malachite-float 0.13.0

// 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::{Coth, CothAssign, PowerOf2};
use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::basic::traits::{
    Infinity, NaN, NegativeInfinity, NegativeZero, One, Zero,
};
use malachite_base::num::conversion::traits::{ExactFrom, RoundingFrom};
use malachite_base::num::float::NiceFloat;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_base::rounding_modes::RoundingMode::{self, *};
use malachite_base::rounding_modes::exhaustive::exhaustive_rounding_modes;
use malachite_base::test_util::generators::{
    primitive_float_gen, unsigned_rounding_mode_pair_gen_var_3,
};
use malachite_float::float::arithmetic::coth::{
    primitive_float_coth, primitive_float_coth_rational,
};
use malachite_float::test_util::common::{
    assert_rounding_ordering_consistent, parse_hex_string, round_once_to_primitive,
    rug_round_try_from_rounding_mode, to_hex_string,
};
use malachite_float::test_util::float::arithmetic::coth::{
    rug_coth, rug_coth_prec, rug_coth_prec_round, rug_coth_rational_prec,
    rug_coth_rational_prec_round, rug_coth_round,
};
use malachite_float::test_util::generators::{
    float_gen, float_rounding_mode_pair_gen_var_47, float_unsigned_pair_gen_var_1,
    float_unsigned_rounding_mode_triple_gen_var_36,
    rational_unsigned_rounding_mode_triple_gen_var_10,
};
use malachite_float::{ComparableFloat, ComparableFloatRef, Float};
use malachite_q::Rational;
use malachite_q::test_util::generators::{rational_gen, rational_unsigned_pair_gen_var_3};
use std::panic::catch_unwind;
use std::str::FromStr;

