turn, 1 (via xr = 0)
    test(
        "360.0",
        "0x168.0#6",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "360.0",
        "0x168.0#6",
        360,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "360.0",
        "0x168.0#6",
        360,
        10,
        Exact,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    // - exact case (b): a sixth of a turn, 1/2
    test(
        "60.0",
        "0x3c.0#4",
        360,
        10,
        Nearest,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "60.0",
        "0x3c.0#4",
        360,
        10,
        Floor,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "60.0",
        "0x3c.0#4",
        360,
        10,
        Exact,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    // - exact case (b): a third of a turn, -1/2
    test(
        "120.0",
        "0x78.0#4",
        360,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "120.0",
        "0x78.0#4",
        360,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "120.0",
        "0x78.0#4",
        360,
        10,
        Exact,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    // - exact case (b): two thirds of a turn, -1/2
    test(
        "240.0",
        "0xf.0E+1#4",
        360,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "240.0",
        "0xf.0E+1#4",
        360,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "240.0",
        "0xf.0E+1#4",
        360,
        10,
        Exact,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    // - exact case (b): five sixths of a turn, 1/2
    test(
        "300.0",
        "0x12c.0#7",
        360,
        10,
        Nearest,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "300.0",
        "0x12c.0#7",
        360,
        10,
        Floor,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "300.0",
        "0x12c.0#7",
        360,
        10,
        Exact,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    // - exact case (a) after reduction, +0
    test(
        "450.0",
        "0x1c2.0#8",
        360,
        10,
        Nearest,
        "0.0",
        "0x0.0",
        Equal,
    );
    test("450.0", "0x1c2.0#8", 360, 10, Floor, "0.0", "0x0.0", Equal);
    test("450.0", "0x1c2.0#8", 360, 10, Exact, "0.0", "0x0.0", Equal);
    // - two full turns, 1
    test(
        "720.0",
        "0x2.dE+2#6",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "720.0",
        "0x2.dE+2#6",
        360,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "720.0",
        "0x2.dE+2#6",
        360,
        10,
        Exact,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        1,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        1,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        1,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        1,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        2,
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        2,
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        2,
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        2,
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        3,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        3,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        3,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        3,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test("1.0", "0x1.0#1", 4, 10, Nearest, "0.0", "0x0.0", Equal);
    test("1.0", "0x1.0#1", 4, 10, Floor, "0.0", "0x0.0", Equal);
    test("1.0", "0x1.0#1", 4, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("1.0", "0x1.0#1", 4, 53, Nearest, "0.0", "0x0.0", Equal);
    test(
        "1.0",
        "0x1.0#1",
        6,
        10,
        Nearest,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        6,
        10,
        Floor,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        6,
        10,
        Ceiling,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        6,
        53,
        Nearest,
        "0.50000000000000000",
        "0x0.80000000000000#53",
        Equal,
    );
    test(
        "1.0",
        "0x1.0#1",
        7,
        10,
        Nearest,
        "0.62305",
        "0x0.9f8#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        7,
        10,
        Floor,
        "0.62305",
        "0x0.9f8#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        7,
        10,
        Ceiling,
        "0.62402",
        "0x0.9fc#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        12,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        12,
        10,
        Floor,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        12,
        10,
        Ceiling,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        360,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        360,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        360,
        53,
        Nearest,
        "0.99984769515639127",
        "0x0.fff604bfad7c50#53",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        1,
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "0.50",
        "0x0.8#1",
        1,
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "0.50",
        "0x0.8#1",
        1,
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "0.50",
        "0x0.8#1",
        1,
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test("0.50", "0x0.8#1", 2, 10, Nearest, "0.0", "0x0.0", Equal);
    test("0.50", "0x0.8#1", 2, 10, Floor, "0.0", "0x0.0", Equal);
    test("0.50", "0x0.8#1", 2, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("0.50", "0x0.8#1", 2, 53, Nearest, "0.0", "0x0.0", Equal);
    test(
        "0.50",
        "0x0.8#1",
        3,
        10,
        Nearest,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "0.50",
        "0x0.8#1",
        3,
        10,
        Floor,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "0.50",
        "0x0.8#1",
        3,
        10,
        Ceiling,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "0.50",
        "0x0.8#1",
        3,
        53,
        Nearest,
        "0.50000000000000000",
        "0x0.80000000000000#53",
        Equal,
    );
    test(
        "0.50",
        "0x0.8#1",
        4,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        4,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        4,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        4,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        6,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        6,
        10,
        Floor,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        6,
        10,
        Ceiling,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        6,
        53,
        Nearest,
        "0.86602540378443860",
        "0x0.ddb3d742c26550#53",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        7,
        10,
        Nearest,
        "0.90137",
        "0x0.e6c#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        7,
        10,
        Floor,
        "0.90039",
        "0x0.e68#10",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        7,
        10,
        Ceiling,
        "0.90137",
        "0x0.e6c#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        12,
        10,
        Nearest,
        "0.96582",
        "0x0.f74#10",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        12,
        10,
        Floor,
        "0.96582",
        "0x0.f74#10",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        12,
        10,
        Ceiling,
        "0.96680",
        "0x0.f78#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        360,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        360,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        360,
        53,
        Nearest,
        "0.99996192306417131",
        "0x0.fffd812cce4e68#53",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test("0.25", "0x0.4#1", 1, 10, Nearest, "0.0", "0x0.0", Equal);
    test("0.25", "0x0.4#1", 1, 10, Floor, "0.0", "0x0.0", Equal);
    test("0.25", "0x0.4#1", 1, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("0.25", "0x0.4#1", 1, 53, Nearest, "0.0", "0x0.0", Equal);
    test(
        "0.25",
        "0x0.4#1",
        2,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        2,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        2,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        2,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        3,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        3,
        10,
        Floor,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        3,
        10,
        Ceiling,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        3,
        53,
        Nearest,
        "0.86602540378443860",
        "0x0.ddb3d742c26550#53",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        4,
        10,
        Nearest,
        "0.92383",
        "0x0.ec8#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        4,
        10,
        Floor,
        "0.92383",
        "0x0.ec8#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        4,
        10,
        Ceiling,
        "0.92480",
        "0x0.ecc#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        4,
        53,
        Nearest,
        "0.92387953251128674",
        "0x0.ec835e79946a30#53",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        6,
        10,
        Nearest,
        "0.96582",
        "0x0.f74#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        6,
        10,
        Floor,
        "0.96582",
        "0x0.f74#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        6,
        10,
        Ceiling,
        "0.96680",
        "0x0.f78#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        6,
        53,
        Nearest,
        "0.96592582628906831",
        "0x0.f746ea3a45f8a8#53",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        7,
        10,
        Nearest,
        "0.97461",
        "0x0.f98#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        7,
        10,
        Floor,
        "0.97461",
        "0x0.f98#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        7,
        10,
        Ceiling,
        "0.97559",
        "0x0.f9c#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        12,
        10,
        Nearest,
        "0.99121",
        "0x0.fdc#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        12,
        10,
        Floor,
        "0.99121",
        "0x0.fdc#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        12,
        10,
        Ceiling,
        "0.99219",
        "0x0.fe0#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        360,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        360,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        360,
        53,
        Nearest,
        "0.99999048072073449",
        "0x0.ffff604b01c270#53",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.25",
        "0x0.4#1",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        1,
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "1.5",
        "0x1.8#2",
        1,
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "1.5",
        "0x1.8#2",
        1,
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "1.5",
        "0x1.8#2",
        1,
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test("1.5", "0x1.8#2", 2, 10, Nearest, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 2, 10, Floor, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 2, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 2, 53, Nearest, "0.0", "0x0.0", Equal);
    test(
        "1.5",
        "0x1.8#2",
        3,
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "1.5",
        "0x1.8#2",
        3,
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "1.5",
        "0x1.8#2",
        3,
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "1.5",
        "0x1.8#2",
        3,
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test(
        "1.5",
        "0x1.8#2",
        4,
        10,
        Nearest,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        4,
        10,
        Floor,
        "-0.70801",
        "-0x0.b54#10",
        Less,
    );
    test(
        "1.5",
        "0x1.8#2",
        4,
        10,
        Ceiling,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        4,
        53,
        Nearest,
        "-0.70710678118654757",
        "-0x0.b504f333f9de68#53",
        Less,
    );
    test("1.5", "0x1.8#2", 6, 10, Nearest, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 6, 10, Floor, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 6, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 6, 53, Nearest, "0.0", "0x0.0", Equal);
    test(
        "1.5",
        "0x1.8#2",
        7,
        10,
        Nearest,
        "0.22241",
        "0x0.38f#10",
        Less,
    );
    test(
        "1.5",
        "0x1.8#2",
        7,
        10,
        Floor,
        "0.22241",
        "0x0.38f#10",
        Less,
    );
    test(
        "1.5",
        "0x1.8#2",
        7,
        10,
        Ceiling,
        "0.22266",
        "0x0.390#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        12,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "1.5",
        "0x1.8#2",
        12,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "1.5",
        "0x1.8#2",
        12,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        360,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.5",
        "0x1.8#2",
        360,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        360,
        53,
        Nearest,
        "0.99965732497555726",
        "0x0.ffe98addfa13a8#53",
        Less,
    );
    test(
        "1.5",
        "0x1.8#2",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.5",
        "0x1.8#2",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.5",
        "0x1.8#2",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.5",
        "0x1.8#2",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        1,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        1,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        1,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        1,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        2,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        2,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        2,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        2,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        3,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        3,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        3,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        3,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        4,
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        4,
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        4,
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        4,
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        6,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        6,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        6,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        6,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        7,
        10,
        Nearest,
        "-0.22241",
        "-0x0.38f#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        7,
        10,
        Floor,
        "-0.22266",
        "-0x0.390#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        7,
        10,
        Ceiling,
        "-0.22241",
        "-0x0.38f#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        12,
        10,
        Nearest,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        12,
        10,
        Floor,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        12,
        10,
        Ceiling,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "2.0",
        "0x2.0#1",
        360,
        10,
        Nearest,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        360,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        360,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        360,
        53,
        Nearest,
        "0.99939082701909576",
        "0x0.ffd813c5f82b38#53",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        1,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        1,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        1,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        1,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        2,
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        2,
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        2,
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        2,
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        3,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        3,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        3,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        3,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test("3.0", "0x3.0#2", 4, 10, Nearest, "0.0", "0x0.0", Equal);
    test("3.0", "0x3.0#2", 4, 10, Floor, "0.0", "0x0.0", Equal);
    test("3.0", "0x3.0#2", 4, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("3.0", "0x3.0#2", 4, 53, Nearest, "0.0", "0x0.0", Equal);
    test(
        "3.0",
        "0x3.0#2",
        6,
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        6,
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        6,
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        6,
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test(
        "3.0",
        "0x3.0#2",
        7,
        10,
        Nearest,
        "-0.90137",
        "-0x0.e6c#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        7,
        10,
        Floor,
        "-0.90137",
        "-0x0.e6c#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        7,
        10,
        Ceiling,
        "-0.90039",
        "-0x0.e68#10",
        Greater,
    );
    test("3.0", "0x3.0#2", 12, 10, Nearest, "0.0", "0x0.0", Equal);
    test("3.0", "0x3.0#2", 12, 10, Floor, "0.0", "0x0.0", Equal);
    test("3.0", "0x3.0#2", 12, 10, Ceiling, "0.0", "0x0.0", Equal);
    test(
        "3.0",
        "0x3.0#2",
        360,
        10,
        Nearest,
        "0.99902",
        "0x0.ffc#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        360,
        10,
        Floor,
        "0.99805",
        "0x0.ff8#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        360,
        10,
        Ceiling,
        "0.99902",
        "0x0.ffc#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        360,
        53,
        Nearest,
        "0.99862953475457383",
        "0x0.ffa62f689730e8#53",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        2,
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        2,
        10,
        Floor,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        2,
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        2,
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        3,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        3,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        3,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        3,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test("-1.0", "-0x1.0#1", 4, 10, Nearest, "0.0", "0x0.0", Equal);
    test("-1.0", "-0x1.0#1", 4, 10, Floor, "0.0", "0x0.0", Equal);
    test("-1.0", "-0x1.0#1", 4, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("-1.0", "-0x1.0#1", 4, 53, Nearest, "0.0", "0x0.0", Equal);
    test(
        "-1.0",
        "-0x1.0#1",
        6,
        10,
        Nearest,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        6,
        10,
        Floor,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        6,
        10,
        Ceiling,
        "0.50000",
        "0x0.800#10",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        6,
        53,
        Nearest,
        "0.50000000000000000",
        "0x0.80000000000000#53",
        Equal,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        7,
        10,
        Nearest,
        "0.62305",
        "0x0.9f8#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        7,
        10,
        Floor,
        "0.62305",
        "0x0.9f8#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        7,
        10,
        Ceiling,
        "0.62402",
        "0x0.9fc#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        12,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        12,
        10,
        Floor,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        12,
        10,
        Ceiling,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        360,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        360,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        360,
        53,
        Nearest,
        "0.99984769515639127",
        "0x0.fff604bfad7c50#53",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "100.0",
        "0x64.0#5",
        1,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        1,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        1,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        1,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        2,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        2,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        2,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        2,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        3,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        3,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        3,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        3,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        4,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        4,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        4,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        4,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        6,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        6,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        6,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        6,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        7,
        10,
        Nearest,
        "-0.22241",
        "-0x0.38f#10",
        Greater,
    );
    test(
        "100.0",
        "0x64.0#5",
        7,
        10,
        Floor,
        "-0.22266",
        "-0x0.390#10",
        Less,
    );
    test(
        "100.0",
        "0x64.0#5",
        7,
        10,
        Ceiling,
        "-0.22241",
        "-0x0.38f#10",
        Greater,
    );
    test(
        "100.0",
        "0x64.0#5",
        12,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        12,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        12,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "100.0",
        "0x64.0#5",
        360,
        10,
        Nearest,