#[test]
fn test_coth_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().coth_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.coth_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.coth_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_coth_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, "1.0", "0x1.0#1", Equal);
    test(
        "-Infinity",
        "-Infinity",
        1,
        Nearest,
        "-1.0",
        "-0x1.0#1",
        Equal,
    );
    test("0.0", "0x0.0", 1, Nearest, "Infinity", "Infinity", Equal);
    test(
        "-0.0",
        "-0x0.0",
        1,
        Nearest,
        "-Infinity",
        "-Infinity",
        Equal,
    );
    test("0.0", "0x0.0", 10, Nearest, "Infinity", "Infinity", Equal);
    // - the first Ziv iteration cannot round, and 1/tanh(x) lies within 2^-prec of 1, but the bound
    //   from x is too weak to round from 1, so the loop retries
    test("1.0", "0x1.0#1", 1, Floor, "1.0", "0x1.0#1", Less);
    test("1.0", "0x1.0#1", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("1.0", "0x1.0#1", 1, Nearest, "1.0", "0x1.0#1", Less);
    // - the first Ziv iteration of 1 / tanh(x) rounds
    test("1.0", "0x1.0#1", 10, Floor, "1.3125", "0x1.500#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        10,
        Ceiling,
        "1.3145",
        "0x1.508#10",
        Greater,
    );
    test("1.0", "0x1.0#1", 10, Nearest, "1.3125", "0x1.500#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        100,
        Floor,
        "1.3130352854993313036361612469298",
        "0x1.50231499b6b1d49f813a188f8#100",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Ceiling,
        "1.3130352854993313036361612469313",
        "0x1.50231499b6b1d49f813a188fa#100",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Nearest,
        "1.3130352854993313036361612469313",
        "0x1.50231499b6b1d49f813a188fa#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Floor,
        "-1.3145",
        "-0x1.508#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Ceiling,
        "-1.3125",
        "-0x1.500#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Nearest,
        "-1.3125",
        "-0x1.500#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Down,
        "-1.3125",
        "-0x1.500#10",
        Greater,
    );
    test("-1.0", "-0x1.0#1", 10, Up, "-1.3145", "-0x1.508#10", Less);
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Floor,
        "-1.3130352854993313036361612469313",
        "-0x1.50231499b6b1d49f813a188fa#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Ceiling,
        "-1.3130352854993313036361612469298",
        "-0x1.50231499b6b1d49f813a188f8#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Nearest,
        "-1.3130352854993313036361612469313",
        "-0x1.50231499b6b1d49f813a188fa#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Down,
        "-1.3130352854993313036361612469298",
        "-0x1.50231499b6b1d49f813a188f8#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Up,
        "-1.3130352854993313036361612469313",
        "-0x1.50231499b6b1d49f813a188fa#100",
        Less,
    );
    test("0.50", "0x0.8#1", 10, Floor, "2.1602", "0x2.29#10", Less);
    test(
        "0.50",
        "0x0.8#1",
        10,
        Ceiling,
        "2.1641",
        "0x2.2a#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        10,
        Nearest,
        "2.1641",
        "0x2.2a#10",
        Greater,
    );
    test("0.50", "0x0.8#1", 10, Down, "2.1602", "0x2.29#10", Less);
    test("0.50", "0x0.8#1", 10, Up, "2.1641", "0x2.2a#10", Greater);
    test(
        "0.50",
        "0x0.8#1",
        100,
        Floor,
        "2.1639534137386528487700040102170",
        "0x2.29f8d9d61337dbaab838a8ad8#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Ceiling,
        "2.1639534137386528487700040102201",
        "0x2.29f8d9d61337dbaab838a8adc#100",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Nearest,
        "2.1639534137386528487700040102170",
        "0x2.29f8d9d61337dbaab838a8ad8#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Down,
        "2.1639534137386528487700040102170",
        "0x2.29f8d9d61337dbaab838a8ad8#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Up,
        "2.1639534137386528487700040102201",
        "0x2.29f8d9d61337dbaab838a8adc#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Floor,
        "3.1094",
        "0x3.1c#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Ceiling,
        "3.1133",
        "0x3.1d#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Nearest,
        "3.1094",
        "0x3.1c#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Down,
        "3.1094",
        "0x3.1c#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Up,
        "3.1133",
        "0x3.1d#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Floor,
        "3.1102966796194437013783752314146",
        "0x3.1c3c6737d2a99a2538dde3dbc#100",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Ceiling,
        "3.1102966796194437013783752314178",
        "0x3.1c3c6737d2a99a2538dde3dc0#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Nearest,
        "3.1102966796194437013783752314178",
        "0x3.1c3c6737d2a99a2538dde3dc0#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Down,
        "3.1102966796194437013783752314146",
        "0x3.1c3c6737d2a99a2538dde3dbc#100",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Up,
        "3.1102966796194437013783752314178",
        "0x3.1c3c6737d2a99a2538dde3dc0#100",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Floor, "1.0371", "0x1.098#10", Less);
    test(
        "2.0",
        "0x2.0#2",
        10,
        Ceiling,
        "1.0391",
        "0x1.0a0#10",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Nearest, "1.0371", "0x1.098#10", Less);
    test("2.0", "0x2.0#2", 10, Down, "1.0371", "0x1.098#10", Less);
    test("2.0", "0x2.0#2", 10, Up, "1.0391", "0x1.0a0#10", Greater);
    test(
        "2.0",
        "0x2.0#2",
        100,
        Floor,
        "1.0373147207275480958778097647664",
        "0x1.098d75212f273ba5d96804eca#100",
        Less,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Ceiling,
        "1.0373147207275480958778097647680",
        "0x1.098d75212f273ba5d96804ecc#100",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Nearest,
        "1.0373147207275480958778097647680",
        "0x1.098d75212f273ba5d96804ecc#100",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Down,
        "1.0373147207275480958778097647664",
        "0x1.098d75212f273ba5d96804eca#100",
        Less,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Up,
        "1.0373147207275480958778097647680",
        "0x1.098d75212f273ba5d96804ecc#100",
        Greater,
    );
    // - |coth(x)| lies within 2^-prec of 1, and the bound from x rounds it from -1
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Floor,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Down,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test("-10.0", "-0xa.0#4", 10, Up, "-1.0020", "-0x1.008#10", Less);
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Floor,
        "-1.0000000041223072533738241840291",
        "-0x1.00000011b48656902ef938492#100",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Ceiling,
        "-1.0000000041223072533738241840275",
        "-0x1.00000011b48656902ef938490#100",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Nearest,
        "-1.0000000041223072533738241840275",
        "-0x1.00000011b48656902ef938490#100",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Down,
        "-1.0000000041223072533738241840275",
        "-0x1.00000011b48656902ef938490#100",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Up,
        "-1.0000000041223072533738241840291",
        "-0x1.00000011b48656902ef938492#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Floor,
        "1.0020",
        "0x1.008#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Ceiling,
        "1.0039",
        "0x1.010#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Nearest,
        "1.0039",
        "0x1.010#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Down,
        "1.0020",
        "0x1.008#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Up,
        "1.0039",
        "0x1.010#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Floor,
        "1.0037418731973212882011765623462",
        "0x1.00f53a37021e3cccc69b27e42#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Ceiling,
        "1.0037418731973212882011765623478",
        "0x1.00f53a37021e3cccc69b27e44#100",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Nearest,
        "1.0037418731973212882011765623462",
        "0x1.00f53a37021e3cccc69b27e42#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Down,
        "1.0037418731973212882011765623462",
        "0x1.00f53a37021e3cccc69b27e42#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Up,
        "1.0037418731973212882011765623478",
        "0x1.00f53a37021e3cccc69b27e44#100",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Floor,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Down,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Up,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Floor,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Ceiling,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Nearest,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Down,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Up,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Floor,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Down,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Up,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Floor,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Ceiling,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Nearest,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Down,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Up,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Floor,
        "1024.0",
        "0x400.0#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Floor,
        "-1026.0",
        "-0x402.0#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Ceiling,
        "1026.0",
        "0x402.0#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Ceiling,
        "-1024.0",
        "-0x400.0#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Nearest,
        "1024.0",
        "0x400.0#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Nearest,
        "-1024.0",
        "-0x400.0#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Down,
        "1024.0",
        "0x400.0#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Down,
        "-1024.0",
        "-0x400.0#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Up,
        "1026.0",
        "0x402.0#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Up,
        "-1026.0",
        "-0x402.0#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Floor,
        "1024.0003255208126372779993985406",
        "0x400.001555553e93e96140be7f0#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Floor,
        "-1024.0003255208126372779993985422",
        "-0x400.001555553e93e96140be7f8#100",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Ceiling,
        "1024.0003255208126372779993985422",
        "0x400.001555553e93e96140be7f8#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Ceiling,
        "-1024.0003255208126372779993985406",
        "-0x400.001555553e93e96140be7f0#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Nearest,
        "1024.0003255208126372779993985406",
        "0x400.001555553e93e96140be7f0#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Nearest,
        "-1024.0003255208126372779993985406",
        "-0x400.001555553e93e96140be7f0#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Down,
        "1024.0003255208126372779993985406",
        "0x400.001555553e93e96140be7f0#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Down,
        "-1024.0003255208126372779993985406",
        "-0x400.001555553e93e96140be7f0#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Up,
        "1024.0003255208126372779993985422",
        "0x400.001555553e93e96140be7f8#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Up,
        "-1024.0003255208126372779993985422",
        "-0x400.001555553e93e96140be7f8#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Floor,
        "1125899906842624.0000000000000000",
        "0x4000000000000.0000000000000#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Floor,
        "-1125899906842624.0000000000000018",
        "-0x4000000000000.0000000000008#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Ceiling,
        "1125899906842624.0000000000000018",
        "0x4000000000000.0000000000008#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Ceiling,
        "-1125899906842624.0000000000000000",
        "-0x4000000000000.0000000000000#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Nearest,
        "1125899906842624.0000000000000000",
        "0x4000000000000.0000000000000#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Nearest,
        "-1125899906842624.0000000000000000",
        "-0x4000000000000.0000000000000#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Down,
        "1125899906842624.0000000000000000",
        "0x4000000000000.0000000000000#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Down,
        "-1125899906842624.0000000000000000",
        "-0x4000000000000.0000000000000#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Up,
        "1125899906842624.0000000000000018",
        "0x4000000000000.0000000000008#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Up,
        "-1125899906842624.0000000000000018",
        "-0x4000000000000.0000000000008#100",
        Less,
    );
    // - x is tiny: rounding 1/x settles coth(x)
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Floor,
        "1.2677e30",
        "0x1.000E+25#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Floor,
        "-1.2701e30",
        "-0x1.008E+25#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Ceiling,
        "1.2701e30",
        "0x1.008E+25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Ceiling,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Nearest,
        "1.2677e30",
        "0x1.000E+25#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Nearest,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Down,
        "1.2677e30",
        "0x1.000E+25#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Down,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Up,
        "1.2701e30",
        "0x1.008E+25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Up,
        "-1.2701e30",
        "-0x1.008E+25#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Floor,
        "1267650600228229401496703205376.0000000000000000000000000000002629536350736706018039095217\
        601",
        "0x10000000000000000000000000.00000000000000000000000005555555555555555555555554#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Floor,
        "-1267650600228229401496703205376.000000000000000000000000000000262953635073670601803909521\
        7613",
        "-0x10000000000000000000000000.00000000000000000000000005555555555555555555555556#300",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Ceiling,
        "1267650600228229401496703205376.0000000000000000000000000000002629536350736706018039095217\
        613",
        "0x10000000000000000000000000.00000000000000000000000005555555555555555555555556#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Ceiling,
        "-1267650600228229401496703205376.000000000000000000000000000000262953635073670601803909521\
        7601",
        "-0x10000000000000000000000000.00000000000000000000000005555555555555555555555554#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Nearest,
        "1267650600228229401496703205376.0000000000000000000000000000002629536350736706018039095217\
        613",
        "0x10000000000000000000000000.00000000000000000000000005555555555555555555555556#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Nearest,
        "-1267650600228229401496703205376.000000000000000000000000000000262953635073670601803909521\
        7613",
        "-0x10000000000000000000000000.00000000000000000000000005555555555555555555555556#300",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Down,
        "1267650600228229401496703205376.0000000000000000000000000000002629536350736706018039095217\
        601",
        "0x10000000000000000000000000.00000000000000000000000005555555555555555555555554#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Down,
        "-1267650600228229401496703205376.000000000000000000000000000000262953635073670601803909521\
        7601",
        "-0x10000000000000000000000000.00000000000000000000000005555555555555555555555554#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Up,
        "1267650600228229401496703205376.0000000000000000000000000000002629536350736706018039095217\
        613",
        "0x10000000000000000000000000.00000000000000000000000005555555555555555555555556#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Up,
        "-1267650600228229401496703205376.000000000000000000000000000000262953635073670601803909521\
        7613",
        "-0x10000000000000000000000000.00000000000000000000000005555555555555555555555556#300",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Floor,
        "2.09857871646738769229e323228496",
        "0x7.fffffffffffffff8E+268435455#64",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Down,
        "2.09857871646738769229e323228496",
        "0x7.fffffffffffffff8E+268435455#64",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "623740651.00",
        "0x252d86eb.0#30",
        1,
        Floor,
        "1.0",
        "0x1.0#1",
        Less,
    );
    test(
        "623740651.00",
        "0x252d86eb.0#30",
        1,
        Ceiling,
        "2.0",
        "0x2.0#1",
        Greater,
    );
    test(
        "623740651.00",
        "0x252d86eb.0#30",
        1,
        Nearest,
        "1.0",
        "0x1.0#1",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Floor,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Down,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Floor,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Ceiling,
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Down,
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Up,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Nearest,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Floor,
        "1.0493e323228496",
        "0x4.00E+268435455#10",
        Less,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Ceiling,
        "1.0513e323228496",
        "0x4.02E+268435455#10",
        Greater,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Down,
        "1.0493e323228496",
        "0x4.00E+268435455#10",
        Less,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Up,
        "1.0513e323228496",
        "0x4.02E+268435455#10",
        Greater,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Nearest,
        "1.0493e323228496",
        "0x4.00E+268435455#10",
        Less,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Floor,
        "-1.0513e323228496",
        "-0x4.02E+268435455#10",