        "-0.17358",
        "-0x0.2c7#10",
        Greater,
    );
    test(
        "100.0",
        "0x64.0#5",
        360,
        10,
        Floor,
        "-0.17383",
        "-0x0.2c8#10",
        Less,
    );
    test(
        "100.0",
        "0x64.0#5",
        360,
        10,
        Ceiling,
        "-0.17358",
        "-0x0.2c7#10",
        Greater,
    );
    test(
        "100.0",
        "0x64.0#5",
        360,
        53,
        Nearest,
        "-0.17364817766693036",
        "-0x0.2c7434fc16e714#53",
        Less,
    );
    test(
        "100.0",
        "0x64.0#5",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "100.0",
        "0x64.0#5",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "100.0",
        "0x64.0#5",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "100.0",
        "0x64.0#5",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "100.0",
        "0x64.0#5",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "100.0",
        "0x64.0#5",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "100.0",
        "0x64.0#5",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1,
        10,
        Nearest,
        "-0.96191",
        "-0x0.f64#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1,
        10,
        Floor,
        "-0.96289",
        "-0x0.f68#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1,
        10,
        Ceiling,
        "-0.96191",
        "-0x0.f64#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1,
        53,
        Nearest,
        "-0.96202767158609115",
        "-0x0.f647720b4f2da0#53",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        2,
        10,
        Nearest,
        "-0.13770",
        "-0x0.234#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        2,
        10,
        Floor,
        "-0.13794",
        "-0x0.235#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        2,
        10,
        Ceiling,
        "-0.13770",
        "-0x0.234#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        2,
        53,
        Nearest,
        "-0.13779029068462850",
        "-0x0.23463978326254#53",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        3,
        10,
        Nearest,
        "0.57715",
        "0x0.93c#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        3,
        10,
        Floor,
        "0.57715",
        "0x0.93c#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        3,
        10,
        Ceiling,
        "0.57812",
        "0x0.940#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        3,
        53,
        Nearest,
        "0.57757270342226230",
        "0x0.93dbce0042cbe8#53",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        4,
        10,
        Nearest,
        "0.65625",
        "0x0.a80#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        4,
        10,
        Floor,
        "0.65625",
        "0x0.a80#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        4,
        10,
        Ceiling,
        "0.65723",
        "0x0.a84#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        4,
        53,
        Nearest,
        "0.65658575575296008",
        "0x0.a816010bfa78e8#53",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        6,
        10,
        Nearest,
        "-0.88770",
        "-0x0.e34#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        6,
        10,
        Floor,
        "-0.88867",
        "-0x0.e38#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        6,
        10,
        Ceiling,
        "-0.88770",
        "-0x0.e34#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        6,
        53,
        Nearest,
        "-0.88813644881354303",
        "-0x0.e35ce90a0a2cc0#53",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        7,
        10,
        Nearest,
        "-0.65430",
        "-0x0.a78#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        7,
        10,
        Floor,
        "-0.65430",
        "-0x0.a78#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        7,
        10,
        Ceiling,
        "-0.65332",
        "-0x0.a74#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        12,
        10,
        Nearest,
        "-0.23657",
        "-0x0.3c9#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        12,
        10,
        Floor,
        "-0.23657",
        "-0x0.3c9#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        12,
        10,
        Ceiling,
        "-0.23633",
        "-0x0.3c8#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        360,
        10,
        Nearest,
        "-0.55176",
        "-0x0.8d4#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        360,
        10,
        Floor,
        "-0.55176",
        "-0x0.8d4#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        360,
        10,
        Ceiling,
        "-0.55078",
        "-0x0.8d0#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        360,
        53,
        Nearest,
        "-0.55129644428558244",
        "-0x0.8d21c3869b8fc8#53",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "123.45600000000000",
        "0x7b.74bc6a7ef9dc#53",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        2,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        2,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        2,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        2,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        3,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        3,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        3,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        3,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        4,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        4,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        4,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        4,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        6,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        6,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        6,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        6,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        7,
        10,
        Nearest,
        "-0.90137",
        "-0x0.e6c#10",
        Less,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        7,
        10,
        Floor,
        "-0.90137",
        "-0x0.e6c#10",
        Less,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        7,
        10,
        Ceiling,
        "-0.90039",
        "-0x0.e68#10",
        Greater,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        12,
        10,
        Nearest,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        12,
        10,
        Floor,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        12,
        10,
        Ceiling,
        "-0.50000",
        "-0x0.800#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        360,
        10,
        Nearest,
        "0.17358",
        "0x0.2c7#10",
        Less,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        360,
        10,
        Floor,
        "0.17358",
        "0x0.2c7#10",
        Less,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        360,
        10,
        Ceiling,
        "0.17383",
        "0x0.2c8#10",
        Greater,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        360,
        53,
        Nearest,
        "0.17364817766693036",
        "0x0.2c7434fc16e714#53",
        Greater,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1000000,
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1099511627776,
        10,
        Nearest,
        "0.99805",
        "0x0.ff8#10",
        Less,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1099511627776,
        10,
        Floor,
        "0.99805",
        "0x0.ff8#10",
        Less,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1099511627776,
        10,
        Ceiling,
        "0.99902",
        "0x0.ffc#10",
        Greater,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1099511627776,
        53,
        Nearest,
        "0.99836765520217097",
        "0x0.ff9505cc7a3f50#53",
        Less,
    );
    test("-0.75", "-0x0.c#2", 1, 10, Nearest, "0.0", "0x0.0", Equal);
    test("-0.75", "-0x0.c#2", 1, 10, Floor, "0.0", "0x0.0", Equal);
    test("-0.75", "-0x0.c#2", 1, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("-0.75", "-0x0.c#2", 1, 53, Nearest, "0.0", "0x0.0", Equal);
    test(
        "-0.75",
        "-0x0.c#2",
        2,
        10,
        Nearest,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        2,
        10,
        Floor,
        "-0.70801",
        "-0x0.b54#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        2,
        10,
        Ceiling,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        2,
        53,
        Nearest,
        "-0.70710678118654757",
        "-0x0.b504f333f9de68#53",
        Less,
    );
    test("-0.75", "-0x0.c#2", 3, 10, Nearest, "0.0", "0x0.0", Equal);
    test("-0.75", "-0x0.c#2", 3, 10, Floor, "0.0", "0x0.0", Equal);
    test("-0.75", "-0x0.c#2", 3, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("-0.75", "-0x0.c#2", 3, 53, Nearest, "0.0", "0x0.0", Equal);
    test(
        "-0.75",
        "-0x0.c#2",
        4,
        10,
        Nearest,
        "0.38281",
        "0x0.620#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        4,
        10,
        Floor,
        "0.38232",
        "0x0.61e#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        4,
        10,
        Ceiling,
        "0.38281",
        "0x0.620#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        4,
        53,
        Nearest,
        "0.38268343236508978",
        "0x0.61f78a9abaa58c#53",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        6,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        6,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        6,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        6,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        7,
        10,
        Nearest,
        "0.78223",
        "0x0.c84#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        7,
        10,
        Floor,
        "0.78125",
        "0x0.c80#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        7,
        10,
        Ceiling,
        "0.78223",
        "0x0.c84#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        12,
        10,
        Nearest,
        "0.92383",
        "0x0.ec8#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        12,
        10,
        Floor,
        "0.92383",
        "0x0.ec8#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        12,
        10,
        Ceiling,
        "0.92480",
        "0x0.ecc#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        360,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        360,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        360,
        53,
        Nearest,
        "0.99991432757400700",
        "0x0.fffa62a7bb70e0#53",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-0.75",
        "-0x0.c#2",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        2,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        2,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        2,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        2,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        3,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        3,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        3,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        3,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        4,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        4,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        4,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        4,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        6,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        6,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        6,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        6,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        7,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        7,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        7,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        12,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        12,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        12,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        360,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        360,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        360,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.0000000000000000e-10",
        "0x6.df37f675ef6ecE-9#53",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        1,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        1,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        1,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        1,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        2,
        10,
        Nearest,
        "0.92383",
        "0x0.ec8#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        2,
        10,
        Floor,
        "0.92383",
        "0x0.ec8#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        2,
        10,
        Ceiling,
        "0.92480",
        "0x0.ecc#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        2,
        53,
        Nearest,
        "0.92387953251128674",
        "0x0.ec835e79946a30#53",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        3,
        10,
        Nearest,
        "0.96582",
        "0x0.f74#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        3,
        10,
        Floor,
        "0.96582",
        "0x0.f74#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        3,
        10,
        Ceiling,
        "0.96680",
        "0x0.f78#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        3,
        53,
        Nearest,
        "0.96592582628906831",
        "0x0.f746ea3a45f8a8#53",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        4,
        10,
        Nearest,
        "0.98047",
        "0x0.fb0#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        4,
        10,
        Floor,
        "0.98047",
        "0x0.fb0#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        4,
        10,
        Ceiling,
        "0.98145",
        "0x0.fb4#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        4,
        53,
        Nearest,
        "0.98078528040323043",
        "0x0.fb14be7fbae580#53",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        6,
        10,
        Nearest,
        "0.99121",
        "0x0.fdc#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        6,
        10,
        Floor,
        "0.99121",
        "0x0.fdc#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        6,
        10,
        Ceiling,
        "0.99219",
        "0x0.fe0#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        6,
        53,
        Nearest,
        "0.99144486137381038",
        "0x0.fdcf54976344d8#53",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        7,
        10,
        Nearest,
        "0.99414",
        "0x0.fe8#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        7,
        10,
        Floor,
        "0.99316",
        "0x0.fe4#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        7,
        10,
        Ceiling,
        "0.99414",
        "0x0.fe8#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        12,
        10,
        Nearest,
        "0.99805",
        "0x0.ff8#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        12,
        10,
        Floor,
        "0.99707",
        "0x0.ff4#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        12,
        10,
        Ceiling,
        "0.99805",
        "0x0.ff8#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        360,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        360,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        360,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        360,
        53,
        Nearest,
        "0.99999762017735183",
        "0x0.ffffd812bd5388#53",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        1000000,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        1000000,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        1000000,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        1099511627776,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        1099511627776,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.12",
        "0x0.2#1",
        1099511627776,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.12",
        "0x0.2#1",
        1099511627776,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    // - small-input shortcut: cos rounds to 1
    test(
        "1.000000000000000e-30",
        "0x1.4484bfeebc2aE-25#48",
        1,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    // - small-input shortcut, rounding down
    test(
        "1.000000000000000e-30",
        "0x1.4484bfeebc2aE-25#48",
        1,
        53,
        Floor,
        "0.99999999999999989",
        "0x0.fffffffffffff8#53",
        Less,
    );
    // - |x| >= u: exact reduction of x mod u
    test(
        "3.8e30",
        "0x3.0E+25#2",
        7,
        53,
        Nearest,
        "0.62348980185873348",
        "0x0.9f9d07145f6e88#53",
        Less,
    );
    // - |x| >= u with x mod u = 0
    test(
        "3.8e30",
        "0x3.0E+25#2",
        3,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    // - tiny x / huge u: the small-input shortcut
    test(
        "4.0e-323228490",
        "0x1.0E-268435450#1",
        18446744073709551615,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    // - x/u near an odd multiple of 1/4: the near-zero path
    test(
        "90.000000000000000000000000000808",
        "0x5a.000000000000000000000040#100",
        360,
        53,
        Nearest,
        "-1.4098657419642452e-29",
        "-0x1.1df46a2529d39E-24#53",
        Greater,
    );
    test(
        "90.000000000000000000000000000808",
        "0x5a.000000000000000000000040#100",
        360,
        53,
        Floor,
        "-1.4098657419642455e-29",
        "-0x1.1df46a2529d3aE-24#53",
        Less,
    );
    test(
        "-90.000000000000000000000000000808",
        "-0x5a.000000000000000000000040#100",
        360,
        53,
        Nearest,
        "-1.4098657419642452e-29",
        "-0x1.1df46a2529d39E-24#53",
        Greater,
    );
    test(
        "269.99999999999999999999999999919",
        "0x10d.ffffffffffffffffffffffc#100",
        360,
        53,
        Nearest,
        "-1.4098657419642452e-29",
        "-0x1.1df46a2529d39E-24#53",
        Greater,
    );
    // - closed-form cases: x/u with denominator 8 (sqrt(2)/2), 12 (sqrt(3)/2), 5 and 10 (phi/2 and
    //   (phi - 1)/2), with all rounding modes and both signs
    test("1.0", "0x1.0#1", 8, 1, Nearest, "0.50", "0x0.8#1", Less);
    test(
        "1.0",
        "0x1.0#1",
        8,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        8,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        8,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        8,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test("1.0", "0x1.0#1", 8, 10, Down, "0.70703", "0x0.b50#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        8,
        10,
        Up,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        8,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test(
        "3.0", "0x3.0#2", 8, 1, Nearest, "-0.50", "-0x0.8#1", Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        8,
        10,
        Nearest,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "-3.0",
        "-0x3.0#2",
        8,
        10,
        Nearest,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        8,
        10,
        Floor,
        "-0.70801",
        "-0x0.b54#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        8,
        10,
        Ceiling,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        8,
        10,
        Down,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test("3.0", "0x3.0#2", 8, 10, Up, "-0.70801", "-0x0.b54#10", Less);
    test(
        "3.0",
        "0x3.0#2",
        8,
        53,
        Nearest,
        "-0.70710678118654757",
        "-0x0.b504f333f9de68#53",
        Less,
    );
    test(
        "5.0", "0x5.0#3", 8, 1, Nearest, "-0.50", "-0x0.8#1", Greater,
    );
    test(
        "5.0",
        "0x5.0#3",
        8,
        10,
        Nearest,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "-5.0",
        "-0x5.0#3",
        8,
        10,
        Nearest,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "5.0",
        "0x5.0#3",
        8,
        10,
        Floor,
        "-0.70801",
        "-0x0.b54#10",
        Less,
    );
    test(
        "5.0",
        "0x5.0#3",
        8,
        10,
        Ceiling,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "5.0",
        "0x5.0#3",
        8,
        10,
        Down,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test("5.0", "0x5.0#3", 8, 10, Up, "-0.70801", "-0x0.b54#10", Less);
    test(
        "5.0",
        "0x5.0#3",
        8,
        53,
        Nearest,
        "-0.70710678118654757",
        "-0x0.b504f333f9de68#53",
        Less,
    );
    test("7.0", "0x7.0#3", 8, 1, Nearest, "0.50", "0x0.8#1", Less);
    test(
        "7.0",
        "0x7.0#3",
        8,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "-7.0",
        "-0x7.0#3",
        8,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "7.0",
        "0x7.0#3",
        8,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "7.0",
        "0x7.0#3",
        8,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test("7.0", "0x7.0#3", 8, 10, Down, "0.70703", "0x0.b50#10", Less);
    test(
        "7.0",
        "0x7.0#3",
        8,
        10,
        Up,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "7.0",
        "0x7.0#3",
        8,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test("9.00", "0x9.0#4", 8, 1, Nearest, "0.50", "0x0.8#1", Less);
    test(
        "9.00",
        "0x9.0#4",
        8,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "-9.00",
        "-0x9.0#4",
        8,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "9.00",
        "0x9.0#4",
        8,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "9.00",
        "0x9.0#4",
        8,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "9.00",
        "0x9.0#4",
        8,
        10,
        Down,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "9.00",
        "0x9.0#4",
        8,
        10,
        Up,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "9.00",
        "0x9.0#4",
        8,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test("1.0", "0x1.0#1", 12, 1, Nearest, "1.0", "0x1.0#1", Greater);
    test(
        "1.0",
        "0x1.0#1",
        12,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        12,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        12,
        10,
        Floor,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        12,
        10,
        Ceiling,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        12,
        10,
        Down,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        12,
        10,
        Up,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        12,
        53,
        Nearest,
        "0.86602540378443860",
        "0x0.ddb3d742c26550#53",
        Less,
    );
    test("5.0", "0x5.0#3", 12, 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test(
        "5.0",
        "0x5.0#3",
        12,
        10,
        Nearest,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "-5.0",
        "-0x5.0#3",
        12,
        10,
        Nearest,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "5.0",
        "0x5.0#3",
        12,
        10,
        Floor,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "5.0",
        "0x5.0#3",
        12,
        10,
        Ceiling,
        "-0.86523",
        "-0x0.dd8#10",
        Greater,
    );
    test(
        "5.0",
        "0x5.0#3",
        12,
        10,
        Down,
        "-0.86523",
        "-0x0.dd8#10",
        Greater,
    );
    test(
        "5.0",
        "0x5.0#3",
        12,
        10,
        Up,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "5.0",
        "0x5.0#3",
        12,
        53,
        Nearest,
        "-0.86602540378443860",
        "-0x0.ddb3d742c26550#53",
        Greater,
    );
    test("7.0", "0x7.0#3", 12, 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test(
        "7.0",
        "0x7.0#3",
        12,
        10,
        Nearest,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "-7.0",
        "-0x7.0#3",
        12,
        10,
        Nearest,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "7.0",
        "0x7.0#3",
        12,
        10,
        Floor,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "7.0",
        "0x7.0#3",
        12,
        10,
        Ceiling,
        "-0.86523",
        "-0x0.dd8#10",
        Greater,
    );
    test(
        "7.0",
        "0x7.0#3",
        12,
        10,
        Down,
        "-0.86523",
        "-0x0.dd8#10",
        Greater,
    );
    test(
        "7.0",
        "0x7.0#3",
        12,
        10,
        Up,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "7.0",
        "0x7.0#3",
        12,
        53,
        Nearest,
        "-0.86602540378443860",
        "-0x0.ddb3d742c26550#53",
        Greater,
    );
    test("11.0", "0xb.0#4", 12, 1, Nearest, "1.0", "0x1.0#1", Greater);
    test(
        "11.0",
        "0xb.0#4",
        12,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "-11.0",
        "-0xb.0#4",
        12,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "11.0",
        "0xb.0#4",
        12,
        10,
        Floor,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "11.0",
        "0xb.0#4",
        12,
        10,
        Ceiling,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "11.0",
        "0xb.0#4",
        12,
        10,
        Down,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "11.0",
        "0xb.0#4",
        12,
        10,
        Up,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "11.0",
        "0xb.0#4",
        12,
        53,
        Nearest,
        "0.86602540378443860",
        "0x0.ddb3d742c26550#53",
        Less,
    );
    test("1.0", "0x1.0#1", 5, 1, Nearest, "0.25", "0x0.4#1", Less);
    test(
        "1.0",
        "0x1.0#1",
        5,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        5,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        5,
        10,
        Floor,
        "0.30859",
        "0x0.4f0#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        5,
        10,
        Ceiling,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test("1.0", "0x1.0#1", 5, 10, Down, "0.30859", "0x0.4f0#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        5,
        10,
        Up,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        5,
        53,
        Nearest,
        "0.30901699437494745",
        "0x0.4f1bbcdcbfa540#53",
        Greater,
    );
    test("2.0", "0x2.0#1", 5, 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test(
        "2.0",
        "0x2.0#1",
        5,
        10,
        Nearest,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "-2.0",
        "-0x2.0#1",
        5,
        10,
        Nearest,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        5,
        10,
        Floor,
        "-0.80957",
        "-0x0.cf4#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        5,
        10,
        Ceiling,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        5,
        10,
        Down,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test("2.0", "0x2.0#1", 5, 10, Up, "-0.80957", "-0x0.cf4#10", Less);
    test(
        "2.0",
        "0x2.0#1",
        5,
        53,
        Nearest,
        "-0.80901699437494745",
        "-0x0.cf1bbcdcbfa540#53",
        Less,
    );
    test("3.0", "0x3.0#2", 5, 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test(
        "3.0",
        "0x3.0#2",
        5,
        10,
        Nearest,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "-3.0",
        "-0x3.0#2",
        5,
        10,
        Nearest,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        5,
        10,
        Floor,
        "-0.80957",
        "-0x0.cf4#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        5,
        10,
        Ceiling,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        5,
        10,
        Down,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test("3.0", "0x3.0#2", 5, 10, Up, "-0.80957", "-0x0.cf4#10", Less);
    test(
        "3.0",
        "0x3.0#2",
        5,
        53,
        Nearest,
        "-0.80901699437494745",
        "-0x0.cf1bbcdcbfa540#53",
        Less,
    );
    test("4.0", "0x4.0#1", 5, 1, Nearest, "0.25", "0x0.4#1", Less);
    test(
        "4.0",
        "0x4.0#1",
        5,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "-4.0",
        "-0x4.0#1",
        5,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "4.0",
        "0x4.0#1",
        5,
        10,
        Floor,
        "0.30859",
        "0x0.4f0#10",
        Less,
    );
    test(
        "4.0",
        "0x4.0#1",
        5,
        10,
        Ceiling,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test("4.0", "0x4.0#1", 5, 10, Down, "0.30859", "0x0.4f0#10", Less);
    test(
        "4.0",
        "0x4.0#1",
        5,
        10,
        Up,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "4.0",
        "0x4.0#1",
        5,
        53,
        Nearest,
        "0.30901699437494745",
        "0x0.4f1bbcdcbfa540#53",
        Greater,
    );
    test("6.0", "0x6.0#2", 5, 1, Nearest, "0.25", "0x0.4#1", Less);
    test(
        "6.0",
        "0x6.0#2",
        5,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "-6.0",
        "-0x6.0#2",
        5,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "6.0",
        "0x6.0#2",
        5,
        10,
        Floor,
        "0.30859",
        "0x0.4f0#10",
        Less,
    );
    test(
        "6.0",
        "0x6.0#2",
        5,
        10,
        Ceiling,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test("6.0", "0x6.0#2", 5, 10, Down, "0.30859", "0x0.4f0#10", Less);
    test(
        "6.0",
        "0x6.0#2",
        5,
        10,
        Up,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "6.0",
        "0x6.0#2",
        5,
        53,
        Nearest,
        "0.30901699437494745",
        "0x0.4f1bbcdcbfa540#53",
        Greater,
    );
    test("1.0", "0x1.0#1", 10, 1, Nearest, "1.0", "0x1.0#1", Greater);
    test(
        "1.0",
        "0x1.0#1",
        10,
        10,
        Nearest,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        10,
        Nearest,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        10,
        10,
        Floor,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        10,
        10,
        Ceiling,
        "0.80957",
        "0x0.cf4#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        10,
        10,
        Down,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        10,
        10,
        Up,
        "0.80957",
        "0x0.cf4#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        10,
        53,
        Nearest,
        "0.80901699437494745",
        "0x0.cf1bbcdcbfa540#53",
        Greater,
    );
    test(
        "3.0", "0x3.0#2", 10, 1, Nearest, "-0.25", "-0x0.4#1", Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        10,
        10,
        Nearest,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "-3.0",
        "-0x3.0#2",
        10,
        10,
        Nearest,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        10,
        10,
        Floor,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        10,
        10,
        Ceiling,
        "-0.30859",
        "-0x0.4f0#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        10,
        10,
        Down,
        "-0.30859",
        "-0x0.4f0#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        10,
        10,
        Up,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        10,
        53,
        Nearest,
        "-0.30901699437494745",
        "-0x0.4f1bbcdcbfa540#53",
        Less,
    );
    test(
        "7.0", "0x7.0#3", 10, 1, Nearest, "-0.25", "-0x0.4#1", Greater,
    );
    test(
        "7.0",
        "0x7.0#3",
        10,
        10,
        Nearest,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "-7.0",
        "-0x7.0#3",
        10,
        10,
        Nearest,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "7.0",
        "0x7.0#3",
        10,
        10,
        Floor,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "7.0",
        "0x7.0#3",
        10,
        10,
        Ceiling,
        "-0.30859",
        "-0x0.4f0#10",
        Greater,
    );
    test(
        "7.0",
        "0x7.0#3",
        10,
        10,
        Down,
        "-0.30859",
        "-0x0.4f0#10",
        Greater,
    );
    test(
        "7.0",
        "0x7.0#3",
        10,
        10,
        Up,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "7.0",
        "0x7.0#3",
        10,
        53,
        Nearest,
        "-0.30901699437494745",
        "-0x0.4f1bbcdcbfa540#53",
        Less,
    );
    test("9.00", "0x9.0#4", 10, 1, Nearest, "1.0", "0x1.0#1", Greater);
    test(
        "9.00",
        "0x9.0#4",
        10,
        10,
        Nearest,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "-9.00",
        "-0x9.0#4",
        10,
        10,
        Nearest,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "9.00",
        "0x9.0#4",
        10,
        10,
        Floor,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "9.00",
        "0x9.0#4",
        10,
        10,
        Ceiling,
        "0.80957",
        "0x0.cf4#10",
        Greater,
    );
    test(
        "9.00",
        "0x9.0#4",
        10,
        10,
        Down,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "9.00",
        "0x9.0#4",
        10,
        10,
        Up,
        "0.80957",
        "0x0.cf4#10",
        Greater,
    );
    test(
        "9.00",
        "0x9.0#4",
        10,
        53,
        Nearest,
        "0.80901699437494745",
        "0x0.cf1bbcdcbfa540#53",
        Greater,
    );
    test("45.0", "0x2d.0#6", 360, 1, Nearest, "0.50", "0x0.8#1", Less);
    test(
        "45.0",
        "0x2d.0#6",
        360,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "-45.0",
        "-0x2d.0#6",
        360,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "45.0",
        "0x2d.0#6",
        360,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "45.0",
        "0x2d.0#6",
        360,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "45.0",
        "0x2d.0#6",
        360,
        10,
        Down,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "45.0",
        "0x2d.0#6",
        360,
        10,
        Up,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "45.0",
        "0x2d.0#6",
        360,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test(
        "135.0", "0x87.0#8", 360, 1, Nearest, "-0.50", "-0x0.8#1", Greater,
    );
    test(
        "135.0",
        "0x87.0#8",
        360,
        10,
        Nearest,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "-135.0",
        "-0x87.0#8",
        360,
        10,
        Nearest,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "135.0",
        "0x87.0#8",
        360,
        10,
        Floor,
        "-0.70801",
        "-0x0.b54#10",
        Less,
    );
    test(
        "135.0",
        "0x87.0#8",
        360,
        10,
        Ceiling,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "135.0",
        "0x87.0#8",
        360,
        10,
        Down,
        "-0.70703",
        "-0x0.b50#10",
        Greater,
    );
    test(
        "135.0",
        "0x87.0#8",
        360,
        10,
        Up,
        "-0.70801",
        "-0x0.b54#10",
        Less,
    );
    test(
        "135.0",
        "0x87.0#8",
        360,
        53,
        Nearest,
        "-0.70710678118654757",
        "-0x0.b504f333f9de68#53",
        Less,
    );
    test(
        "30.0", "0x1e.0#4", 360, 1, Nearest, "1.0", "0x1.0#1", Greater,
    );
    test(
        "30.0",
        "0x1e.0#4",
        360,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "-30.0",
        "-0x1e.0#4",
        360,
        10,
        Nearest,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "30.0",
        "0x1e.0#4",
        360,
        10,
        Floor,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "30.0",
        "0x1e.0#4",
        360,
        10,
        Ceiling,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "30.0",
        "0x1e.0#4",
        360,
        10,
        Down,
        "0.86523",
        "0x0.dd8#10",
        Less,
    );
    test(
        "30.0",
        "0x1e.0#4",
        360,
        10,
        Up,
        "0.86621",
        "0x0.ddc#10",
        Greater,
    );
    test(
        "30.0",
        "0x1e.0#4",
        360,
        53,
        Nearest,
        "0.86602540378443860",
        "0x0.ddb3d742c26550#53",
        Less,
    );
    test(
        "150.0", "0x96.0#7", 360, 1, Nearest, "-1.0", "-0x1.0#1", Less,
    );
    test(
        "150.0",
        "0x96.0#7",
        360,
        10,
        Nearest,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "-150.0",
        "-0x96.0#7",
        360,
        10,
        Nearest,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "150.0",
        "0x96.0#7",
        360,
        10,
        Floor,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "150.0",
        "0x96.0#7",
        360,
        10,
        Ceiling,
        "-0.86523",
        "-0x0.dd8#10",
        Greater,
    );
    test(
        "150.0",
        "0x96.0#7",
        360,
        10,
        Down,
        "-0.86523",
        "-0x0.dd8#10",
        Greater,
    );
    test(
        "150.0",
        "0x96.0#7",
        360,
        10,
        Up,
        "-0.86621",
        "-0x0.ddc#10",
        Less,
    );
    test(
        "150.0",
        "0x96.0#7",
        360,
        53,
        Nearest,
        "-0.86602540378443860",
        "-0x0.ddb3d742c26550#53",
        Greater,
    );
    test("72.0", "0x48.0#4", 360, 1, Nearest, "0.25", "0x0.4#1", Less);
    test(
        "72.0",
        "0x48.0#4",
        360,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "-72.0",
        "-0x48.0#4",
        360,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "72.0",
        "0x48.0#4",
        360,
        10,
        Floor,
        "0.30859",
        "0x0.4f0#10",
        Less,
    );
    test(
        "72.0",
        "0x48.0#4",
        360,
        10,
        Ceiling,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "72.0",
        "0x48.0#4",
        360,
        10,
        Down,
        "0.30859",
        "0x0.4f0#10",
        Less,
    );
    test(
        "72.0",
        "0x48.0#4",
        360,
        10,
        Up,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "72.0",
        "0x48.0#4",
        360,
        53,
        Nearest,
        "0.30901699437494745",
        "0x0.4f1bbcdcbfa540#53",
        Greater,
    );
    test(
        "144.0",
        "0x9.0E+1#4",
        360,
        1,
        Nearest,
        "-1.0",
        "-0x1.0#1",
        Less,
    );
    test(
        "144.0",
        "0x9.0E+1#4",
        360,
        10,
        Nearest,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "-144.0",
        "-0x9.0E+1#4",
        360,
        10,
        Nearest,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "144.0",
        "0x9.0E+1#4",
        360,
        10,
        Floor,
        "-0.80957",
        "-0x0.cf4#10",
        Less,
    );
    test(
        "144.0",
        "0x9.0E+1#4",
        360,
        10,
        Ceiling,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "144.0",
        "0x9.0E+1#4",
        360,
        10,
        Down,
        "-0.80859",
        "-0x0.cf0#10",
        Greater,
    );
    test(
        "144.0",
        "0x9.0E+1#4",
        360,
        10,
        Up,
        "-0.80957",
        "-0x0.cf4#10",
        Less,
    );
    test(
        "144.0",
        "0x9.0E+1#4",
        360,
        53,
        Nearest,
        "-0.80901699437494745",
        "-0x0.cf1bbcdcbfa540#53",
        Less,
    );
    test(
        "36.0", "0x24.0#4", 360, 1, Nearest, "1.0", "0x1.0#1", Greater,
    );
    test(
        "36.0",
        "0x24.0#4",
        360,
        10,
        Nearest,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "-36.0",
        "-0x24.0#4",
        360,
        10,
        Nearest,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "36.0",
        "0x24.0#4",
        360,
        10,
        Floor,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "36.0",
        "0x24.0#4",
        360,
        10,
        Ceiling,
        "0.80957",
        "0x0.cf4#10",
        Greater,
    );
    test(
        "36.0",
        "0x24.0#4",
        360,
        10,
        Down,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "36.0",
        "0x24.0#4",
        360,
        10,
        Up,
        "0.80957",
        "0x0.cf4#10",
        Greater,
    );
    test(
        "36.0",
        "0x24.0#4",
        360,
        53,
        Nearest,
        "0.80901699437494745",
        "0x0.cf1bbcdcbfa540#53",
        Greater,
    );
    test(
        "108.0", "0x6c.0#5", 360, 1, Nearest, "-0.25", "-0x0.4#1", Greater,
    );
    test(
        "108.0",
        "0x6c.0#5",
        360,
        10,
        Nearest,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "-108.0",
        "-0x6c.0#5",
        360,
        10,
        Nearest,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "108.0",
        "0x6c.0#5",
        360,
        10,
        Floor,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "108.0",
        "0x6c.0#5",
        360,
        10,
        Ceiling,
        "-0.30859",
        "-0x0.4f0#10",
        Greater,
    );
    test(
        "108.0",
        "0x6c.0#5",
        360,
        10,
        Down,
        "-0.30859",
        "-0x0.4f0#10",
        Greater,
    );
    test(
        "108.0",
        "0x6c.0#5",
        360,
        10,
        Up,
        "-0.30908",
        "-0x0.4f2#10",
        Less,
    );
    test(
        "108.0",
        "0x6c.0#5",
        360,
        53,
        Nearest,
        "-0.30901699437494745",
        "-0x0.4f1bbcdcbfa540#53",
        Less,
    );
    test("2.0", "0x2.0#1", 16, 1, Nearest, "0.50", "0x0.8#1", Less);
    test(
        "2.0",
        "0x2.0#1",
        16,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "-2.0",
        "-0x2.0#1",
        16,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        16,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        16,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        16,
        10,
        Down,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "2.0",
        "0x2.0#1",
        16,
        10,
        Up,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#1",
        16,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test("3.0", "0x3.0#2", 24, 1, Nearest, "0.50", "0x0.8#1", Less);
    test(
        "3.0",
        "0x3.0#2",
        24,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "-3.0",
        "-0x3.0#2",
        24,
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        24,
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        24,
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        24,
        10,
        Down,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "3.0",
        "0x3.0#2",
        24,
        10,
        Up,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "3.0",
        "0x3.0#2",
        24,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test("4.0", "0x4.0#1", 20, 1, Nearest, "0.25", "0x0.4#1", Less);
    test(
        "4.0",
        "0x4.0#1",
        20,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "-4.0",
        "-0x4.0#1",
        20,
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "4.0",
        "0x4.0#1",
        20,
        10,
        Floor,
        "0.30859",
        "0x0.4f0#10",
        Less,
    );
    test(
        "4.0",
        "0x4.0#1",
        20,
        10,
        Ceiling,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "4.0",
        "0x4.0#1",
        20,
        10,
        Down,
        "0.30859",
        "0x0.4f0#10",
        Less,
    );
    test(
        "4.0",
        "0x4.0#1",
        20,
        10,
        Up,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "4.0",
        "0x4.0#1",
        20,
        53,
        Nearest,
        "0.30901699437494745",
        "0x0.4f1bbcdcbfa540#53",
        Greater,
    );
    test("6.0", "0x6.0#2", 60, 1, Nearest, "1.0", "0x1.0#1", Greater);
    test(
        "6.0",
        "0x6.0#2",
        60,
        10,
        Nearest,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "-6.0",
        "-0x6.0#2",
        60,
        10,
        Nearest,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "6.0",
        "0x6.0#2",
        60,
        10,
        Floor,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "6.0",
        "0x6.0#2",
        60,
        10,
        Ceiling,
        "0.80957",
        "0x0.cf4#10",
        Greater,
    );
    test(
        "6.0",
        "0x6.0#2",
        60,
        10,
        Down,
        "0.80859",
        "0x0.cf0#10",
        Less,
    );
    test(
        "6.0",
        "0x6.0#2",
        60,
        10,
        Up,
        "0.80957",
        "0x0.cf4#10",
        Greater,
    );
    test(
        "6.0",
        "0x6.0#2",
        60,
        53,
        Nearest,
        "0.80901699437494745",
        "0x0.cf1bbcdcbfa540#53",
        Greater,
    );
}