        Less,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Ceiling,
        "-1.0493e323228496",
        "-0x4.00E+268435455#10",
        Greater,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Down,
        "-1.0493e323228496",
        "-0x4.00E+268435455#10",
        Greater,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Up,
        "-1.0513e323228496",
        "-0x4.02E+268435455#10",
        Less,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Nearest,
        "-1.0493e323228496",
        "-0x4.00E+268435455#10",
        Greater,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Floor,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Down,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Up,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "2.4e-30",
        "0x3.0E-25#2",
        10,
        Floor,
        "4.2214e29",
        "0x5.54E+24#10",
        Less,
    );
    test(
        "0.000976562500000000000000",
        "0x0.0040000000000000000#64",
        10,
        Floor,
        "1024.0",
        "0x400.0#10",
        Less,
    );
    test(
        "-0.000976562500000000000000",
        "-0x0.0040000000000000000#64",
        10,
        Floor,
        "-1026.0",
        "-0x402.0#10",
        Less,
    );
    test(
        "2.4e-30",
        "0x3.0E-25#2",
        10,
        Ceiling,
        "4.2276e29",
        "0x5.56E+24#10",
        Greater,
    );
    test(
        "0.000976562500000000000000",
        "0x0.0040000000000000000#64",
        10,
        Ceiling,
        "1026.0",
        "0x402.0#10",
        Greater,
    );
    test(
        "-0.000976562500000000000000",
        "-0x0.0040000000000000000#64",
        10,
        Ceiling,
        "-1024.0",
        "-0x400.0#10",
        Greater,
    );
    test(
        "2.4e-30",
        "0x3.0E-25#2",
        10,
        Nearest,
        "4.2276e29",
        "0x5.56E+24#10",
        Greater,
    );
    test(
        "0.000976562500000000000000",
        "0x0.0040000000000000000#64",
        10,
        Nearest,
        "1024.0",
        "0x400.0#10",
        Less,
    );
    test(
        "-0.000976562500000000000000",
        "-0x0.0040000000000000000#64",
        10,
        Nearest,
        "-1024.0",
        "-0x400.0#10",
        Greater,
    );
    test("20.0", "0x14.0#5", 1, Floor, "1.0", "0x1.0#1", Less);
    test("20.0", "0x14.0#5", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("20.0", "0x14.0#5", 1, Down, "1.0", "0x1.0#1", Less);
    test("20.0", "0x14.0#5", 1, Up, "2.0", "0x2.0#1", Greater);
    test("20.0", "0x14.0#5", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("20.0", "0x14.0#5", 10, Floor, "1.0000", "0x1.000#10", Less);
    test(
        "20.0",
        "0x14.0#5",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test("20.0", "0x14.0#5", 10, Down, "1.0000", "0x1.000#10", Less);
    test("20.0", "0x14.0#5", 10, Up, "1.0020", "0x1.008#10", Greater);
    test(
        "20.0",
        "0x14.0#5",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "20.0",
        "0x14.0#5",
        64,
        Floor,
        "1.00000000000000000846",
        "0x1.000000000000009c#64",
        Less,
    );
    test(
        "20.0",
        "0x14.0#5",
        64,
        Ceiling,
        "1.00000000000000000857",
        "0x1.000000000000009e#64",
        Greater,
    );
    test(
        "20.0",
        "0x14.0#5",
        64,
        Down,
        "1.00000000000000000846",
        "0x1.000000000000009c#64",
        Less,
    );
    test(
        "20.0",
        "0x14.0#5",
        64,
        Up,
        "1.00000000000000000857",
        "0x1.000000000000009e#64",
        Greater,
    );
    test(
        "20.0",
        "0x14.0#5",
        64,
        Nearest,
        "1.00000000000000000846",
        "0x1.000000000000009c#64",
        Less,
    );
    test(
        "20.0",
        "0x14.0#5",
        100,
        Floor,
        "1.0000000000000000084967085105823",
        "0x1.000000000000009cbc924cd8c#100",
        Less,
    );
    test(
        "20.0",
        "0x14.0#5",
        100,
        Ceiling,
        "1.0000000000000000084967085105839",
        "0x1.000000000000009cbc924cd8e#100",
        Greater,
    );
    test(
        "20.0",
        "0x14.0#5",
        100,
        Down,
        "1.0000000000000000084967085105823",
        "0x1.000000000000009cbc924cd8c#100",
        Less,
    );
    test(
        "20.0",
        "0x14.0#5",
        100,
        Up,
        "1.0000000000000000084967085105839",
        "0x1.000000000000009cbc924cd8e#100",
        Greater,
    );
    test(
        "20.0",
        "0x14.0#5",
        100,
        Nearest,
        "1.0000000000000000084967085105839",
        "0x1.000000000000009cbc924cd8e#100",
        Greater,
    );
    test("-20.0", "-0x14.0#5", 1, Floor, "-2.0", "-0x2.0#1", Less);
    test(
        "-20.0",
        "-0x14.0#5",
        1,
        Ceiling,
        "-1.0",
        "-0x1.0#1",
        Greater,
    );
    test("-20.0", "-0x14.0#5", 1, Down, "-1.0", "-0x1.0#1", Greater);
    test("-20.0", "-0x14.0#5", 1, Up, "-2.0", "-0x2.0#1", Less);
    test(
        "-20.0",
        "-0x14.0#5",
        1,
        Nearest,
        "-1.0",
        "-0x1.0#1",
        Greater,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        10,
        Floor,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        10,
        Down,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test("-20.0", "-0x14.0#5", 10, Up, "-1.0020", "-0x1.008#10", Less);
    test(
        "-20.0",
        "-0x14.0#5",
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        64,
        Floor,
        "-1.00000000000000000857",
        "-0x1.000000000000009e#64",
        Less,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        64,
        Ceiling,
        "-1.00000000000000000846",
        "-0x1.000000000000009c#64",
        Greater,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        64,
        Down,
        "-1.00000000000000000846",
        "-0x1.000000000000009c#64",
        Greater,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        64,
        Up,
        "-1.00000000000000000857",
        "-0x1.000000000000009e#64",
        Less,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        64,
        Nearest,
        "-1.00000000000000000846",
        "-0x1.000000000000009c#64",
        Greater,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        100,
        Floor,
        "-1.0000000000000000084967085105839",
        "-0x1.000000000000009cbc924cd8e#100",
        Less,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        100,
        Ceiling,
        "-1.0000000000000000084967085105823",
        "-0x1.000000000000009cbc924cd8c#100",
        Greater,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        100,
        Down,
        "-1.0000000000000000084967085105823",
        "-0x1.000000000000009cbc924cd8c#100",
        Greater,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        100,
        Up,
        "-1.0000000000000000084967085105839",
        "-0x1.000000000000009cbc924cd8e#100",
        Less,
    );
    test(
        "-20.0",
        "-0x14.0#5",
        100,
        Nearest,
        "-1.0000000000000000084967085105839",
        "-0x1.000000000000009cbc924cd8e#100",
        Less,
    );
    test("256.0", "0x100.0#9", 1, Floor, "1.0", "0x1.0#1", Less);
    test("256.0", "0x100.0#9", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("256.0", "0x100.0#9", 1, Down, "1.0", "0x1.0#1", Less);
    test("256.0", "0x100.0#9", 1, Up, "2.0", "0x2.0#1", Greater);
    test("256.0", "0x100.0#9", 1, Nearest, "1.0", "0x1.0#1", Less);
    test(
        "256.0",
        "0x100.0#9",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "256.0",
        "0x100.0#9",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test("256.0", "0x100.0#9", 10, Down, "1.0000", "0x1.000#10", Less);
    test(
        "256.0",
        "0x100.0#9",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "256.0",
        "0x100.0#9",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "256.0",
        "0x100.0#9",
        64,
        Floor,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Less,
    );
    test(
        "256.0",
        "0x100.0#9",
        64,
        Ceiling,
        "1.00000000000000000011",
        "0x1.0000000000000002#64",
        Greater,
    );
    test(
        "256.0",
        "0x100.0#9",
        64,
        Down,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Less,
    );
    test(
        "256.0",
        "0x100.0#9",
        64,
        Up,
        "1.00000000000000000011",
        "0x1.0000000000000002#64",
        Greater,
    );
    test(
        "256.0",
        "0x100.0#9",
        64,
        Nearest,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Less,
    );
    test(
        "256.0",
        "0x100.0#9",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "256.0",
        "0x100.0#9",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "256.0",
        "0x100.0#9",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "256.0",
        "0x100.0#9",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "256.0",
        "0x100.0#9",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test("-256.0", "-0x100.0#9", 1, Floor, "-2.0", "-0x2.0#1", Less);
    test(
        "-256.0",
        "-0x100.0#9",
        1,
        Ceiling,
        "-1.0",
        "-0x1.0#1",
        Greater,
    );
    test("-256.0", "-0x100.0#9", 1, Down, "-1.0", "-0x1.0#1", Greater);
    test("-256.0", "-0x100.0#9", 1, Up, "-2.0", "-0x2.0#1", Less);
    test(
        "-256.0",
        "-0x100.0#9",
        1,
        Nearest,
        "-1.0",
        "-0x1.0#1",
        Greater,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        10,
        Floor,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        10,
        Down,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        10,
        Up,
        "-1.0020",
        "-0x1.008#10",
        Less,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        64,
        Floor,
        "-1.00000000000000000011",
        "-0x1.0000000000000002#64",
        Less,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        64,
        Ceiling,
        "-1.00000000000000000000",
        "-0x1.0000000000000000#64",
        Greater,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        64,
        Down,
        "-1.00000000000000000000",
        "-0x1.0000000000000000#64",
        Greater,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        64,
        Up,
        "-1.00000000000000000011",
        "-0x1.0000000000000002#64",
        Less,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        64,
        Nearest,
        "-1.00000000000000000000",
        "-0x1.0000000000000000#64",
        Greater,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        100,
        Floor,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        100,
        Ceiling,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        100,
        Down,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        100,
        Up,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "-256.0",
        "-0x100.0#9",
        100,
        Nearest,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test("12.0", "0xc.0#4", 1, Floor, "1.0", "0x1.0#1", Less);
    test("12.0", "0xc.0#4", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("12.0", "0xc.0#4", 1, Down, "1.0", "0x1.0#1", Less);
    test("12.0", "0xc.0#4", 1, Up, "2.0", "0x2.0#1", Greater);
    test("12.0", "0xc.0#4", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("12.0", "0xc.0#4", 10, Floor, "1.0000", "0x1.000#10", Less);
    test(
        "12.0",
        "0xc.0#4",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test("12.0", "0xc.0#4", 10, Down, "1.0000", "0x1.000#10", Less);
    test("12.0", "0xc.0#4", 10, Up, "1.0020", "0x1.008#10", Greater);
    test("12.0", "0xc.0#4", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "12.0",
        "0xc.0#4",
        64,
        Floor,
        "1.00000000007550269080",
        "0x1.0000000053041e3e#64",
        Less,
    );
    test(
        "12.0",
        "0xc.0#4",
        64,
        Ceiling,
        "1.00000000007550269090",
        "0x1.0000000053041e40#64",
        Greater,
    );
    test(
        "12.0",
        "0xc.0#4",
        64,
        Down,
        "1.00000000007550269080",
        "0x1.0000000053041e3e#64",
        Less,
    );
    test(
        "12.0",
        "0xc.0#4",
        64,
        Up,
        "1.00000000007550269090",
        "0x1.0000000053041e40#64",
        Greater,
    );
    test(
        "12.0",
        "0xc.0#4",
        64,
        Nearest,
        "1.00000000007550269090",
        "0x1.0000000053041e40#64",
        Greater,
    );
    test(
        "12.0",
        "0xc.0#4",
        100,
        Floor,
        "1.0000000000755026908884322831979",
        "0x1.0000000053041e3fb1fffdff8#100",
        Less,
    );
    test(
        "12.0",
        "0xc.0#4",
        100,
        Ceiling,
        "1.0000000000755026908884322831994",
        "0x1.0000000053041e3fb1fffdffa#100",
        Greater,
    );
    test(
        "12.0",
        "0xc.0#4",
        100,
        Down,
        "1.0000000000755026908884322831979",
        "0x1.0000000053041e3fb1fffdff8#100",
        Less,
    );
    test(
        "12.0",
        "0xc.0#4",
        100,
        Up,
        "1.0000000000755026908884322831994",
        "0x1.0000000053041e3fb1fffdffa#100",
        Greater,
    );
    test(
        "12.0",
        "0xc.0#4",
        100,
        Nearest,
        "1.0000000000755026908884322831979",
        "0x1.0000000053041e3fb1fffdff8#100",
        Less,
    );
    test("1.0", "0x1.0#1", 1, Down, "1.0", "0x1.0#1", Less);
    test("1.0", "0x1.0#1", 1, Up, "2.0", "0x2.0#1", Greater);
    test("1.0", "0x1.0#1", 10, Down, "1.3125", "0x1.500#10", Less);
    test("1.0", "0x1.0#1", 10, Up, "1.3145", "0x1.508#10", Greater);
    test(
        "1.0",
        "0x1.0#1",
        64,
        Floor,
        "1.31303528549933130355",
        "0x1.50231499b6b1d49e#64",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        64,
        Ceiling,
        "1.31303528549933130366",
        "0x1.50231499b6b1d4a0#64",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        64,
        Down,
        "1.31303528549933130355",
        "0x1.50231499b6b1d49e#64",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        64,
        Up,
        "1.31303528549933130366",
        "0x1.50231499b6b1d4a0#64",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        64,
        Nearest,
        "1.31303528549933130366",
        "0x1.50231499b6b1d4a0#64",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Down,
        "1.3130352854993313036361612469298",
        "0x1.50231499b6b1d49f813a188f8#100",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Up,
        "1.3130352854993313036361612469313",
        "0x1.50231499b6b1d49f813a188fa#100",
        Greater,
    );
    test("8.00", "0x8.0#4", 1, Floor, "1.0", "0x1.0#1", Less);
    test("8.00", "0x8.0#4", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("8.00", "0x8.0#4", 1, Down, "1.0", "0x1.0#1", Less);
    test("8.00", "0x8.0#4", 1, Up, "2.0", "0x2.0#1", Greater);
    test("8.00", "0x8.0#4", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("8.00", "0x8.0#4", 10, Floor, "1.0000", "0x1.000#10", Less);
    test(
        "8.00",
        "0x8.0#4",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test("8.00", "0x8.0#4", 10, Down, "1.0000", "0x1.000#10", Less);
    test("8.00", "0x8.0#4", 10, Up, "1.0020", "0x1.008#10", Greater);
    test("8.00", "0x8.0#4", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "8.00",
        "0x8.0#4",
        64,
        Floor,
        "1.00000022507037476685",
        "0x1.000003c6ab7e7eea#64",
        Less,
    );
    test(
        "8.00",
        "0x8.0#4",
        64,
        Ceiling,
        "1.00000022507037476696",
        "0x1.000003c6ab7e7eec#64",
        Greater,
    );
    test(
        "8.00",
        "0x8.0#4",
        64,
        Down,
        "1.00000022507037476685",
        "0x1.000003c6ab7e7eea#64",
        Less,
    );
    test(
        "8.00",
        "0x8.0#4",
        64,
        Up,
        "1.00000022507037476696",
        "0x1.000003c6ab7e7eec#64",
        Greater,
    );
    test(
        "8.00",
        "0x8.0#4",
        64,
        Nearest,
        "1.00000022507037476685",
        "0x1.000003c6ab7e7eea#64",
        Less,
    );
    test(
        "8.00",
        "0x8.0#4",
        100,
        Floor,
        "1.0000002250703747668521775443869",
        "0x1.000003c6ab7e7eea04a97bc96#100",
        Less,
    );
    test(
        "8.00",
        "0x8.0#4",
        100,
        Ceiling,
        "1.0000002250703747668521775443885",
        "0x1.000003c6ab7e7eea04a97bc98#100",
        Greater,
    );
    test(
        "8.00",
        "0x8.0#4",
        100,
        Down,
        "1.0000002250703747668521775443869",
        "0x1.000003c6ab7e7eea04a97bc96#100",
        Less,
    );
    test(
        "8.00",
        "0x8.0#4",
        100,
        Up,
        "1.0000002250703747668521775443885",
        "0x1.000003c6ab7e7eea04a97bc98#100",
        Greater,
    );
    test(
        "8.00",
        "0x8.0#4",
        100,
        Nearest,
        "1.0000002250703747668521775443885",
        "0x1.000003c6ab7e7eea04a97bc98#100",
        Greater,
    );
    test("64.00", "0x40.0#7", 1, Floor, "1.0", "0x1.0#1", Less);
    test("64.00", "0x40.0#7", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("64.00", "0x40.0#7", 1, Down, "1.0", "0x1.0#1", Less);
    test("64.00", "0x40.0#7", 1, Up, "2.0", "0x2.0#1", Greater);
    test("64.00", "0x40.0#7", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("64.00", "0x40.0#7", 10, Floor, "1.0000", "0x1.000#10", Less);
    test(
        "64.00",
        "0x40.0#7",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test("64.00", "0x40.0#7", 10, Down, "1.0000", "0x1.000#10", Less);
    test("64.00", "0x40.0#7", 10, Up, "1.0020", "0x1.008#10", Greater);
    test(
        "64.00",
        "0x40.0#7",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "64.00",
        "0x40.0#7",
        64,
        Floor,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Less,
    );
    test(
        "64.00",
        "0x40.0#7",
        64,
        Ceiling,
        "1.00000000000000000011",
        "0x1.0000000000000002#64",
        Greater,
    );
    test(
        "64.00",
        "0x40.0#7",
        64,
        Down,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Less,
    );
    test(
        "64.00",
        "0x40.0#7",
        64,
        Up,
        "1.00000000000000000011",
        "0x1.0000000000000002#64",
        Greater,
    );
    test(
        "64.00",
        "0x40.0#7",
        64,
        Nearest,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Less,
    );
    test(
        "64.00",
        "0x40.0#7",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "64.00",
        "0x40.0#7",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "64.00",
        "0x40.0#7",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "64.00",
        "0x40.0#7",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "64.00",
        "0x40.0#7",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
}

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

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

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

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

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

    let (c_alt, o_alt) = x.coth_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.coth_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_coth_prec_round(&rug::Float::exact_from(&x), prec, rug_rm);
        assert_eq!(
            ComparableFloatRef(&Float::from(&rug_c)),
            ComparableFloatRef(&c)
        );
        assert_eq!(rug_o, o);
    }

    // coth is odd
    let (c_neg, o_neg) = (-&x).coth_prec_round(prec, -rm);
    assert_eq!(ComparableFloatRef(&c_neg), ComparableFloatRef(&-&c));
    assert_eq!(o_neg, o.reverse());

    // coth x has the sign of x
    if !x.is_nan() {
        assert_eq!(c.is_sign_positive(), x.is_sign_positive());
    }
    // |coth x| > |1/x| for finite nonzero x, so coth x is on the far side of 1/x rounded the same
    // way, and |coth x| > 1
    if x.is_normal() {
        let r = x.reciprocal_prec_round_ref(prec, rm).0;
        if x > 0u32 {
            assert!(c >= r);
            assert!(c >= 1u32);
        } else {
            assert!(c <= r);
            assert!(c <= -1i32);
        }
    }
    if c.is_normal() {
        assert_eq!(c.get_prec(), Some(prec));
    }

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

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

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

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

        let (c, o) = Float::NEGATIVE_INFINITY.coth_prec_round(prec, rm);
        assert_eq!(ComparableFloat(c), ComparableFloat(-Float::one_prec(prec)));
        assert_eq!(o, Equal);

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

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

#[test]
fn coth_round_properties() {
    float_rounding_mode_pair_gen_var_47().test_properties(|(x, rm)| {
        let (c, o) = x.clone().coth_round(rm);
        assert!(c.is_valid());
        assert_rounding_ordering_consistent(&c, rm, o);
        let (c_alt, o_alt) = x.coth_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.coth_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.coth_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_coth_round(&rug::Float::exact_from(&x), rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    });
}

#[test]
fn coth_prec_properties() {
    float_unsigned_pair_gen_var_1().test_properties(|(x, prec)| {
        let (c, o) = x.clone().coth_prec(prec);
        assert!(c.is_valid());
        let (c_alt, o_alt) = x.coth_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.coth_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.coth_prec_round_ref(prec, Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

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

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

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

        let c_alt = x.coth_prec_round_ref(x.significant_bits(), Nearest).0;
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));

        assert_eq!(
            ComparableFloatRef(&<Float as From<&rug::Float>>::from(&rug_coth(
                &rug::Float::exact_from(&x)
            ))),
            ComparableFloatRef(&c)
        );

        assert_eq!(ComparableFloatRef(&(-&x).coth()), ComparableFloatRef(&-&c));
        if !x.is_nan() {
            assert_eq!(c.is_sign_positive(), x.is_sign_positive());
        }
    });
}