#[test]
#[should_panic]
fn cos_with_period_prec_round_fail_1() {
    Float::ONE.cos_with_period_prec_round(3, 0, Floor);
}

#[test]
#[should_panic]
fn cos_with_period_prec_round_fail_2() {
    Float::ONE.cos_with_period_prec_round(5, 10, Exact);
}

#[test]
#[should_panic]
fn cos_with_period_prec_round_ref_fail() {
    Float::ONE.cos_with_period_prec_round_ref(5, 10, Exact);
}

#[test]
#[should_panic]
fn cos_with_period_prec_fail() {
    Float::ONE.cos_with_period_prec(3, 0);
}

#[test]
#[should_panic]
fn cos_with_period_round_fail() {
    Float::ONE.cos_with_period_round(5, Exact);
}

#[allow(clippy::needless_pass_by_value)]
fn cos_with_period_prec_round_properties_helper(x: Float, u: u64, prec: u64, rm: RoundingMode) {
    if rm == Exact {
        // Exact is only allowed when the result is exactly representable; otherwise panic.
        let (c, o) = x.cos_with_period_prec_round_ref(u, prec, Nearest);
        if o == Equal {
            let (ce, oe) = x.cos_with_period_prec_round_ref(u, prec, Exact);
            assert_eq!(ComparableFloatRef(&ce), ComparableFloatRef(&c));
            assert_eq!(oe, Equal);
        } else {
            assert_panic!(x.cos_with_period_prec_round_ref(u, prec, Exact));
        }
        return;
    }
    let (c, o) = x.clone().cos_with_period_prec_round(u, prec, rm);
    assert!(c.is_valid());
    assert_rounding_ordering_consistent(&c, rm, o);

    let (c_alt, o_alt) = x.cos_with_period_prec_round_ref(u, prec, rm);
    assert!(c_alt.is_valid());
    assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
    assert_eq!(o_alt, o);

    let mut c_alt = x.clone();
    let o_alt = c_alt.cos_with_period_prec_round_assign(u, prec, rm);
    assert!(c_alt.is_valid());
    assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
    assert_eq!(o_alt, o);

    if let Ok(rrm) = rug_round_try_from_rounding_mode(rm)
        && u32::try_from(u).is_ok()
    {
        let (rug_c, rug_o) =
            rug_cos_with_period_prec_round(&rug::Float::exact_from(&x), u, prec, rrm);
        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_c)),
            ComparableFloatRef(&c)
        );
        assert_eq!(rug_o, o);
    }

    // cos_with_period is NaN exactly for u = 0 and non-finite x, and otherwise lies in [-1, 1]
    assert_eq!(c.is_nan(), u == 0 || !x.is_finite());
    if !c.is_nan() {
        assert!(c.le_abs(&1u32));
        if c.is_normal() {
            assert_eq!(c.get_prec(), Some(prec));
        }
        // cos_with_period is even
        let (c_neg, o_neg) = (-&x).cos_with_period_prec_round(u, prec, rm);
        assert_eq!(ComparableFloatRef(&c_neg), ComparableFloatRef(&c));
        assert_eq!(o_neg, o);
        // cos_with_period has period u
        if x.is_finite() && u != 0 {
            let (shifted, os) =
                x.add_prec_round_ref_val(Float::from(u), x.significant_bits() + 64, Nearest);
            if os == Equal {
                let (c_shifted, o_shifted) = shifted.cos_with_period_prec_round(u, prec, rm);
                assert_eq!(ComparableFloatRef(&c_shifted), ComparableFloatRef(&c));
                assert_eq!(o_shifted, o);
            }
        }
    }

    if o == Equal {
        for rm in exhaustive_rounding_modes() {
            let (s, oo) = x.cos_with_period_prec_round_ref(u, prec, rm);
            assert_eq!(ComparableFloatRef(&s), ComparableFloatRef(&c));
            assert_eq!(oo, Equal);
        }
    } else {
        assert_panic!(x.cos_with_period_prec_round_ref(u, prec, Exact));
    }
}

#[test]
fn cos_with_period_prec_round_properties() {
    float_unsigned_unsigned_rounding_mode_quadruple_gen_var_15().test_properties(
        |(x, u, prec, rm)| {
            cos_with_period_prec_round_properties_helper(x, u, prec, rm);
        },
    );

    float_unsigned_unsigned_rounding_mode_quadruple_gen_var_16().test_properties(
        |(x, u, prec, rm)| {
            cos_with_period_prec_round_properties_helper(x, u, prec, rm);
        },
    );

    unsigned_rounding_mode_pair_gen_var_3().test_properties(|(prec, rm)| {
        // cos_with_period(0) = 1 and cos_with_period(x, 0) = NaN, exactly
        let (c, o) = Float::ZERO.cos_with_period_prec_round(4, prec, rm);
        assert_eq!(ComparableFloat(c), ComparableFloat(Float::one_prec(prec)));
        assert_eq!(o, Equal);
        let (c, o) = Float::ONE.cos_with_period_prec_round(0, prec, rm);
        assert!(c.is_nan());
        assert_eq!(o, Equal);
        // exact cases: quarter turns
        for (k, expected) in [
            (0u32, Float::one_prec(prec)),
            (1, Float::ZERO),
            (2, -Float::one_prec(prec)),
            (3, Float::ZERO),
        ] {
            let (c, o) = Float::from(k).cos_with_period_prec_round(4, prec, rm);
            assert_eq!(ComparableFloat(c), ComparableFloat(expected));
            assert_eq!(o, Equal);
        }
        // exact cases: sixth turns
        let half = Float::one_prec(prec) >> 1u32;
        for (k, expected) in [(1u32, half.clone()), (2, -&half), (4, -&half), (5, half.clone())] {
            let (c, o) = Float::from(k).cos_with_period_prec_round(6, prec, rm);
            assert_eq!(ComparableFloat(c), ComparableFloat(expected));
            assert_eq!(o, Equal);
        }
    });
}

#[test]
fn cos_with_period_prec_properties() {
    float_unsigned_unsigned_triple_gen_var_1::<u64, u64>().test_properties(|(x, u, prec)| {
        let (c, o) = x.clone().cos_with_period_prec(u, prec);
        assert!(c.is_valid());
        let (c_alt, o_alt) = x.cos_with_period_prec_ref(u, prec);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let (c_alt, o_alt) = x.cos_with_period_prec_round_ref(u, prec, Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let mut c_alt = x.clone();
        let o_alt = c_alt.cos_with_period_prec_assign(u, prec);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        if u32::try_from(u).is_ok() {
            let (rug_c, rug_o) = rug_cos_with_period_prec(&rug::Float::exact_from(&x), u, prec);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    });
}

#[test]
fn cos_with_period_round_properties() {
    float_unsigned_rounding_mode_triple_gen_var_38().test_properties(|(x, u, rm)| {
        let (c, o) = x.clone().cos_with_period_round(u, rm);
        assert!(c.is_valid());
        assert_rounding_ordering_consistent(&c, rm, o);
        let (c_alt, o_alt) = x.cos_with_period_round_ref(u, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let (c_alt, o_alt) = x.cos_with_period_prec_round_ref(u, x.significant_bits(), rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let mut c_alt = x.clone();
        let o_alt = c_alt.cos_with_period_round_assign(u, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
    });
}

#[test]
fn cos_with_period_properties() {
    float_unsigned_pair_gen_var_2::<u64>().test_properties(|(x, u)| {
        let c = x.clone().cos_with_period(u);
        assert!(c.is_valid());
        let c_alt = x.cos_with_period_ref(u);
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        let mut c_alt = x.clone();
        c_alt.cos_with_period_assign(u);
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        // the same as rounding to the input's precision, to nearest
        let (c_alt, _) = x.cos_with_period_prec_round_ref(u, x.significant_bits(), Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        // cos_with_period is even
        assert_eq!(
            ComparableFloatRef(&(-&x).cos_with_period(u)),
            ComparableFloatRef(&c)
        );
    });
}

// The `Rational` inputs include exact and closed-form cases hit directly (1/3, 1/8, 1/5, 1/10 of a
// turn), which the `Float` version can only reach through a divisor, and non-dyadic inputs whose
// cosines MPFR cannot compute exactly, since it must round the input first.
#[test]
fn test_cos_with_period_rational_prec_round() {
    let test = |s, u: u64, prec: u64, rm, out: &str, out_hex: &str, o_out: Ordering| {
        let x = Rational::from_str(s).unwrap();

        let (c, o) = Float::cos_with_period_rational_prec_round(x.clone(), u, prec, rm);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, o_out);