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_coth() {
    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_coth(x)), NiceFloat(out));
    }
    test::<f32>(f32::NAN, f32::NAN);
    test::<f32>(f32::INFINITY, 1.0);
    test::<f32>(f32::NEGATIVE_INFINITY, -1.0);
    test::<f32>(0.0, f32::INFINITY);
    test::<f32>(-0.0, f32::NEGATIVE_INFINITY);
    test::<f32>(1.0, 1.3130352);
    test::<f32>(-1.0, -1.3130352);
    test::<f32>(0.5, 2.1639533);
    test::<f32>(2.0, 1.0373148);
    test::<f32>(10.0, 1.0);
    test::<f32>(1.0e-20, 1.0e20);
    test::<f32>(1.0e-38, 1.0000001e38);
    test::<f32>(3.0e-39, 3.3333327e38);
    test::<f32>(1.0e-45, f32::INFINITY);
    test::<f32>(3.4028235e38, 1.0);

    test::<f64>(f64::NAN, f64::NAN);
    test::<f64>(f64::INFINITY, 1.0);
    test::<f64>(f64::NEGATIVE_INFINITY, -1.0);
    test::<f64>(0.0, f64::INFINITY);
    test::<f64>(-0.0, f64::NEGATIVE_INFINITY);
    test::<f64>(1.0, 1.3130352854993312);
    test::<f64>(-1.0, -1.3130352854993312);
    test::<f64>(0.5, 2.163953413738653);
    test::<f64>(2.0, 1.0373147207275482);
    test::<f64>(10.0, 1.0000000041223072);
    test::<f64>(20.0, 1.0);
    test::<f64>(1.0e-200, 1.0e200);
    test::<f64>(1.0e-308, 1.0e308);
    test::<f64>(5.0e-309, f64::INFINITY);
    test::<f64>(5.0e-324, f64::INFINITY);
    test::<f64>(1.7976931348623157e308, 1.0);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_coth_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_coth(x);
        // coth is NaN exactly for NaN inputs, and otherwise has the sign of its input and magnitude
        // at least 1
        assert_eq!(c.is_nan(), x.is_nan());
        if !x.is_nan() {
            assert_eq!(c.is_sign_positive(), x.is_sign_positive());
            assert!(c >= T::ONE || c <= T::NEGATIVE_ONE);
            // coth is odd
            assert_eq!(NiceFloat(primitive_float_coth(-x)), NiceFloat(-c));
        }
        if x.is_finite() {
            // the result is the correctly rounded hyperbolic cotangent as given by the oracle and
            // rounded once to the primitive type
            let rug_c: T = round_once_to_primitive(|p| {
                <Float as From<&rug::Float>>::from(
                    &rug_coth_prec(&rug::Float::exact_from(&Float::from(x)), p).0,
                )
            });
            assert_eq!(NiceFloat(rug_c), NiceFloat(c));
        }
    });
}

#[test]
fn primitive_float_coth_properties() {
    apply_fn_to_primitive_floats!(primitive_float_coth_properties_helper);
}

#[test]
fn test_coth_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::coth_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::coth_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);