        let (c_alt, o_alt) = Float::cos_with_period_rational_prec_round_ref(&x, u, prec, rm);
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        if rm == Nearest {
            let (c_alt, o_alt) = Float::cos_with_period_rational_prec(x.clone(), u, prec);
            assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
            assert_eq!(o_alt, o);
            let (c_alt, o_alt) = Float::cos_with_period_rational_prec_ref(&x, u, prec);
            assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
            assert_eq!(o_alt, o);
        }
    };
    test("0", 4, 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("0", 4, 10, Nearest, "1.0000", "0x1.000#10", Equal);
    test("0", 4, 10, Floor, "1.0000", "0x1.000#10", Equal);
    test("0", 4, 10, Ceiling, "1.0000", "0x1.000#10", Equal);
    test("0", 4, 10, Exact, "1.0000", "0x1.000#10", Equal);
    test(
        "0",
        4,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test("0", 0, 1, Nearest, "NaN", "NaN", Equal);
    // - u = 0: NaN
    test("0", 0, 10, Nearest, "NaN", "NaN", Equal);
    test("0", 0, 10, Floor, "NaN", "NaN", Equal);
    test("0", 0, 10, Ceiling, "NaN", "NaN", Equal);
    test("0", 0, 10, Exact, "NaN", "NaN", Equal);
    test("0", 0, 53, Nearest, "NaN", "NaN", Equal);
    test("1", 0, 1, Nearest, "NaN", "NaN", Equal);
    test("1", 0, 10, Nearest, "NaN", "NaN", Equal);
    test("1", 0, 10, Floor, "NaN", "NaN", Equal);
    test("1", 0, 10, Ceiling, "NaN", "NaN", Equal);
    test("1", 0, 10, Exact, "NaN", "NaN", Equal);
    test("1", 0, 53, Nearest, "NaN", "NaN", Equal);
    test("90", 360, 1, Nearest, "0.0", "0x0.0", Equal);
    // - exact: a quarter turn
    test("90", 360, 10, Nearest, "0.0", "0x0.0", Equal);
    test("90", 360, 10, Floor, "0.0", "0x0.0", Equal);
    test("90", 360, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("90", 360, 10, Exact, "0.0", "0x0.0", Equal);
    test("90", 360, 53, Nearest, "0.0", "0x0.0", Equal);
    test("180", 360, 1, Nearest, "-1.0", "-0x1.0#1", Equal);
    test("180", 360, 10, Nearest, "-1.0000", "-0x1.000#10", Equal);
    test("180", 360, 10, Floor, "-1.0000", "-0x1.000#10", Equal);
    test("180", 360, 10, Ceiling, "-1.0000", "-0x1.000#10", Equal);
    test("180", 360, 10, Exact, "-1.0000", "-0x1.000#10", Equal);
    test(
        "180",
        360,
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test("270", 360, 1, Nearest, "0.0", "0x0.0", Equal);
    test("270", 360, 10, Nearest, "0.0", "0x0.0", Equal);
    test("270", 360, 10, Floor, "0.0", "0x0.0", Equal);
    test("270", 360, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("270", 360, 10, Exact, "0.0", "0x0.0", Equal);
    test("270", 360, 53, Nearest, "0.0", "0x0.0", Equal);
    test("360", 360, 1, Nearest, "1.0", "0x1.0#1", Equal);
    // - a full turn: reduced to 0
    test("360", 360, 10, Nearest, "1.0000", "0x1.000#10", Equal);
    test("360", 360, 10, Floor, "1.0000", "0x1.000#10", Equal);
    test("360", 360, 10, Ceiling, "1.0000", "0x1.000#10", Equal);
    test("360", 360, 10, Exact, "1.0000", "0x1.000#10", Equal);
    test(
        "360",
        360,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test("450", 360, 1, Nearest, "0.0", "0x0.0", Equal);
    test("450", 360, 10, Nearest, "0.0", "0x0.0", Equal);
    test("450", 360, 10, Floor, "0.0", "0x0.0", Equal);
    test("450", 360, 10, Ceiling, "0.0", "0x0.0", Equal);
    test("450", 360, 10, Exact, "0.0", "0x0.0", Equal);
    test("450", 360, 53, Nearest, "0.0", "0x0.0", Equal);
    test("60", 360, 1, Nearest, "0.50", "0x0.8#1", Equal);
    // - exact: a sixth of a turn
    test("60", 360, 10, Nearest, "0.50000", "0x0.800#10", Equal);
    test("60", 360, 10, Floor, "0.50000", "0x0.800#10", Equal);
    test("60", 360, 10, Ceiling, "0.50000", "0x0.800#10", Equal);
    test("60", 360, 10, Exact, "0.50000", "0x0.800#10", Equal);
    test(
        "60",
        360,
        53,
        Nearest,
        "0.50000000000000000",
        "0x0.80000000000000#53",
        Equal,
    );
    test("120", 360, 1, Nearest, "-0.50", "-0x0.8#1", Equal);
    test("120", 360, 10, Nearest, "-0.50000", "-0x0.800#10", Equal);
    test("120", 360, 10, Floor, "-0.50000", "-0x0.800#10", Equal);
    test("120", 360, 10, Ceiling, "-0.50000", "-0x0.800#10", Equal);
    test("120", 360, 10, Exact, "-0.50000", "-0x0.800#10", Equal);
    test(
        "120",
        360,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test("240", 360, 1, Nearest, "-0.50", "-0x0.8#1", Equal);
    test("240", 360, 10, Nearest, "-0.50000", "-0x0.800#10", Equal);
    test("240", 360, 10, Floor, "-0.50000", "-0x0.800#10", Equal);
    test("240", 360, 10, Ceiling, "-0.50000", "-0x0.800#10", Equal);
    test("240", 360, 10, Exact, "-0.50000", "-0x0.800#10", Equal);
    test(
        "240",
        360,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test("300", 360, 1, Nearest, "0.50", "0x0.8#1", Equal);
    test("300", 360, 10, Nearest, "0.50000", "0x0.800#10", Equal);
    test("300", 360, 10, Floor, "0.50000", "0x0.800#10", Equal);
    test("300", 360, 10, Ceiling, "0.50000", "0x0.800#10", Equal);
    test("300", 360, 10, Exact, "0.50000", "0x0.800#10", Equal);
    test(
        "300",
        360,
        53,
        Nearest,
        "0.50000000000000000",
        "0x0.80000000000000#53",
        Equal,
    );
    test("45", 360, 1, Nearest, "0.50", "0x0.8#1", Less);
    // - closed form: sqrt(2)/2
    test("45", 360, 10, Nearest, "0.70703", "0x0.b50#10", Less);
    test("45", 360, 10, Floor, "0.70703", "0x0.b50#10", Less);
    test("45", 360, 10, Ceiling, "0.70801", "0x0.b54#10", Greater);
    test(
        "45",
        360,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test("135", 360, 1, Nearest, "-0.50", "-0x0.8#1", Greater);
    test("135", 360, 10, Nearest, "-0.70703", "-0x0.b50#10", Greater);
    test("135", 360, 10, Floor, "-0.70801", "-0x0.b54#10", Less);
    test("135", 360, 10, Ceiling, "-0.70703", "-0x0.b50#10", Greater);
    test(
        "135",
        360,
        53,
        Nearest,
        "-0.70710678118654757",
        "-0x0.b504f333f9de68#53",
        Less,
    );
    test("30", 360, 1, Nearest, "1.0", "0x1.0#1", Greater);
    // - closed form: sqrt(3)/2
    test("30", 360, 10, Nearest, "0.86621", "0x0.ddc#10", Greater);
    test("30", 360, 10, Floor, "0.86523", "0x0.dd8#10", Less);
    test("30", 360, 10, Ceiling, "0.86621", "0x0.ddc#10", Greater);
    test(
        "30",
        360,
        53,
        Nearest,
        "0.86602540378443860",
        "0x0.ddb3d742c26550#53",
        Less,
    );
    test("150", 360, 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test("150", 360, 10, Nearest, "-0.86621", "-0x0.ddc#10", Less);
    test("150", 360, 10, Floor, "-0.86621", "-0x0.ddc#10", Less);
    test("150", 360, 10, Ceiling, "-0.86523", "-0x0.dd8#10", Greater);
    test(
        "150",
        360,
        53,
        Nearest,
        "-0.86602540378443860",
        "-0x0.ddb3d742c26550#53",
        Greater,
    );
    test("72", 360, 1, Nearest, "0.25", "0x0.4#1", Less);
    // - closed form: (phi - 1)/2
    test("72", 360, 10, Nearest, "0.30908", "0x0.4f2#10", Greater);
    test("72", 360, 10, Floor, "0.30859", "0x0.4f0#10", Less);
    test("72", 360, 10, Ceiling, "0.30908", "0x0.4f2#10", Greater);
    test(
        "72",
        360,
        53,
        Nearest,
        "0.30901699437494745",
        "0x0.4f1bbcdcbfa540#53",
        Greater,
    );
    test("144", 360, 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test("144", 360, 10, Nearest, "-0.80859", "-0x0.cf0#10", Greater);
    test("144", 360, 10, Floor, "-0.80957", "-0x0.cf4#10", Less);
    test("144", 360, 10, Ceiling, "-0.80859", "-0x0.cf0#10", Greater);
    test(
        "144",
        360,
        53,
        Nearest,
        "-0.80901699437494745",
        "-0x0.cf1bbcdcbfa540#53",
        Less,
    );
    test("36", 360, 1, Nearest, "1.0", "0x1.0#1", Greater);
    // - closed form: phi/2
    test("36", 360, 10, Nearest, "0.80859", "0x0.cf0#10", Less);
    test("36", 360, 10, Floor, "0.80859", "0x0.cf0#10", Less);
    test("36", 360, 10, Ceiling, "0.80957", "0x0.cf4#10", Greater);
    test(
        "36",
        360,
        53,
        Nearest,
        "0.80901699437494745",
        "0x0.cf1bbcdcbfa540#53",
        Greater,
    );
    test("108", 360, 1, Nearest, "-0.25", "-0x0.4#1", Greater);
    test("108", 360, 10, Nearest, "-0.30908", "-0x0.4f2#10", Less);
    test("108", 360, 10, Floor, "-0.30908", "-0x0.4f2#10", Less);
    test("108", 360, 10, Ceiling, "-0.30859", "-0x0.4f0#10", Greater);
    test(
        "108",
        360,
        53,
        Nearest,
        "-0.30901699437494745",
        "-0x0.4f1bbcdcbfa540#53",
        Less,
    );
    test("1/3", 1, 1, Nearest, "-0.50", "-0x0.8#1", Equal);
    // - a third of a turn, from a rational directly
    test("1/3", 1, 10, Nearest, "-0.50000", "-0x0.800#10", Equal);
    test("1/3", 1, 10, Floor, "-0.50000", "-0x0.800#10", Equal);
    test("1/3", 1, 10, Ceiling, "-0.50000", "-0x0.800#10", Equal);
    test("1/3", 1, 10, Exact, "-0.50000", "-0x0.800#10", Equal);
    test(
        "1/3",
        1,
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test("1/8", 1, 1, Nearest, "0.50", "0x0.8#1", Less);
    test("1/8", 1, 10, Nearest, "0.70703", "0x0.b50#10", Less);
    test("1/8", 1, 10, Floor, "0.70703", "0x0.b50#10", Less);
    test("1/8", 1, 10, Ceiling, "0.70801", "0x0.b54#10", Greater);
    test(
        "1/8",
        1,
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test("1/5", 1, 1, Nearest, "0.25", "0x0.4#1", Less);
    test("1/5", 1, 10, Nearest, "0.30908", "0x0.4f2#10", Greater);
    test("1/5", 1, 10, Floor, "0.30859", "0x0.4f0#10", Less);
    test("1/5", 1, 10, Ceiling, "0.30908", "0x0.4f2#10", Greater);
    test(
        "1/5",
        1,
        53,
        Nearest,
        "0.30901699437494745",
        "0x0.4f1bbcdcbfa540#53",
        Greater,
    );
    test("-1/10", 1, 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("-1/10", 1, 10, Nearest, "0.80859", "0x0.cf0#10", Less);
    test("-1/10", 1, 10, Floor, "0.80859", "0x0.cf0#10", Less);
    test("-1/10", 1, 10, Ceiling, "0.80957", "0x0.cf4#10", Greater);
    test(
        "-1/10",
        1,
        53,
        Nearest,
        "0.80901699437494745",
        "0x0.cf1bbcdcbfa540#53",
        Greater,
    );
    test("1/7", 1, 1, Nearest, "0.50", "0x0.8#1", Less);
    // - general case
    test("1/7", 1, 10, Nearest, "0.62305", "0x0.9f8#10", Less);
    test("1/7", 1, 10, Floor, "0.62305", "0x0.9f8#10", Less);
    test("1/7", 1, 10, Ceiling, "0.62402", "0x0.9fc#10", Greater);
    test(
        "1/7",
        1,
        53,
        Nearest,
        "0.62348980185873348",
        "0x0.9f9d07145f6e88#53",
        Less,
    );
    test("2/7", 1, 1, Nearest, "-0.25", "-0x0.4#1", Less);
    test("2/7", 1, 10, Nearest, "-0.22241", "-0x0.38f#10", Greater);
    test("2/7", 1, 10, Floor, "-0.22266", "-0x0.390#10", Less);
    test("2/7", 1, 10, Ceiling, "-0.22241", "-0x0.38f#10", Greater);
    test(
        "2/7",
        1,
        53,
        Nearest,
        "-0.22252093395631439",
        "-0x0.38f721c6048b04#53",
        Greater,
    );
    test("-3/7", 1, 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test("-3/7", 1, 10, Nearest, "-0.90137", "-0x0.e6c#10", Less);
    test("-3/7", 1, 10, Floor, "-0.90137", "-0x0.e6c#10", Less);
    test("-3/7", 1, 10, Ceiling, "-0.90039", "-0x0.e68#10", Greater);
    test(
        "-3/7",
        1,
        53,
        Nearest,
        "-0.90096886790241915",
        "-0x0.e6a5e54e5ae388#53",
        Less,
    );
    test("22/7", 1, 1, Nearest, "0.50", "0x0.8#1", Less);
    // - reduced modulo 1
    test("22/7", 1, 10, Nearest, "0.62305", "0x0.9f8#10", Less);
    test("22/7", 1, 10, Floor, "0.62305", "0x0.9f8#10", Less);
    test("22/7", 1, 10, Ceiling, "0.62402", "0x0.9fc#10", Greater);
    test(
        "22/7",
        1,
        53,
        Nearest,
        "0.62348980185873348",
        "0x0.9f9d07145f6e88#53",
        Less,
    );
    test("1/7", 3, 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1/7", 3, 10, Nearest, "0.95605", "0x0.f4c#10", Greater);
    test("1/7", 3, 10, Floor, "0.95508", "0x0.f48#10", Less);
    test("1/7", 3, 10, Ceiling, "0.95605", "0x0.f4c#10", Greater);
    test(
        "1/7",
        3,
        53,
        Nearest,
        "0.95557280578614068",
        "0x0.f4a06b5dcc6628#53",
        Less,
    );
    test("355/113", 360, 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("355/113", 360, 10, Nearest, "0.99805", "0x0.ff8#10", Less);
    test("355/113", 360, 10, Floor, "0.99805", "0x0.ff8#10", Less);
    test(
        "355/113",
        360,
        10,
        Ceiling,
        "0.99902",
        "0x0.ffc#10",
        Greater,
    );
    test(
        "355/113",
        360,
        53,
        Nearest,
        "0.99849714960870273",
        "0x0.ff9d825ab7f600#53",
        Greater,
    );
    test("1", 7, 1, Nearest, "0.50", "0x0.8#1", Less);
    test("1", 7, 10, Nearest, "0.62305", "0x0.9f8#10", Less);
    test("1", 7, 10, Floor, "0.62305", "0x0.9f8#10", Less);
    test("1", 7, 10, Ceiling, "0.62402", "0x0.9fc#10", Greater);
    test(
        "1",
        7,
        53,
        Nearest,
        "0.62348980185873348",
        "0x0.9f9d07145f6e88#53",
        Less,
    );
    test("1000000", 7, 1, Nearest, "0.50", "0x0.8#1", Less);
    test("1000000", 7, 10, Nearest, "0.62305", "0x0.9f8#10", Less);
    test("1000000", 7, 10, Floor, "0.62305", "0x0.9f8#10", Less);
    test("1000000", 7, 10, Ceiling, "0.62402", "0x0.9fc#10", Greater);
    test(
        "1000000",
        7,
        53,
        Nearest,
        "0.62348980185873348",
        "0x0.9f9d07145f6e88#53",
        Less,
    );
    test("1/1000000", 1, 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1/1000000", 1, 10, Nearest, "1.0000", "0x1.000#10", Greater);
    test("1/1000000", 1, 10, Floor, "0.99902", "0x0.ffc#10", Less);
    test("1/1000000", 1, 10, Ceiling, "1.0000", "0x1.000#10", Greater);
    test(
        "1/1000000",
        1,
        53,
        Nearest,
        "0.99999999998026079",
        "0x0.ffffffffea4be8#53",
        Less,
    );
    test(
        "1/1000000000000000000000000000000",
        1,
        1,
        Nearest,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    // - small input: the cosine rounds to 1
    test(
        "1/1000000000000000000000000000000",
        1,
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1000000000000000000000000000000",
        1,
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1/1000000000000000000000000000000",
        1,
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/1000000000000000000000000000000",
        1,
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "100000000000000000000000000000000000000001",
        4,
        1,
        Nearest,
        "0.0",
        "0x0.0",
        Equal,
    );
    // - huge numerator, reduced exactly
    test(
        "100000000000000000000000000000000000000001",
        4,
        10,
        Nearest,
        "0.0",
        "0x0.0",
        Equal,
    );
    test(
        "100000000000000000000000000000000000000001",
        4,
        10,
        Floor,
        "0.0",
        "0x0.0",
        Equal,
    );
    test(
        "100000000000000000000000000000000000000001",
        4,
        10,
        Ceiling,
        "0.0",
        "0x0.0",
        Equal,
    );
    test(
        "100000000000000000000000000000000000000001",
        4,
        10,
        Exact,
        "0.0",
        "0x0.0",
        Equal,
    );
    test(
        "100000000000000000000000000000000000000001",
        4,
        53,
        Nearest,
        "0.0",
        "0x0.0",
        Equal,
    );
    // - x/u near an odd multiple of 1/4: the near-zero path
    test(
        "111414603535684224740921180161/1237940039285380274899124224",
        360,
        53,
        Nearest,
        "-1.4098657419642452e-29",
        "-0x1.1df46a2529d39E-24#53",
        Greater,
    );
    test(
        "111414603535684224740921180161/1237940039285380274899124224",
        360,
        53,
        Floor,
        "-1.4098657419642455e-29",
        "-0x1.1df46a2529d3aE-24#53",
        Less,
    );
    test(
        "342265662061621938404109865451519/1267650600228229401496703205376",
        360,
        10,
        Nearest,
        "-1.3770e-32",
        "-0x4.78E-27#10",
        Less,
    );
}

#[test]
#[should_panic]
fn cos_with_period_rational_prec_round_fail_1() {
    Float::cos_with_period_rational_prec_round(Rational::ONE, 7, 0, Floor);
}

#[test]
#[should_panic]
fn cos_with_period_rational_prec_round_fail_2() {
    Float::cos_with_period_rational_prec_round(Rational::ONE, 7, 10, Exact);
}

#[test]
#[should_panic]
fn cos_with_period_rational_prec_round_ref_fail() {
    Float::cos_with_period_rational_prec_round_ref(&Rational::ONE, 7, 10, Exact);
}

#[test]
#[should_panic]
fn cos_with_period_rational_prec_fail() {
    Float::cos_with_period_rational_prec(Rational::ONE, 7, 0);
}

#[allow(clippy::needless_pass_by_value)]
fn cos_with_period_rational_prec_round_properties_helper(
    x: Rational,
    u: u64,
    prec: u64,
    rm: RoundingMode,
) {
    if rm == Exact {
        // Exact is only allowed when the result is exactly representable; otherwise panic.
        let (c, o) = Float::cos_with_period_rational_prec_round_ref(&x, u, prec, Nearest);
        if o == Equal {
            let (ce, oe) = Float::cos_with_period_rational_prec_round_ref(&x, u, prec, Exact);
            assert_eq!(ComparableFloatRef(&ce), ComparableFloatRef(&c));
            assert_eq!(oe, Equal);
        } else {
            assert_panic!(Float::cos_with_period_rational_prec_round_ref(
                &x, u, prec, Exact
            ));
        }
        return;
    }
    let (c, o) = Float::cos_with_period_rational_prec_round(x.clone(), u, prec, rm);
    assert!(c.is_valid());
    assert_rounding_ordering_consistent(&c, rm, o);

    let (c_alt, o_alt) = Float::cos_with_period_rational_prec_round_ref(&x, u, prec, rm);
    assert!(c_alt.is_valid());
    assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
    assert_eq!(o_alt, o);

    // MPFR rounds the input to a `Float` first, so it cannot see the exact cases of non-dyadic
    // inputs (1/3 of a turn, say); those are checked separately below.
    if o != Equal
        && let Ok(rrm) = rug_round_try_from_rounding_mode(rm)
        && u32::try_from(u).is_ok()
    {
        let (rug_c, rug_o) = rug_cos_with_period_rational_prec_round(&x, u, prec, rrm);
        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_c)),
            ComparableFloatRef(&c)
        );
        assert_eq!(rug_o, o);
    }

    // NaN exactly for u = 0, and otherwise in [-1, 1]
    assert_eq!(c.is_nan(), u == 0);
    if u != 0 {
        assert!(c.le_abs(&1u32));
        if c.is_normal() {
            assert_eq!(c.get_prec(), Some(prec));
        }
        // even, and periodic with period u
        let (c_neg, o_neg) = Float::cos_with_period_rational_prec_round(-&x, u, prec, rm);
        assert_eq!(ComparableFloatRef(&c_neg), ComparableFloatRef(&c));
        assert_eq!(o_neg, o);
        let (c_shifted, o_shifted) =
            Float::cos_with_period_rational_prec_round(&x + Rational::from(u), u, prec, rm);
        assert_eq!(ComparableFloatRef(&c_shifted), ComparableFloatRef(&c));
        assert_eq!(o_shifted, o);
        // a Float input agrees with the Float version
        if let Ok(f) = Float::try_from(&x) {
            let (c_alt, o_alt) = f.cos_with_period_prec_round(u, prec, rm);
            assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
            assert_eq!(o_alt, o);
        }
    }

    if o == Equal {
        for rm in exhaustive_rounding_modes() {
            let (s, oo) = Float::cos_with_period_rational_prec_round_ref(&x, u, prec, rm);
            assert_eq!(ComparableFloatRef(&s), ComparableFloatRef(&c));
            assert_eq!(oo, Equal);
        }
    } else {
        assert_panic!(Float::cos_with_period_rational_prec_round_ref(
            &x, u, prec, Exact
        ));
    }
}

#[test]
fn cos_with_period_rational_prec_round_properties() {
    rational_unsigned_unsigned_rounding_mode_quadruple_gen_var_4().test_properties(
        |(x, u, prec, rm)| {
            cos_with_period_rational_prec_round_properties_helper(x, u, prec, rm);
        },
    );

    unsigned_rounding_mode_pair_gen_var_3().test_properties(|(prec, rm)| {
        let (c, o) = Float::cos_with_period_rational_prec_round(Rational::ZERO, 4, prec, rm);
        assert_eq!(ComparableFloat(c), ComparableFloat(Float::one_prec(prec)));
        assert_eq!(o, Equal);
        let (c, o) = Float::cos_with_period_rational_prec_round(Rational::ONE, 0, prec, rm);
        assert!(c.is_nan());
        assert_eq!(o, Equal);
        // exact cases, straight from a fraction of a turn
        for (s, expected) in [
            ("1/4", Float::ZERO),
            ("1/2", -Float::one_prec(prec)),
            ("3/4", Float::ZERO),
            ("1", Float::one_prec(prec)),
            ("1/6", Float::one_prec(prec) >> 1u32),
            ("1/3", -(Float::one_prec(prec) >> 1u32)),
        ] {
            let (c, o) = Float::cos_with_period_rational_prec_round(
                Rational::from_str(s).unwrap(),
                1,
                prec,
                rm,
            );
            assert_eq!(ComparableFloat(c), ComparableFloat(expected));
            assert_eq!(o, Equal);
        }
    });
}

#[test]
fn cos_with_period_rational_prec_properties() {
    rational_unsigned_unsigned_rounding_mode_quadruple_gen_var_4().test_properties(
        |(x, u, prec, _)| {
            let (c, o) = Float::cos_with_period_rational_prec(x.clone(), u, prec);
            assert!(c.is_valid());
            let (c_alt, o_alt) = Float::cos_with_period_rational_prec_ref(&x, u, prec);
            assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
            assert_eq!(o_alt, o);
            let (c_alt, o_alt) =
                Float::cos_with_period_rational_prec_round_ref(&x, u, prec, Nearest);
            assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
            assert_eq!(o_alt, o);
            if o != Equal && u32::try_from(u).is_ok() {
                let (rug_c, rug_o) = rug_cos_with_period_rational_prec(&x, u, prec);
                assert_eq!(
                    ComparableFloatRef(&Float::from(&rug_c)),
                    ComparableFloatRef(&c)
                );
                assert_eq!(rug_o, o);
            }
        },
    );
}

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_cos_with_period() {
    fn test<T: PrimitiveFloat>(x: T, u: u64, out: T)
    where
        Float: From<T> + PartialOrd<T>,
        for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
    {
        assert_eq!(
            NiceFloat(primitive_float_cos_with_period(x, u)),
            NiceFloat(out)
        );
    }
    test::<f32>(f32::NAN, 360, f32::NAN);
    test::<f32>(f32::INFINITY, 360, f32::NAN);
    test::<f32>(f32::NEGATIVE_INFINITY, 360, f32::NAN);
    test::<f32>(1.0, 0, f32::NAN);
    test::<f32>(0.0, 360, 1.0);
    test::<f32>(-0.0, 360, 1.0);
    test::<f32>(90.0, 360, 0.0);
    test::<f32>(180.0, 360, -1.0);
    test::<f32>(270.0, 360, 0.0);
    test::<f32>(360.0, 360, 1.0);
    test::<f32>(60.0, 360, 0.5);
    test::<f32>(120.0, 360, -0.5);
    test::<f32>(45.0, 360, core::f32::consts::FRAC_1_SQRT_2);
    test::<f32>(30.0, 360, 0.8660254);
    test::<f32>(72.0, 360, 0.309017);
    test::<f32>(36.0, 360, 0.809017);
    test::<f32>(1.0, 7, 0.6234898);
    test::<f32>(-1.0, 7, 0.6234898);
    test::<f32>(2.0, 7, -0.22252093);
    test::<f32>(1.0, 360, 0.9998477);
    test::<f32>(100.0, 360, -0.17364818);
    test::<f32>(1.0e10, 360, 0.17364818);
    test::<f32>(1.0e30, 7, 0.6234898);
    test::<f32>(1.0e-30, 7, 1.0);
    test::<f32>(3.4028235e38, 360, 1.0);
    test::<f32>(0.5, 1, -1.0);
    test::<f32>(0.25, 1, 0.0);
    test::<f32>(0.1, 1, 0.809017);

    test::<f64>(f64::NAN, 360, f64::NAN);
    test::<f64>(f64::INFINITY, 360, f64::NAN);
    test::<f64>(f64::NEGATIVE_INFINITY, 360, f64::NAN);
    test::<f64>(1.0, 0, f64::NAN);
    test::<f64>(0.0, 360, 1.0);
    test::<f64>(-0.0, 360, 1.0);
    test::<f64>(90.0, 360, 0.0);
    test::<f64>(180.0, 360, -1.0);
    test::<f64>(270.0, 360, 0.0);
    test::<f64>(360.0, 360, 1.0);
    test::<f64>(60.0, 360, 0.5);
    test::<f64>(120.0, 360, -0.5);
    test::<f64>(45.0, 360, core::f64::consts::FRAC_1_SQRT_2);
    test::<f64>(30.0, 360, 0.8660254037844386);
    test::<f64>(72.0, 360, 0.30901699437494745);
    test::<f64>(36.0, 360, 0.8090169943749475);
    test::<f64>(1.0, 7, 0.6234898018587335);
    test::<f64>(-1.0, 7, 0.6234898018587335);
    test::<f64>(2.0, 7, -0.2225209339563144);
    test::<f64>(1.0, 360, 0.9998476951563913);
    test::<f64>(100.0, 360, -0.17364817766693036);
    test::<f64>(1.0e10, 360, 0.17364817766693036);
    test::<f64>(1.0e100, 7, -0.2225209339563144);
    test::<f64>(1.0e-100, 7, 1.0);
    test::<f64>(1.7976931348623157e308, 360, -0.6156614753256583);
    test::<f64>(0.5, 1, -1.0);
    test::<f64>(0.25, 1, 0.0);
    test::<f64>(0.1, 1, 0.8090169943749475);
}

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_cos_with_period_rational() {
    fn test<T: PrimitiveFloat>(s: &str, u: u64, out: T)
    where
        Float: From<T> + PartialOrd<T>,
        for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
    {
        let x = Rational::from_str(s).unwrap();
        assert_eq!(
            NiceFloat(primitive_float_cos_with_period_rational::<T>(&x, u)),
            NiceFloat(out)
        );
    }
    test::<f32>("0", 360, 1.0);
    test::<f32>("1", 0, f32::NAN);
    test::<f32>("90", 360, 0.0);
    test::<f32>("180", 360, -1.0);
    test::<f32>("60", 360, 0.5);
    test::<f32>("45", 360, core::f32::consts::FRAC_1_SQRT_2);
    test::<f32>("36", 360, 0.809017);
    test::<f32>("1/3", 1, -0.5);
    test::<f32>("1/8", 1, core::f32::consts::FRAC_1_SQRT_2);
    test::<f32>("1/5", 1, 0.309017);
    test::<f32>("1/7", 1, 0.6234898);
    test::<f32>("-2/7", 1, -0.22252093);
    test::<f32>("22/7", 1, 0.6234898);
    test::<f32>("1", 7, 0.6234898);
    test::<f32>("1000000", 7, 0.6234898);
    test::<f32>("1/1000000", 1, 1.0);
    test::<f32>("355/113", 360, 0.9984971);

    test::<f64>("0", 360, 1.0);
    test::<f64>("1", 0, f64::NAN);
    test::<f64>("90", 360, 0.0);
    test::<f64>("180", 360, -1.0);
    test::<f64>("60", 360, 0.5);
    test::<f64>("45", 360, core::f64::consts::FRAC_1_SQRT_2);
    test::<f64>("36", 360, 0.8090169943749475);
    test::<f64>("1/3", 1, -0.5);
    test::<f64>("1/8", 1, core::f64::consts::FRAC_1_SQRT_2);
    test::<f64>("1/5", 1, 0.30901699437494745);
    test::<f64>("1/7", 1, 0.6234898018587335);
    test::<f64>("-2/7", 1, -0.2225209339563144);
    test::<f64>("22/7", 1, 0.6234898018587335);
    test::<f64>("1", 7, 0.6234898018587335);
    test::<f64>("1000000", 7, 0.6234898018587335);
    test::<f64>("1/1000000", 1, 0.9999999999802608);
    test::<f64>("355/113", 360, 0.9984971496087027);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_cos_with_period_properties_helper<T: PrimitiveFloat>()
where
    Float: From<T> + PartialOrd<T>,
    for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
{
    primitive_float_unsigned_pair_gen_var_1::<T, u64>().test_properties(|(x, u)| {
        let c = primitive_float_cos_with_period(x, u);
        // NaN exactly for u = 0 (the inputs are finite), and otherwise in [-1, 1]
        assert_eq!(c.is_nan(), u == 0);
        if u != 0 {
            assert!(c >= T::NEGATIVE_ONE && c <= T::ONE);
            // even
            assert_eq!(
                NiceFloat(primitive_float_cos_with_period(-x, u)),
                NiceFloat(c)
            );
            // the result is the correctly rounded cosine, as computed by MPFR at the same precision
            let rug_c = rug_cos_with_period_prec(
                &rug::Float::exact_from(&Float::from(x)),
                u,
                T::MANTISSA_WIDTH + 1,
            )
            .0;
            let rug_c: T = T::exact_from(&<Float as From<&rug::Float>>::from(&rug_c));
            assert_eq!(NiceFloat(rug_c), NiceFloat(c));
        }
    });

    primitive_float_gen::<T>().test_properties(|x| {
        // NaN exactly for NaN and infinite inputs
        assert_eq!(
            primitive_float_cos_with_period(x, 7).is_nan(),
            !x.is_finite()
        );
    });
}

#[test]
fn primitive_float_cos_with_period_properties() {
    apply_fn_to_primitive_floats!(primitive_float_cos_with_period_properties_helper);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_cos_with_period_rational_properties_helper<T: PrimitiveFloat>()
where
    Float: From<T> + PartialOrd<T>,
    Rational: ExactFrom<T>,
    for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
{
    rational_unsigned_pair_gen_var_1::<u64>().test_properties(|(x, u)| {
        let c = primitive_float_cos_with_period_rational::<T>(&x, u);
        assert_eq!(c.is_nan(), u == 0);
        if u != 0 {
            assert!(c >= T::NEGATIVE_ONE && c <= T::ONE);
            // even, and periodic with period u
            assert_eq!(
                NiceFloat(primitive_float_cos_with_period_rational::<T>(&-&x, u)),
                NiceFloat(c)
            );
            assert_eq!(
                NiceFloat(primitive_float_cos_with_period_rational::<T>(
                    &(&x + Rational::from(u)),
                    u
                )),
                NiceFloat(c)
            );
            // MPFR agrees, except that it cannot see the exact cases of non-dyadic inputs
            let (c_float, o) =
                Float::cos_with_period_rational_prec_ref(&x, u, T::MANTISSA_WIDTH + 1);
            assert_eq!(NiceFloat(T::exact_from(&c_float)), NiceFloat(c));
            if o != Equal {
                let rug_c = rug_cos_with_period_rational_prec(&x, u, T::MANTISSA_WIDTH + 1).0;
                let rug_c: T = T::exact_from(&<Float as From<&rug::Float>>::from(&rug_c));
                assert_eq!(NiceFloat(rug_c), NiceFloat(c));
            }
        }
    });

    primitive_float_unsigned_pair_gen_var_1::<T, u64>().test_properties(|(x, u)| {
        // The cosine of a finite primitive float, taken through the `Rational` path, matches the
        // direct primitive-float cosine.
        assert_eq!(
            NiceFloat(primitive_float_cos_with_period_rational::<T>(
                &Rational::exact_from(x),
                u
            )),
            NiceFloat(primitive_float_cos_with_period(x, u))
        );
    });
}