        if let Ok(rug_rm) = rug_round_try_from_rounding_mode(rm) {
            let (rug_c, rug_o) = rug_coth_rational_prec_round(&x, prec, rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    };
    test("0", 1, Down, "Infinity", "Infinity", Equal);
    test("0", 10, Down, "Infinity", "Infinity", Equal);
    test("0", 1, Up, "Infinity", "Infinity", Equal);
    test("0", 10, Up, "Infinity", "Infinity", Equal);
    test("0", 1, Floor, "Infinity", "Infinity", Equal);
    test("0", 10, Floor, "Infinity", "Infinity", Equal);
    test("0", 1, Ceiling, "Infinity", "Infinity", Equal);
    test("0", 10, Ceiling, "Infinity", "Infinity", Equal);
    test("0", 1, Nearest, "Infinity", "Infinity", Equal);
    test("0", 10, Nearest, "Infinity", "Infinity", Equal);
    test("0", 1, Exact, "Infinity", "Infinity", Equal);
    test("0", 10, Exact, "Infinity", "Infinity", Equal);
    // - the first bracket of x rounds the same way at both ends
    test("3/5", 1, Floor, "1.0", "0x1.0#1", Less);
    test("3/5", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("3/5", 1, Nearest, "2.0", "0x2.0#1", Greater);
    test("3/5", 10, Floor, "1.8613", "0x1.dc8#10", Less);
    test("3/5", 10, Ceiling, "1.8633", "0x1.dd0#10", Greater);
    test("3/5", 10, Nearest, "1.8613", "0x1.dc8#10", Less);
    test(
        "3/5",
        100,
        Floor,
        "1.8620255213866662476380145582087",
        "0x1.dcadb45eac4efa4a942f4f704#100",
        Less,
    );
    test(
        "3/5",
        100,
        Ceiling,
        "1.8620255213866662476380145582103",
        "0x1.dcadb45eac4efa4a942f4f706#100",
        Greater,
    );
    test(
        "3/5",
        100,
        Nearest,
        "1.8620255213866662476380145582087",
        "0x1.dcadb45eac4efa4a942f4f704#100",
        Less,
    );
    test("-3/5", 1, Floor, "-2.0", "-0x2.0#1", Less);
    test("-3/5", 1, Ceiling, "-1.0", "-0x1.0#1", Greater);
    test("-3/5", 1, Nearest, "-2.0", "-0x2.0#1", Less);
    test("-3/5", 10, Floor, "-1.8633", "-0x1.dd0#10", Less);
    test("-3/5", 10, Ceiling, "-1.8613", "-0x1.dc8#10", Greater);
    test("-3/5", 10, Nearest, "-1.8613", "-0x1.dc8#10", Greater);
    test(
        "-3/5",
        100,
        Floor,
        "-1.8620255213866662476380145582103",
        "-0x1.dcadb45eac4efa4a942f4f706#100",
        Less,
    );
    test(
        "-3/5",
        100,
        Ceiling,
        "-1.8620255213866662476380145582087",
        "-0x1.dcadb45eac4efa4a942f4f704#100",
        Greater,
    );
    test(
        "-3/5",
        100,
        Nearest,
        "-1.8620255213866662476380145582087",
        "-0x1.dcadb45eac4efa4a942f4f704#100",
        Greater,
    );
    test("1/3", 1, Floor, "2.0", "0x2.0#1", Less);
    test("1/3", 1, Ceiling, "4.0", "0x4.0#1", Greater);
    test("1/3", 1, Nearest, "4.0", "0x4.0#1", Greater);
    test("1/3", 10, Floor, "3.1094", "0x3.1c#10", Less);
    test("1/3", 10, Ceiling, "3.1133", "0x3.1d#10", Greater);
    test("1/3", 10, Nearest, "3.1094", "0x3.1c#10", Less);
    test(
        "1/3",
        100,
        Floor,
        "3.1102966796194437013783752314146",
        "0x3.1c3c6737d2a99a2538dde3dbc#100",
        Less,
    );
    test(
        "1/3",
        100,
        Ceiling,
        "3.1102966796194437013783752314178",
        "0x3.1c3c6737d2a99a2538dde3dc0#100",
        Greater,
    );
    test(
        "1/3",
        100,
        Nearest,
        "3.1102966796194437013783752314178",
        "0x3.1c3c6737d2a99a2538dde3dc0#100",
        Greater,
    );
    // - |coth(x)| lies within 2^-prec of 1, and a bound from a lower bound on |x| rounds it from 1
    test("22/7", 1, Floor, "1.0", "0x1.0#1", Less);
    test("22/7", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("22/7", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("22/7", 10, Floor, "1.0020", "0x1.008#10", Less);
    test("22/7", 10, Ceiling, "1.0039", "0x1.010#10", Greater);
    test("22/7", 10, Nearest, "1.0039", "0x1.010#10", Greater);
    test(
        "22/7",
        100,
        Floor,
        "1.0037324043984771186938350250943",
        "0x1.00f49b5ad3b018d5106a69232#100",
        Less,
    );
    test(
        "22/7",
        100,
        Ceiling,
        "1.0037324043984771186938350250959",
        "0x1.00f49b5ad3b018d5106a69234#100",
        Greater,
    );
    test(
        "22/7",
        100,
        Nearest,
        "1.0037324043984771186938350250959",
        "0x1.00f49b5ad3b018d5106a69234#100",
        Greater,
    );
    test("100", 1, Floor, "1.0", "0x1.0#1", Less);
    test("100", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("100", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("100", 10, Floor, "1.0000", "0x1.000#10", Less);
    test("100", 10, Ceiling, "1.0020", "0x1.008#10", Greater);
    test("100", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "100",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "100",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "100",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test("-100", 1, Floor, "-2.0", "-0x2.0#1", Less);
    test("-100", 1, Ceiling, "-1.0", "-0x1.0#1", Greater);
    test("-100", 1, Nearest, "-1.0", "-0x1.0#1", Greater);
    test("-100", 10, Floor, "-1.0020", "-0x1.008#10", Less);
    test("-100", 10, Ceiling, "-1.0000", "-0x1.000#10", Greater);
    test("-100", 10, Nearest, "-1.0000", "-0x1.000#10", Greater);
    test(
        "-100",
        100,
        Floor,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "-100",
        100,
        Ceiling,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-100",
        100,
        Nearest,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    // - tiny x: the rounding of 1/x, nudged away from zero
    test("1/1000", 1, Floor, "5.1e2", "0x2.0E+2#1", Less);
    test("1/1000", 1, Ceiling, "1.0e3", "0x4.0E+2#1", Greater);
    test("1/1000", 1, Nearest, "1.0e3", "0x4.0E+2#1", Greater);
    test("1/1000", 10, Floor, "1000.0", "0x3e8.0#10", Less);
    test("1/1000", 10, Ceiling, "1001.0", "0x3e9.0#10", Greater);
    test("1/1000", 10, Nearest, "1000.0", "0x3e8.0#10", Less);
    // - small x: bracketed by quotients of series bounds on cosh(x) and sinh(x)
    test(
        "1/1000",
        100,
        Floor,
        "1000.0003333333111111132275130154",
        "0x3e8.0015d867ab7de2ee29e334c#100",
        Less,
    );
    test(
        "1/1000",
        100,
        Ceiling,
        "1000.0003333333111111132275130162",
        "0x3e8.0015d867ab7de2ee29e3350#100",
        Greater,
    );
    test(
        "1/1000",
        100,
        Nearest,
        "1000.0003333333111111132275130162",
        "0x3e8.0015d867ab7de2ee29e3350#100",
        Greater,
    );
    test("-1/1000000", 1, Floor, "-1.0e6", "-0x1.0E+5#1", Less);
    test("-1/1000000", 1, Ceiling, "-5.2e5", "-0x8.0E+4#1", Greater);
    test("-1/1000000", 1, Nearest, "-1.0e6", "-0x1.0E+5#1", Less);
    test("-1/1000000", 10, Floor, "-1.0004e6", "-0xf.44E+4#10", Less);
    test(
        "-1/1000000",
        10,
        Ceiling,
        "-9.9942e5",
        "-0xf.40E+4#10",
        Greater,
    );
    test(
        "-1/1000000",
        10,
        Nearest,
        "-1.0004e6",
        "-0xf.44E+4#10",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Floor,
        "-1000000.0000003333333333333111115",
        "-0xf4240.00000597a7e03ca41b77#100",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Ceiling,
        "-1000000.0000003333333333333111107",
        "-0xf4240.00000597a7e03ca41b76#100",
        Greater,
    );
    test(
        "-1/1000000",
        100,
        Nearest,
        "-1000000.0000003333333333333111115",
        "-0xf4240.00000597a7e03ca41b77#100",
        Less,
    );
    test(
        "1/100000000000000000000",
        1,
        Floor,
        "7.4e19",
        "0x4.0E+16#1",
        Less,
    );
    test(
        "1/100000000000000000000",
        1,
        Ceiling,
        "1.5e20",
        "0x8.0E+16#1",
        Greater,
    );
    test(
        "1/100000000000000000000",
        1,
        Nearest,
        "7.4e19",
        "0x4.0E+16#1",
        Less,
    );
    test(
        "1/100000000000000000000",
        10,
        Floor,
        "9.9872e19",
        "0x5.6aE+16#10",
        Less,
    );
    test(
        "1/100000000000000000000",
        10,
        Ceiling,
        "1.0002e20",
        "0x5.6cE+16#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        10,
        Nearest,
        "1.0002e20",
        "0x5.6cE+16#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Floor,
        "100000000000000000000.00000000000",
        "0x56bc75e2d63100000.000000000#100",
        Less,
    );
    test(
        "1/100000000000000000000",
        100,
        Ceiling,
        "100000000000000000000.00000000012",
        "0x56bc75e2d63100000.000000008#100",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Nearest,
        "100000000000000000000.00000000000",
        "0x56bc75e2d63100000.000000000#100",
        Less,
    );
    test("1488522235/2", 1, Floor, "1.0", "0x1.0#1", Less);
    test("1488522235/2", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("1488522235/2", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("1488522235/2", 10, Floor, "1.0000", "0x1.000#10", Less);
    test("1488522235/2", 10, Ceiling, "1.0020", "0x1.008#10", Greater);
    test("1488522235/2", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "1488522235/2",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "1488522235/2",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "1488522235/2",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test("7442611177/10", 1, Floor, "1.0", "0x1.0#1", Less);
    test("7442611177/10", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("7442611177/10", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("7442611177/10", 10, Floor, "1.0000", "0x1.000#10", Less);
    test(
        "7442611177/10",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test("7442611177/10", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "7442611177/10",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "7442611177/10",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "7442611177/10",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test("-7442611185/10", 1, Floor, "-2.0", "-0x2.0#1", Less);
    test("-7442611185/10", 1, Ceiling, "-1.0", "-0x1.0#1", Greater);
    test("-7442611185/10", 1, Nearest, "-1.0", "-0x1.0#1", Greater);
    test("-7442611185/10", 10, Floor, "-1.0020", "-0x1.008#10", Less);
    test(
        "-7442611185/10",
        10,
        Ceiling,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-7442611185/10",
        10,
        Nearest,
        "-1.0000",
        "-0x1.000#10",
        Greater,
    );
    test(
        "-7442611185/10",
        100,
        Floor,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "-7442611185/10",
        100,
        Ceiling,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-7442611185/10",
        100,
        Nearest,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test("744261119", 1, Floor, "1.0", "0x1.0#1", Less);
    test("744261119", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("744261119", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("744261119", 10, Floor, "1.0000", "0x1.000#10", Less);
    test("744261119", 10, Ceiling, "1.0020", "0x1.008#10", Greater);
    test("744261119", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "744261119",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261119",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261119",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test("7442611196/10", 1, Floor, "1.0", "0x1.0#1", Less);
    test("7442611196/10", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("7442611196/10", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("7442611196/10", 10, Floor, "1.0000", "0x1.000#10", Less);
    test(
        "7442611196/10",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test("7442611196/10", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "7442611196/10",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "7442611196/10",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "7442611196/10",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test("744261120", 1, Floor, "1.0", "0x1.0#1", Less);
    test("744261120", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("744261120", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("744261120", 10, Floor, "1.0000", "0x1.000#10", Less);
    test("744261120", 10, Ceiling, "1.0020", "0x1.008#10", Greater);
    test("744261120", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "744261120",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "744261120",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "744261120",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test("10000000000", 1, Floor, "1.0", "0x1.0#1", Less);
    test("10000000000", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("10000000000", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("10000000000", 10, Floor, "1.0000", "0x1.000#10", Less);
    test("10000000000", 10, Ceiling, "1.0020", "0x1.008#10", Greater);
    test("10000000000", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "10000000000",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "10000000000",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "10000000000",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "1/1000",
        100,
        Down,
        "1000.0003333333111111132275130154",
        "0x3e8.0015d867ab7de2ee29e334c#100",
        Less,
    );
    test(
        "744261119",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "1/1000",
        100,
        Up,
        "1000.0003333333111111132275130162",
        "0x3e8.0015d867ab7de2ee29e3350#100",
        Greater,
    );
    test(
        "744261119",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test("2/13", 7, Floor, "6.500", "0x6.8#7", Less);
    test("2/13", 7, Ceiling, "6.562", "0x6.9#7", Greater);
    test("2/13", 7, Nearest, "6.562", "0x6.9#7", Greater);
    test(
        "1/1267650600228229401496703205376",
        10,
        Floor,
        "1.2677e30",
        "0x1.000E+25#10",
        Less,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Floor,
        "-1.2701e30",
        "-0x1.008E+25#10",
        Less,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Floor,
        "3.8030e30",
        "0x3.00E+25#10",
        Less,
    );
    test(
        "1/1267650600228229401496703205377",
        100,
        Floor,
        "1267650600228229401496703205376.0",
        "0x10000000000000000000000000.0#100",
        Less,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Floor,
        "-1267650600228229401496703205378.0",
        "-0x10000000000000000000000002.0#100",
        Less,
    );
    test("-22/7", 20, Floor, "-1.0037327", "-0x1.00f4a#20", Less);
    test("-1/1000", 10, Floor, "-1001.0", "-0x3e9.0#10", Less);
    test("-744261120", 10, Floor, "-1.0020", "-0x1.008#10", Less);
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Floor,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Ceiling,
        "1.2701e30",
        "0x1.008E+25#10",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Ceiling,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Greater,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Ceiling,
        "3.8079e30",
        "0x3.01E+25#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205377",
        100,
        Ceiling,
        "1267650600228229401496703205378.0",
        "0x10000000000000000000000002.0#100",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Ceiling,
        "-1267650600228229401496703205376.0",
        "-0x10000000000000000000000000.0#100",
        Greater,
    );
    test("-22/7", 20, Ceiling, "-1.0037308", "-0x1.00f48#20", Greater);
    test("-1/1000", 10, Ceiling, "-1000.0", "-0x3e8.0#10", Greater);
    test("-744261120", 10, Ceiling, "-1.0000", "-0x1.000#10", Greater);
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Ceiling,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Down,
        "1.2677e30",
        "0x1.000E+25#10",
        Less,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Down,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Greater,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Down,
        "3.8030e30",
        "0x3.00E+25#10",
        Less,
    );
    test(
        "1/1267650600228229401496703205377",
        100,
        Down,
        "1267650600228229401496703205376.0",
        "0x10000000000000000000000000.0#100",
        Less,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Down,
        "-1267650600228229401496703205376.0",
        "-0x10000000000000000000000000.0#100",
        Greater,
    );
    test(
        "1/3",
        100,
        Down,
        "3.1102966796194437013783752314146",
        "0x3.1c3c6737d2a99a2538dde3dbc#100",
        Less,
    );
    test("-22/7", 20, Down, "-1.0037308", "-0x1.00f48#20", Greater);
    test("1/1000", 10, Down, "1000.0", "0x3e8.0#10", Less);
    test("-1/1000", 10, Down, "-1000.0", "-0x3e8.0#10", Greater);
    test("744261120", 10, Down, "1.0000", "0x1.000#10", Less);
    test("-744261120", 10, Down, "-1.0000", "-0x1.000#10", Greater);
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Down,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Up,
        "1.2701e30",
        "0x1.008E+25#10",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Up,
        "-1.2701e30",
        "-0x1.008E+25#10",
        Less,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Up,
        "3.8079e30",
        "0x3.01E+25#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205377",
        100,
        Up,
        "1267650600228229401496703205378.0",
        "0x10000000000000000000000002.0#100",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Up,
        "-1267650600228229401496703205378.0",
        "-0x10000000000000000000000002.0#100",
        Less,
    );
    test(
        "1/3",
        100,
        Up,
        "3.1102966796194437013783752314178",
        "0x3.1c3c6737d2a99a2538dde3dc0#100",
        Greater,
    );
    test("-22/7", 20, Up, "-1.0037327", "-0x1.00f4a#20", Less);
    test("1/1000", 10, Up, "1001.0", "0x3e9.0#10", Greater);
    test("-1/1000", 10, Up, "-1001.0", "-0x3e9.0#10", Less);
    test("744261120", 10, Up, "1.0020", "0x1.008#10", Greater);
    test("-744261120", 10, Up, "-1.0020", "-0x1.008#10", Less);
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Up,
        "1.0020",
        "0x1.008#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Nearest,
        "1.2677e30",
        "0x1.000E+25#10",
        Less,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Nearest,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Greater,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Nearest,
        "3.8030e30",
        "0x3.00E+25#10",
        Less,
    );
    test(
        "1/1267650600228229401496703205377",
        100,
        Nearest,
        "1267650600228229401496703205378.0",
        "0x10000000000000000000000002.0#100",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Nearest,
        "-1267650600228229401496703205378.0",
        "-0x10000000000000000000000002.0#100",
        Less,
    );
    test("-22/7", 20, Nearest, "-1.0037327", "-0x1.00f4a#20", Less);
    test("-1/1000", 10, Nearest, "-1000.0", "-0x3e8.0#10", Greater);
    test("-744261120", 10, Nearest, "-1.0000", "-0x1.000#10", Greater);
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Less,
    );
    test(
        "3/257",
        40,
        Floor,
        "85.670557681820",
        "0x55.aba9ab118#40",
        Less,
    );
    test(
        "3/257",
        40,
        Ceiling,
        "85.670557681937",
        "0x55.aba9ab120#40",
        Greater,
    );
    test(
        "3/257",
        40,
        Nearest,
        "85.670557681937",
        "0x55.aba9ab120#40",
        Greater,
    );
    test("20", 1, Floor, "1.0", "0x1.0#1", Less);
    test("20", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("20", 1, Down, "1.0", "0x1.0#1", Less);
    test("20", 1, Up, "2.0", "0x2.0#1", Greater);
    test("20", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("20", 10, Floor, "1.0000", "0x1.000#10", Less);
    test("20", 10, Ceiling, "1.0020", "0x1.008#10", Greater);
    test("20", 10, Down, "1.0000", "0x1.000#10", Less);
    test("20", 10, Up, "1.0020", "0x1.008#10", Greater);
    test("20", 10, Nearest, "1.0000", "0x1.000#10", Less);
    // - x is exactly representable at the working precision
    test(
        "20",
        64,
        Floor,
        "1.00000000000000000846",
        "0x1.000000000000009c#64",
        Less,
    );
    test(
        "20",
        64,
        Ceiling,
        "1.00000000000000000857",
        "0x1.000000000000009e#64",
        Greater,
    );
    test(
        "20",
        64,
        Down,
        "1.00000000000000000846",
        "0x1.000000000000009c#64",
        Less,
    );
    test(
        "20",
        64,
        Up,
        "1.00000000000000000857",
        "0x1.000000000000009e#64",
        Greater,
    );
    test(
        "20",
        64,
        Nearest,
        "1.00000000000000000846",
        "0x1.000000000000009c#64",
        Less,
    );
    test(
        "20",
        100,
        Floor,
        "1.0000000000000000084967085105823",
        "0x1.000000000000009cbc924cd8c#100",
        Less,
    );
    test(
        "20",
        100,
        Ceiling,
        "1.0000000000000000084967085105839",
        "0x1.000000000000009cbc924cd8e#100",
        Greater,
    );
    test(
        "20",
        100,
        Down,
        "1.0000000000000000084967085105823",
        "0x1.000000000000009cbc924cd8c#100",
        Less,
    );
    test(
        "20",
        100,
        Up,
        "1.0000000000000000084967085105839",
        "0x1.000000000000009cbc924cd8e#100",
        Greater,
    );
    test(
        "20",
        100,
        Nearest,
        "1.0000000000000000084967085105839",
        "0x1.000000000000009cbc924cd8e#100",
        Greater,
    );
    test("-20", 1, Floor, "-2.0", "-0x2.0#1", Less);
    test("-20", 1, Ceiling, "-1.0", "-0x1.0#1", Greater);
    test("-20", 1, Down, "-1.0", "-0x1.0#1", Greater);
    test("-20", 1, Up, "-2.0", "-0x2.0#1", Less);
    test("-20", 1, Nearest, "-1.0", "-0x1.0#1", Greater);
    test("-20", 10, Floor, "-1.0020", "-0x1.008#10", Less);
    test("-20", 10, Ceiling, "-1.0000", "-0x1.000#10", Greater);
    test("-20", 10, Down, "-1.0000", "-0x1.000#10", Greater);
    test("-20", 10, Up, "-1.0020", "-0x1.008#10", Less);
    test("-20", 10, Nearest, "-1.0000", "-0x1.000#10", Greater);
    test(
        "-20",
        64,
        Floor,
        "-1.00000000000000000857",
        "-0x1.000000000000009e#64",
        Less,
    );
    test(
        "-20",
        64,
        Ceiling,
        "-1.00000000000000000846",
        "-0x1.000000000000009c#64",
        Greater,
    );
    test(
        "-20",
        64,
        Down,
        "-1.00000000000000000846",
        "-0x1.000000000000009c#64",
        Greater,
    );
    test(
        "-20",
        64,
        Up,
        "-1.00000000000000000857",
        "-0x1.000000000000009e#64",
        Less,
    );
    test(
        "-20",
        64,
        Nearest,
        "-1.00000000000000000846",
        "-0x1.000000000000009c#64",
        Greater,
    );
    test(
        "-20",
        100,
        Floor,
        "-1.0000000000000000084967085105839",
        "-0x1.000000000000009cbc924cd8e#100",
        Less,
    );
    test(
        "-20",
        100,
        Ceiling,
        "-1.0000000000000000084967085105823",
        "-0x1.000000000000009cbc924cd8c#100",
        Greater,
    );
    test(
        "-20",
        100,
        Down,
        "-1.0000000000000000084967085105823",
        "-0x1.000000000000009cbc924cd8c#100",
        Greater,
    );
    test(
        "-20",
        100,
        Up,
        "-1.0000000000000000084967085105839",
        "-0x1.000000000000009cbc924cd8e#100",
        Less,
    );
    test(
        "-20",
        100,
        Nearest,
        "-1.0000000000000000084967085105839",
        "-0x1.000000000000009cbc924cd8e#100",
        Less,
    );
    test("41/2", 1, Floor, "1.0", "0x1.0#1", Less);
    test("41/2", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("41/2", 1, Down, "1.0", "0x1.0#1", Less);
    test("41/2", 1, Up, "2.0", "0x2.0#1", Greater);
    test("41/2", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("41/2", 10, Floor, "1.0000", "0x1.000#10", Less);
    test("41/2", 10, Ceiling, "1.0020", "0x1.008#10", Greater);
    test("41/2", 10, Down, "1.0000", "0x1.000#10", Less);
    test("41/2", 10, Up, "1.0020", "0x1.008#10", Greater);
    test("41/2", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "41/2",
        64,
        Floor,
        "1.00000000000000000304",
        "0x1.0000000000000038#64",
        Less,
    );
    test(
        "41/2",
        64,
        Ceiling,
        "1.00000000000000000314",
        "0x1.000000000000003a#64",
        Greater,
    );
    test(
        "41/2",
        64,
        Down,
        "1.00000000000000000304",
        "0x1.0000000000000038#64",
        Less,
    );
    test(
        "41/2",
        64,
        Up,
        "1.00000000000000000314",
        "0x1.000000000000003a#64",
        Greater,
    );
    test(
        "41/2",
        64,
        Nearest,
        "1.00000000000000000314",
        "0x1.000000000000003a#64",
        Greater,
    );
    test(
        "41/2",
        100,
        Floor,
        "1.0000000000000000031257643786692",
        "0x1.0000000000000039a901436e8#100",
        Less,
    );
    test(
        "41/2",
        100,
        Ceiling,
        "1.0000000000000000031257643786708",
        "0x1.0000000000000039a901436ea#100",
        Greater,
    );
    test(
        "41/2",
        100,
        Down,
        "1.0000000000000000031257643786692",
        "0x1.0000000000000039a901436e8#100",
        Less,
    );
    test(
        "41/2",
        100,
        Up,
        "1.0000000000000000031257643786708",
        "0x1.0000000000000039a901436ea#100",
        Greater,
    );
    test(
        "41/2",
        100,
        Nearest,
        "1.0000000000000000031257643786708",
        "0x1.0000000000000039a901436ea#100",
        Greater,
    );
    test("100000", 1, Floor, "1.0", "0x1.0#1", Less);
    test("100000", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("100000", 1, Down, "1.0", "0x1.0#1", Less);
    test("100000", 1, Up, "2.0", "0x2.0#1", Greater);
    test("100000", 1, Nearest, "1.0", "0x1.0#1", Less);
    test("100000", 10, Floor, "1.0000", "0x1.000#10", Less);
    test("100000", 10, Ceiling, "1.0020", "0x1.008#10", Greater);
    test("100000", 10, Down, "1.0000", "0x1.000#10", Less);
    test("100000", 10, Up, "1.0020", "0x1.008#10", Greater);
    test("100000", 10, Nearest, "1.0000", "0x1.000#10", Less);
    test(
        "100000",
        64,
        Floor,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Less,
    );
    test(
        "100000",
        64,
        Ceiling,
        "1.00000000000000000011",
        "0x1.0000000000000002#64",
        Greater,
    );
    test(
        "100000",
        64,
        Down,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Less,
    );
    test(
        "100000",
        64,
        Up,
        "1.00000000000000000011",
        "0x1.0000000000000002#64",
        Greater,
    );
    test(
        "100000",
        64,
        Nearest,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Less,
    );
    test(
        "100000",
        100,
        Floor,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "100000",
        100,
        Ceiling,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "100000",
        100,
        Down,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test(
        "100000",
        100,
        Up,
        "1.0000000000000000000000000000016",
        "0x1.0000000000000000000000002#100",
        Greater,
    );
    test(
        "100000",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Less,
    );
    test("-100000", 1, Floor, "-2.0", "-0x2.0#1", Less);
    test("-100000", 1, Ceiling, "-1.0", "-0x1.0#1", Greater);
    test("-100000", 1, Down, "-1.0", "-0x1.0#1", Greater);
    test("-100000", 1, Up, "-2.0", "-0x2.0#1", Less);
    test("-100000", 1, Nearest, "-1.0", "-0x1.0#1", Greater);
    test("-100000", 10, Floor, "-1.0020", "-0x1.008#10", Less);
    test("-100000", 10, Ceiling, "-1.0000", "-0x1.000#10", Greater);
    test("-100000", 10, Down, "-1.0000", "-0x1.000#10", Greater);
    test("-100000", 10, Up, "-1.0020", "-0x1.008#10", Less);
    test("-100000", 10, Nearest, "-1.0000", "-0x1.000#10", Greater);
    test(
        "-100000",
        64,
        Floor,
        "-1.00000000000000000011",
        "-0x1.0000000000000002#64",
        Less,
    );
    test(
        "-100000",
        64,
        Ceiling,
        "-1.00000000000000000000",
        "-0x1.0000000000000000#64",
        Greater,
    );
    test(
        "-100000",
        64,
        Down,
        "-1.00000000000000000000",
        "-0x1.0000000000000000#64",
        Greater,
    );
    test(
        "-100000",
        64,
        Up,
        "-1.00000000000000000011",
        "-0x1.0000000000000002#64",
        Less,
    );
    test(
        "-100000",
        64,
        Nearest,
        "-1.00000000000000000000",
        "-0x1.0000000000000000#64",
        Greater,
    );
    test(
        "-100000",
        100,
        Floor,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "-100000",
        100,
        Ceiling,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-100000",
        100,
        Down,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-100000",
        100,
        Up,
        "-1.0000000000000000000000000000016",
        "-0x1.0000000000000000000000002#100",
        Less,
    );
    test(
        "-100000",
        100,
        Nearest,
        "-1.0000000000000000000000000000000",
        "-0x1.0000000000000000000000000#100",
        Greater,
    );
    test("1/1705", 30, Floor, "1705.0001945", "0x6a9.000cc#30", Less);
    test(
        "1/1705",
        30,
        Ceiling,
        "1705.0001965",
        "0x6a9.000ce#30",
        Greater,
    );
    // - the first series bracket straddles a rounding boundary, so the series is refined
    test(
        "1/1705",
        30,
        Nearest,
        "1705.0001965",
        "0x6a9.000ce#30",
        Greater,
    );
    // - the bracket ends round differently, so the working precision grows
    test("50267/100003", 20, Floor, "2.1542320", "0x2.277bc#20", Less);
    test(
        "50267/100003",
        20,
        Ceiling,
        "2.1542358",
        "0x2.277c0#20",
        Greater,
    );
    test(
        "50267/100003",
        20,
        Nearest,
        "2.1542320",
        "0x2.277bc#20",
        Less,
    );
}