#[test]
fn primitive_float_cos_with_period_rational_properties() {
    apply_fn_to_primitive_floats!(primitive_float_cos_with_period_rational_properties_helper);
}

// Inputs within 2^(-2^30) of an odd quarter turn, without being one, whose cosines underflow.
// Unlike `cos`, this needs no pi at 2^30 bits: the distance to the quarter turn is rational and
// computed exactly, so the test is fast despite the 2^30-bit inputs.
#[test]
fn test_cos_with_period_underflow() {
    let min_positive = Float::one_prec(10) >> (1u64 << 30);
    // 90 +- 2^-(2^30 + 70), which need 2^30 + 77 bits (the offset alone is below the exponent
    // range, so the sum is built from a `Rational`)
    let eps = Rational::power_of_2(-((1i64 << 30) + 70));
    let above =
        Float::from_rational_prec_round(Rational::from(90u32) + &eps, (1u64 << 30) + 78, Exact).0;
    let below =
        Float::from_rational_prec_round(Rational::from(90u32) - eps, (1u64 << 30) + 78, Exact).0;
    // just past a quarter turn: cos is negative and tiny
    let (c, o) = above.cos_with_period_prec_round_ref(360, 10, Nearest);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::NEGATIVE_ZERO));
    assert_eq!(o, Greater);
    let (c, o) = above.cos_with_period_prec_round_ref(360, 10, Floor);
    assert_eq!(ComparableFloat(c), ComparableFloat(-&min_positive));
    assert_eq!(o, Less);
    // just short of it: positive and tiny
    let (c, o) = below.cos_with_period_prec_round_ref(360, 10, Ceiling);
    assert_eq!(ComparableFloatRef(&c), ComparableFloatRef(&min_positive));
    assert_eq!(o, Greater);
    let (c, o) = below.cos_with_period_prec_round_ref(360, 10, Down);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::ZERO));
    assert_eq!(o, Less);
}

#[test]
fn test_cos_with_period_rational_underflow() {
    let min_positive = Float::one_prec(10) >> (1u64 << 30);
    let eps = Rational::power_of_2(-((1i64 << 30) + 70));
    let above = Rational::from(90u32) + &eps;
    let below = Rational::from(90u32) - eps;
    let (c, o) = Float::cos_with_period_rational_prec_round_ref(&above, 360, 10, Nearest);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::NEGATIVE_ZERO));
    assert_eq!(o, Greater);
    let (c, o) = Float::cos_with_period_rational_prec_round_ref(&above, 360, 10, Floor);
    assert_eq!(ComparableFloat(c), ComparableFloat(-&min_positive));
    assert_eq!(o, Less);
    let (c, o) = Float::cos_with_period_rational_prec_round_ref(&below, 360, 10, Ceiling);
    assert_eq!(ComparableFloatRef(&c), ComparableFloatRef(&min_positive));
    assert_eq!(o, Greater);
    let (c, o) = Float::cos_with_period_rational_prec_round_ref(&below, 360, 10, Down);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::ZERO));
    assert_eq!(o, Less);
    // a non-dyadic version: 1/4 + 1/(3 * 2^(2^30 + 70)) of a turn
    let tiny = Rational::power_of_2(-((1i64 << 30) + 70)) / Rational::from(3u32);
    let x = Rational::from_unsigneds(1u32, 4u32) + tiny;
    let (c, o) = Float::cos_with_period_rational_prec_round_ref(&x, 1, 10, Nearest);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::NEGATIVE_ZERO));
    assert_eq!(o, Greater);
}

// Inputs within 2^(-2^30) of a multiple of the period, on either side, whose cosines are just below
// 1: the fraction of a turn is reduced to [-1/2, 1/2], so these take the small-input shortcut
// rather than a Ziv loop that would have to reach 2^31 bits to see the cancellation in 1 - cos (the
// negative `Rational` inputs used to do exactly that).
#[test]
fn test_cos_with_period_near_turn() {
    let eps = Rational::power_of_2(-((1i64 << 30) + 70));
    // 720 - eps needs 10 + 2^30 + 70 bits
    let p = (1u64 << 30) + 80;
    let below_turn = Float::from_rational_prec_round(Rational::from(360u32) - &eps, p, Exact).0;
    // the offset alone is below the exponent range, so the negative input is the smallest one
    let neg = -(Float::one_prec(10) >> (1u64 << 30));
    let below_two_turns =
        Float::from_rational_prec_round(Rational::from(720u32) - &eps, p, Exact).0;
    let one = Float::one_prec(10);
    for x in [&below_turn, &neg, &below_two_turns] {
        let (c, o) = x.cos_with_period_prec_round_ref(360, 10, Nearest);
        assert_eq!(ComparableFloatRef(&c), ComparableFloatRef(&one));
        assert_eq!(o, Greater);
        let (c, o) = x.cos_with_period_prec_round_ref(360, 10, Floor);
        assert_eq!(c.to_string(), "0.99902");
        assert_eq!(o, Less);
        let (c, o) = x.cos_with_period_prec_round_ref(360, 10, Ceiling);
        assert_eq!(ComparableFloatRef(&c), ComparableFloatRef(&one));
        assert_eq!(o, Greater);
    }
    for x in [
        Rational::from(360u32) - &eps,
        -&eps,
        Rational::from(720u32) - &eps,
        -Rational::from(360u32) - &eps,
        -(&eps / Rational::from(3u32)),
    ] {
        let (c, o) = Float::cos_with_period_rational_prec_round_ref(&x, 360, 10, Nearest);
        assert_eq!(ComparableFloatRef(&c), ComparableFloatRef(&one));
        assert_eq!(o, Greater);
        let (c, o) = Float::cos_with_period_rational_prec_round_ref(&x, 360, 10, Floor);
        assert_eq!(c.to_string(), "0.99902");
        assert_eq!(o, Less);
    }
    // a `Rational` with a modest denominator, well within a Float's reach, just below a turn
    let x = Rational::from(360u32) - Rational::power_of_2(-100i64);
    let (c, o) = Float::cos_with_period_rational_prec_round_ref(&x, 360, 10, Floor);
    assert_eq!(c.to_string(), "0.99902");
    assert_eq!(o, Less);
}

#[test]
fn test_cos_pi_prec_round() {
    let test = |s, s_hex, prec: u64, rm, out: &str, out_hex: &str, o_out: Ordering| {
        let x = parse_hex_string(s_hex);
        assert_eq!(x.to_string(), s);

        let (c, o) = x.clone().cos_pi_prec_round(prec, rm);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, o_out);

        let (c_alt, o_alt) = x.cos_pi_prec_round_ref(prec, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        let mut c_alt = x.clone();
        let o_alt = c_alt.cos_pi_prec_round_assign(prec, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        if rm == Nearest {
            let (c_alt, o_alt) = x.cos_pi_prec_ref(prec);
            assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
            assert_eq!(o_alt, o);
        }

        if let Ok(rug_rm) = rug_round_try_from_rounding_mode(rm) {
            let (rug_c, rug_o) = rug_cos_pi_prec_round(&rug::Float::exact_from(&x), prec, rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    };
    test("NaN", "NaN", 1, Nearest, "NaN", "NaN", Equal);
    test("NaN", "NaN", 10, Nearest, "NaN", "NaN", Equal);
    test("NaN", "NaN", 10, Floor, "NaN", "NaN", Equal);
    test("NaN", "NaN", 10, Ceiling, "NaN", "NaN", Equal);
    test("NaN", "NaN", 10, Exact, "NaN", "NaN", Equal);
    test("NaN", "NaN", 53, Nearest, "NaN", "NaN", Equal);
    test("Infinity", "Infinity", 1, Nearest, "NaN", "NaN", Equal);
    test("Infinity", "Infinity", 10, Nearest, "NaN", "NaN", Equal);
    test("Infinity", "Infinity", 10, Floor, "NaN", "NaN", Equal);
    test("Infinity", "Infinity", 10, Ceiling, "NaN", "NaN", Equal);
    test("Infinity", "Infinity", 10, Exact, "NaN", "NaN", Equal);
    test("Infinity", "Infinity", 53, Nearest, "NaN", "NaN", Equal);
    test("0.0", "0x0.0", 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("0.0", "0x0.0", 10, Nearest, "1.0000", "0x1.000#10", Equal);
    test("0.0", "0x0.0", 10, Floor, "1.0000", "0x1.000#10", Equal);
    test("0.0", "0x0.0", 10, Ceiling, "1.0000", "0x1.000#10", Equal);
    test("0.0", "0x0.0", 10, Exact, "1.0000", "0x1.000#10", Equal);
    test(
        "0.0",
        "0x0.0",
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test("0.50", "0x0.8#1", 1, Nearest, "0.0", "0x0.0", Equal);
    // - a half-integer: exactly +0
    test("0.50", "0x0.8#1", 10, Nearest, "0.0", "0x0.0", Equal);
    test("0.50", "0x0.8#1", 10, Floor, "0.0", "0x0.0", Equal);
    test("0.50", "0x0.8#1", 10, Ceiling, "0.0", "0x0.0", Equal);
    test("0.50", "0x0.8#1", 10, Exact, "0.0", "0x0.0", Equal);
    test("0.50", "0x0.8#1", 53, Nearest, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 1, Nearest, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 10, Nearest, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 10, Floor, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 10, Ceiling, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 10, Exact, "0.0", "0x0.0", Equal);
    test("1.5", "0x1.8#2", 53, Nearest, "0.0", "0x0.0", Equal);
    test("1.0", "0x1.0#1", 1, Nearest, "-1.0", "-0x1.0#1", Equal);
    // - an integer: exactly -1
    test(
        "1.0",
        "0x1.0#1",
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test("1.0", "0x1.0#1", 10, Floor, "-1.0000", "-0x1.000#10", Equal);
    test(
        "1.0",
        "0x1.0#1",
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Equal,
    );
    test("1.0", "0x1.0#1", 10, Exact, "-1.0000", "-0x1.000#10", Equal);
    test(
        "1.0",
        "0x1.0#1",
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test("2.0", "0x2.0#1", 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("2.0", "0x2.0#1", 10, Nearest, "1.0000", "0x1.000#10", Equal);
    test("2.0", "0x2.0#1", 10, Floor, "1.0000", "0x1.000#10", Equal);
    test("2.0", "0x2.0#1", 10, Ceiling, "1.0000", "0x1.000#10", Equal);
    test("2.0", "0x2.0#1", 10, Exact, "1.0000", "0x1.000#10", Equal);
    test(
        "2.0",
        "0x2.0#1",
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test("0.25", "0x0.4#1", 1, Nearest, "0.50", "0x0.8#1", Less);
    // - closed form: sqrt(2)/2
    test(
        "0.25",
        "0x0.4#1",
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test("0.25", "0x0.4#1", 10, Floor, "0.70703", "0x0.b50#10", Less);
    test(
        "0.25",
        "0x0.4#1",
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "0.25",
        "0x0.4#1",
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test(
        "0.10000000000000001",
        "0x0.1999999999999a#52",
        1,
        Nearest,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    // - general case
    test(
        "0.10000000000000001",
        "0x0.1999999999999a#52",
        10,
        Nearest,
        "0.95117",
        "0x0.f38#10",
        Greater,
    );
    test(
        "0.10000000000000001",
        "0x0.1999999999999a#52",
        10,
        Floor,
        "0.95020",
        "0x0.f34#10",
        Less,
    );
    test(
        "0.10000000000000001",
        "0x0.1999999999999a#52",
        10,
        Ceiling,
        "0.95117",
        "0x0.f38#10",
        Greater,
    );
    test(
        "0.10000000000000001",
        "0x0.1999999999999a#52",
        53,
        Nearest,
        "0.95105651629515353",
        "0x0.f378709a22a7f8#53",
        Less,
    );
    test(
        "0.40000000000000002",
        "0x0.66666666666668#52",
        1,
        Nearest,
        "0.25",
        "0x0.4#1",
        Less,
    );
    test(
        "0.40000000000000002",
        "0x0.66666666666668#52",
        10,
        Nearest,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "0.40000000000000002",
        "0x0.66666666666668#52",
        10,
        Floor,
        "0.30859",
        "0x0.4f0#10",
        Less,
    );
    test(
        "0.40000000000000002",
        "0x0.66666666666668#52",
        10,
        Ceiling,
        "0.30908",
        "0x0.4f2#10",
        Greater,
    );
    test(
        "0.40000000000000002",
        "0x0.66666666666668#52",
        53,
        Nearest,
        "0.30901699437494734",
        "0x0.4f1bbcdcbfa538#53",
        Less,
    );
    test("100.2", "0x64.4#9", 1, Nearest, "0.50", "0x0.8#1", Less);
    test(
        "100.2",
        "0x64.4#9",
        10,
        Nearest,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "100.2",
        "0x64.4#9",
        10,
        Floor,
        "0.70703",
        "0x0.b50#10",
        Less,
    );
    test(
        "100.2",
        "0x64.4#9",
        10,
        Ceiling,
        "0.70801",
        "0x0.b54#10",
        Greater,
    );
    test(
        "100.2",
        "0x64.4#9",
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        1,
        Nearest,
        "1.0",
        "0x1.0#1",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        10,
        Exact,
        "1.0000",
        "0x1.000#10",
        Equal,
    );
    test(
        "1.00000000e10",
        "0x2.540be4E+8#24",
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test(
        "1.000000000000000e-30",
        "0x1.4484bfeebc2aE-25#48",
        1,
        Nearest,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1.000000000000000e-30",
        "0x1.4484bfeebc2aE-25#48",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.000000000000000e-30",
        "0x1.4484bfeebc2aE-25#48",
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1.000000000000000e-30",
        "0x1.4484bfeebc2aE-25#48",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1.000000000000000e-30",
        "0x1.4484bfeebc2aE-25#48",
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Greater,
    );
    test(
        "-0.10000000000000001",
        "-0x0.1999999999999a#52",
        1,
        Nearest,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "-0.10000000000000001",
        "-0x0.1999999999999a#52",
        10,
        Nearest,
        "0.95117",
        "0x0.f38#10",
        Greater,
    );
    test(
        "-0.10000000000000001",
        "-0x0.1999999999999a#52",
        10,
        Floor,
        "0.95020",
        "0x0.f34#10",
        Less,
    );
    test(
        "-0.10000000000000001",
        "-0x0.1999999999999a#52",
        10,
        Ceiling,
        "0.95117",
        "0x0.f38#10",
        Greater,
    );
    test(
        "-0.10000000000000001",
        "-0x0.1999999999999a#52",
        53,
        Nearest,
        "0.95105651629515353",
        "0x0.f378709a22a7f8#53",
        Less,
    );
}

#[test]
fn test_cos_pi_rational_prec_round() {
    let test = |s, prec: u64, rm, out: &str, out_hex: &str, o_out: Ordering| {
        let x = Rational::from_str(s).unwrap();

        let (c, o) = Float::cos_pi_rational_prec_round(x.clone(), prec, rm);
        assert!(c.is_valid());
        assert_eq!(c.to_string(), out);
        assert_eq!(to_hex_string(&c), out_hex);
        assert_eq!(o, o_out);

        let (c_alt, o_alt) = Float::cos_pi_rational_prec_round_ref(&x, prec, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

        if rm == Nearest {
            let (c_alt, o_alt) = Float::cos_pi_rational_prec(x.clone(), prec);
            assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
            assert_eq!(o_alt, o);
            let (c_alt, o_alt) = Float::cos_pi_rational_prec_ref(&x, prec);
            assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
            assert_eq!(o_alt, o);
        }
    };
    test("0", 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("0", 10, Nearest, "1.0000", "0x1.000#10", Equal);
    test("0", 10, Floor, "1.0000", "0x1.000#10", Equal);
    test("0", 10, Ceiling, "1.0000", "0x1.000#10", Equal);
    test("0", 10, Exact, "1.0000", "0x1.000#10", Equal);
    test(
        "0",
        53,
        Nearest,
        "1.0000000000000000",
        "0x1.0000000000000#53",
        Equal,
    );
    test("1/2", 1, Nearest, "0.0", "0x0.0", Equal);
    // - a half-integer: exactly +0
    test("1/2", 10, Nearest, "0.0", "0x0.0", Equal);
    test("1/2", 10, Floor, "0.0", "0x0.0", Equal);
    test("1/2", 10, Ceiling, "0.0", "0x0.0", Equal);
    test("1/2", 10, Exact, "0.0", "0x0.0", Equal);
    test("1/2", 53, Nearest, "0.0", "0x0.0", Equal);
    test("1", 1, Nearest, "-1.0", "-0x1.0#1", Equal);
    test("1", 10, Nearest, "-1.0000", "-0x1.000#10", Equal);
    test("1", 10, Floor, "-1.0000", "-0x1.000#10", Equal);
    test("1", 10, Ceiling, "-1.0000", "-0x1.000#10", Equal);
    test("1", 10, Exact, "-1.0000", "-0x1.000#10", Equal);
    test(
        "1",
        53,
        Nearest,
        "-1.0000000000000000",
        "-0x1.0000000000000#53",
        Equal,
    );
    test("1/3", 1, Nearest, "0.50", "0x0.8#1", Equal);
    // - a third of a half-turn: exactly 1/2
    test("1/3", 10, Nearest, "0.50000", "0x0.800#10", Equal);
    test("1/3", 10, Floor, "0.50000", "0x0.800#10", Equal);
    test("1/3", 10, Ceiling, "0.50000", "0x0.800#10", Equal);
    test("1/3", 10, Exact, "0.50000", "0x0.800#10", Equal);
    test(
        "1/3",
        53,
        Nearest,
        "0.50000000000000000",
        "0x0.80000000000000#53",
        Equal,
    );
    test("2/3", 1, Nearest, "-0.50", "-0x0.8#1", Equal);
    test("2/3", 10, Nearest, "-0.50000", "-0x0.800#10", Equal);
    test("2/3", 10, Floor, "-0.50000", "-0x0.800#10", Equal);
    test("2/3", 10, Ceiling, "-0.50000", "-0x0.800#10", Equal);
    test("2/3", 10, Exact, "-0.50000", "-0x0.800#10", Equal);
    test(
        "2/3",
        53,
        Nearest,
        "-0.50000000000000000",
        "-0x0.80000000000000#53",
        Equal,
    );
    test("1/4", 1, Nearest, "0.50", "0x0.8#1", Less);
    // - closed form: sqrt(2)/2
    test("1/4", 10, Nearest, "0.70703", "0x0.b50#10", Less);
    test("1/4", 10, Floor, "0.70703", "0x0.b50#10", Less);
    test("1/4", 10, Ceiling, "0.70801", "0x0.b54#10", Greater);
    test(
        "1/4",
        53,
        Nearest,
        "0.70710678118654757",
        "0x0.b504f333f9de68#53",
        Greater,
    );
    test("1/6", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1/6", 10, Nearest, "0.86621", "0x0.ddc#10", Greater);
    test("1/6", 10, Floor, "0.86523", "0x0.dd8#10", Less);
    test("1/6", 10, Ceiling, "0.86621", "0x0.ddc#10", Greater);
    test(
        "1/6",
        53,
        Nearest,
        "0.86602540378443860",
        "0x0.ddb3d742c26550#53",
        Less,
    );
    test("1/5", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1/5", 10, Nearest, "0.80859", "0x0.cf0#10", Less);
    test("1/5", 10, Floor, "0.80859", "0x0.cf0#10", Less);
    test("1/5", 10, Ceiling, "0.80957", "0x0.cf4#10", Greater);
    test(
        "1/5",
        53,
        Nearest,
        "0.80901699437494745",
        "0x0.cf1bbcdcbfa540#53",
        Greater,
    );
    test("2/5", 1, Nearest, "0.25", "0x0.4#1", Less);
    test("2/5", 10, Nearest, "0.30908", "0x0.4f2#10", Greater);
    test("2/5", 10, Floor, "0.30859", "0x0.4f0#10", Less);
    test("2/5", 10, Ceiling, "0.30908", "0x0.4f2#10", Greater);
    test(
        "2/5",
        53,
        Nearest,
        "0.30901699437494745",
        "0x0.4f1bbcdcbfa540#53",
        Greater,
    );
    test("1/7", 1, Nearest, "1.0", "0x1.0#1", Greater);
    // - general case
    test("1/7", 10, Nearest, "0.90137", "0x0.e6c#10", Greater);
    test("1/7", 10, Floor, "0.90039", "0x0.e68#10", Less);
    test("1/7", 10, Ceiling, "0.90137", "0x0.e6c#10", Greater);
    test(
        "1/7",
        53,
        Nearest,
        "0.90096886790241915",
        "0x0.e6a5e54e5ae388#53",
        Greater,
    );
    test("-3/7", 1, Nearest, "0.25", "0x0.4#1", Greater);
    test("-3/7", 10, Nearest, "0.22241", "0x0.38f#10", Less);
    test("-3/7", 10, Floor, "0.22241", "0x0.38f#10", Less);
    test("-3/7", 10, Ceiling, "0.22266", "0x0.390#10", Greater);
    test(
        "-3/7",
        53,
        Nearest,
        "0.22252093395631439",
        "0x0.38f721c6048b04#53",
        Less,
    );
    test("22/7", 1, Nearest, "-1.0", "-0x1.0#1", Less);
    test("22/7", 10, Nearest, "-0.90137", "-0x0.e6c#10", Less);
    test("22/7", 10, Floor, "-0.90137", "-0x0.e6c#10", Less);
    test("22/7", 10, Ceiling, "-0.90039", "-0x0.e68#10", Greater);
    test(
        "22/7",
        53,
        Nearest,
        "-0.90096886790241915",
        "-0x0.e6a5e54e5ae388#53",
        Less,
    );
    test("1/1000000", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1/1000000", 10, Nearest, "1.0000", "0x1.000#10", Greater);
    test("1/1000000", 10, Floor, "0.99902", "0x0.ffc#10", Less);
    test("1/1000000", 10, Ceiling, "1.0000", "0x1.000#10", Greater);
    test(
        "1/1000000",
        53,
        Nearest,
        "0.99999999999506517",
        "0x0.fffffffffa92f8#53",
        Less,
    );
}

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_cos_pi() {
    fn test<T: PrimitiveFloat>(x: T, out: T)
    where
        Float: From<T> + PartialOrd<T>,
        for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
    {
        assert_eq!(NiceFloat(primitive_float_cos_pi(x)), NiceFloat(out));
    }
    test::<f32>(f32::NAN, f32::NAN);
    test::<f32>(0.5, 0.0);
    test::<f32>(1.0, -1.0);
    test::<f32>(0.25, core::f32::consts::FRAC_1_SQRT_2);
    test::<f32>(0.1, 0.95105654);
    test::<f32>(-0.1, 0.95105654);
    test::<f32>(100.25, core::f32::consts::FRAC_1_SQRT_2);
    test::<f32>(1.0e10, 1.0);

    test::<f64>(f64::NAN, f64::NAN);
    test::<f64>(0.5, 0.0);
    test::<f64>(1.0, -1.0);
    test::<f64>(0.25, core::f64::consts::FRAC_1_SQRT_2);
    test::<f64>(0.1, 0.9510565162951535);
    test::<f64>(-0.1, 0.9510565162951535);
    test::<f64>(100.25, core::f64::consts::FRAC_1_SQRT_2);
    test::<f64>(1.0e10, 1.0);
}

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_cos_pi_rational() {
    fn test<T: PrimitiveFloat>(s: &str, out: T)
    where
        Float: From<T> + PartialOrd<T>,
        for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
    {
        let x = Rational::from_str(s).unwrap();
        assert_eq!(
            NiceFloat(primitive_float_cos_pi_rational::<T>(&x)),
            NiceFloat(out)
        );
    }
    test::<f32>("1/2", 0.0);
    test::<f32>("1/3", 0.5);
    test::<f32>("1/4", core::f32::consts::FRAC_1_SQRT_2);
    test::<f32>("1/7", 0.90096885);
    test::<f32>("-3/7", 0.22252093);
    test::<f32>("22/7", -0.90096885);

    test::<f64>("1/2", 0.0);
    test::<f64>("1/3", 0.5);
    test::<f64>("1/4", core::f64::consts::FRAC_1_SQRT_2);
    test::<f64>("1/7", 0.9009688679024191);
    test::<f64>("-3/7", 0.2225209339563144);
    test::<f64>("22/7", -0.9009688679024191);
}

#[test]
#[should_panic]
fn cos_pi_prec_round_fail_1() {
    Float::from(0.1f64).cos_pi_prec_round(0, Floor);
}

#[test]
#[should_panic]
fn cos_pi_prec_round_fail_2() {
    Float::from(0.1f64).cos_pi_prec_round(10, Exact);
}

#[test]
#[should_panic]
fn cos_pi_rational_prec_round_fail() {
    Float::cos_pi_rational_prec_round(Rational::from_unsigneds(1u8, 7), 10, Exact);
}

// Every `cos_pi` variant is `cos_with_period` with a period of 2.
#[test]
fn cos_pi_properties() {
    // The borrowed generators admit `Exact` for inputs whose cosine is not exact, so `Exact` is
    // checked against the exactness of the result.
    let exact_ok = |x: &Float, prec: u64, rm: RoundingMode| {
        rm != Exact || x.cos_with_period_prec_round_ref(2, prec, Nearest).1 == Equal
    };
    float_unsigned_rounding_mode_triple_gen_var_36().test_properties(|(x, prec, rm)| {
        if !exact_ok(&x, prec, rm) {
            assert_panic!(x.cos_pi_prec_round_ref(prec, Exact));
            return;
        }
        let (c, o) = x.clone().cos_pi_prec_round(prec, rm);
        assert!(c.is_valid());
        assert_rounding_ordering_consistent(&c, rm, o);
        let (c_alt, o_alt) = x.cos_with_period_prec_round_ref(2, prec, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let (c_alt, o_alt) = x.cos_pi_prec_round_ref(prec, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let mut c_alt = x.clone();
        let o_alt = c_alt.cos_pi_prec_round_assign(prec, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        if let Ok(rrm) = rug_round_try_from_rounding_mode(rm) {
            let (rug_c, rug_o) = rug_cos_pi_prec_round(&rug::Float::exact_from(&x), prec, rrm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    });

    float_unsigned_rounding_mode_triple_gen_var_37().test_properties(|(x, prec, rm)| {
        if !exact_ok(&x, prec, rm) {
            return;
        }
        let (c, o) = x.cos_pi_prec_round_ref(prec, rm);
        let (c_alt, o_alt) = x.cos_with_period_prec_round_ref(2, prec, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
    });

    float_unsigned_pair_gen_var_1().test_properties(|(x, prec)| {
        let (c, o) = x.clone().cos_pi_prec(prec);
        let (c_alt, o_alt) = x.cos_with_period_prec_ref(2, prec);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let (c_alt, o_alt) = x.cos_pi_prec_ref(prec);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let mut c_alt = x.clone();
        let o_alt = c_alt.cos_pi_prec_assign(prec);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
    });

    float_rounding_mode_pair_gen_var_47().test_properties(|(x, rm)| {
        if !exact_ok(&x, x.significant_bits(), rm) {
            return;
        }
        let (c, o) = x.clone().cos_pi_round(rm);
        assert_rounding_ordering_consistent(&c, rm, o);
        let (c_alt, o_alt) = x.cos_with_period_round_ref(2, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let (c_alt, o_alt) = x.cos_pi_round_ref(rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let mut c_alt = x.clone();
        let o_alt = c_alt.cos_pi_round_assign(rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
    });

    rational_unsigned_rounding_mode_triple_gen_var_10().test_properties(|(x, prec, rm)| {
        if rm == Exact && Float::cos_with_period_rational_prec_ref(&x, 2, prec).1 != Equal {
            assert_panic!(Float::cos_pi_rational_prec_round_ref(&x, prec, Exact));
            return;
        }
        let (c, o) = Float::cos_pi_rational_prec_round(x.clone(), prec, rm);
        assert!(c.is_valid());
        assert_rounding_ordering_consistent(&c, rm, o);
        let (c_alt, o_alt) = Float::cos_with_period_rational_prec_round_ref(&x, 2, prec, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let (c_alt, o_alt) = Float::cos_pi_rational_prec_round_ref(&x, prec, rm);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        // MPFR agrees, except that it cannot see the exact cases of non-dyadic inputs
        if o != Equal
            && let Ok(rrm) = rug_round_try_from_rounding_mode(rm)
        {
            let (rug_c, rug_o) = rug_cos_pi_rational_prec_round(&x, prec, rrm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    });

    rational_unsigned_pair_gen_var_3().test_properties(|(x, prec)| {
        let (c, o) = Float::cos_pi_rational_prec(x.clone(), prec);
        let (c_alt, o_alt) = Float::cos_with_period_rational_prec_ref(&x, 2, prec);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
        let (c_alt, o_alt) = Float::cos_pi_rational_prec_ref(&x, prec);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
    });

    float_gen().test_properties(|x| {
        let c = x.clone().cos_pi();
        assert!(c.is_valid());
        let c_alt = x.cos_pi_ref();
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        let mut c_alt = x.clone();
        c_alt.cos_pi_assign();
        assert!(c_alt.is_valid());
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        // the same as cos_with_period with a period of 2, and as rounding to the input's precision,
        // to nearest
        let c_alt = x.cos_with_period_ref(2);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        let (c_alt, _) = x.cos_pi_prec_round_ref(x.significant_bits(), Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
    });
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_cos_pi_properties_helper<T: PrimitiveFloat>()
where
    Float: From<T> + PartialOrd<T>,
    Rational: ExactFrom<T>,
    for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
{
    primitive_float_gen::<T>().test_properties(|x| {
        assert_eq!(
            NiceFloat(primitive_float_cos_pi(x)),
            NiceFloat(primitive_float_cos_with_period(x, 2))
        );
    });
    rational_gen().test_properties(|x| {
        assert_eq!(
            NiceFloat(primitive_float_cos_pi_rational::<T>(&x)),
            NiceFloat(primitive_float_cos_with_period_rational::<T>(&x, 2))
        );
    });
}

#[test]
fn primitive_float_cos_pi_properties() {
    apply_fn_to_primitive_floats!(primitive_float_cos_pi_properties_helper);
}