#[test]
fn test_coth_rational_extreme() {
    // |x| = 2^(-2^30 - 10) is too small to be a `Float`; coth(x) is just above 2^(2^30 + 10),
    // beyond the largest finite `Float`, so it overflows
    let x = Rational::power_of_2(-(1i64 << 30) - 10);
    let max = Float::max_finite_value_with_prec(10);
    for (rm, out, o_out) in [
        (Floor, max.clone(), Less),
        (Down, max.clone(), Less),
        (Nearest, Float::INFINITY, Greater),
        (Ceiling, Float::INFINITY, Greater),
        (Up, Float::INFINITY, Greater),
    ] {
        let (c, o) = Float::coth_rational_prec_round_ref(&x, 10, rm);
        assert_eq!(ComparableFloatRef(&c), ComparableFloatRef(&out));
        assert_eq!(o, o_out);
        let (c_neg, o_neg) = Float::coth_rational_prec_round(-&x, 10, -rm);
        assert_eq!(ComparableFloat(c_neg), ComparableFloat(-c));
        assert_eq!(o_neg, o.reverse());
    }

    // |x| = 2^(2^30) is too large to be a `Float`, and coth(x) is within 2^(-2^31) of 1, above it
    let x = Rational::power_of_2(1i64 << 30);
    let (c, o) = Float::coth_rational_prec_round_ref(&x, 10, Nearest);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::one_prec(10)));
    assert_eq!(o, Less);
    let (c, o) = Float::coth_rational_prec_round(-x, 10, Up);
    assert_eq!(c.to_string(), "-1.0020");
    assert_eq!(c.get_prec(), Some(10));
    assert_eq!(o, Less);
}

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

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

#[test]
#[should_panic]
fn coth_rational_prec_round_fail_1() {
    Float::coth_rational_prec_round(Rational::ONE, 0, Floor);
}

#[test]
#[should_panic]
fn coth_rational_prec_round_fail_2() {
    Float::coth_rational_prec_round(Rational::ONE, 10, Exact);
}

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

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

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

    if x != 0u32 {
        // coth x has the sign of x, and coth is odd (a `Rational` has no negative zero, so x = 0 is
        // excluded)
        assert_eq!(c.is_sign_positive(), x > 0u32);
        assert!(c >= 1u32 || c <= -1i32);
        let (c_neg, o_neg) = Float::coth_rational_prec_round(-&x, prec, -rm);
        assert_eq!(ComparableFloatRef(&c_neg), ComparableFloatRef(&-&c));
        assert_eq!(o_neg, o.reverse());
    }

    if let Ok(rrm) = rug_round_try_from_rounding_mode(rm) {
        let (rug_c, rug_o) = rug_coth_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::coth_rational_prec_round_ref(&x, prec, rm);
            assert_eq!(ComparableFloatRef(&s), ComparableFloatRef(&c));
            assert_eq!(oo, Equal);
        }
    } else {
        assert_panic!(Float::coth_rational_prec_round_ref(&x, prec, Exact));
    }
}

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

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

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

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

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

    // the hyperbolic cotangent of an exactly representable nonzero rational is the Float hyperbolic
    // cotangent
    if x != 0u32
        && let Ok(f) = Float::try_from(&x)
    {
        let (c_alt, o_alt) = f.coth_prec(prec);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);
    }
}

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

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_coth_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_coth_rational::<T>(&x)),
            NiceFloat(out)
        );
    }
    test::<f32>("0", f32::INFINITY);
    test::<f32>("1", 1.3130352);
    test::<f32>("-1", -1.3130352);
    test::<f32>("1/3", 3.1102967);
    test::<f32>("22/7", 1.0037324);
    test::<f32>("20", 1.0);
    test::<f32>("-20", -1.0);
    test::<f32>("100", 1.0);
    test::<f32>("10000", 1.0);
    test::<f32>("1/100000000000000000000", 1.0e20);
    test::<f32>("1/10000000000000000000000000000000000000000", f32::INFINITY);

    test::<f64>("0", f64::INFINITY);
    test::<f64>("1", 1.3130352854993312);
    test::<f64>("-1", -1.3130352854993312);
    test::<f64>("1/3", 3.110296679619444);
    test::<f64>("22/7", 1.0037324043984772);
    test::<f64>("20", 1.0);
    test::<f64>("-20", -1.0);
    test::<f64>("100", 1.0);
    test::<f64>("10000", 1.0);
    test::<f64>("1/100000000000000000000", 1.0e20);
    test::<f64>("1/10000000000000000000000000000000000000000", 1.0e40);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_coth_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_coth_rational::<T>(&x);
        // the hyperbolic cotangent of a rational is never NaN
        assert!(!c.is_nan());
        if x != 0u32 {
            // coth x has the sign of x, and coth is odd
            assert_eq!(c.is_sign_positive(), x > 0u32);
            assert!(c >= T::ONE || c <= T::NEGATIVE_ONE);
            assert_eq!(
                NiceFloat(primitive_float_coth_rational::<T>(&-&x)),
                NiceFloat(-c)
            );
        }
        // the result is the correctly rounded hyperbolic cotangent, as computed by MPFR with bits
        // to spare, so that a subnormal result is rounded once by the conversion rather than twice.
        // For a tiny x, coth x = 1/x + x/3 + ... lies within about x^2 (relatively) of 1/x, which
        // may be exactly halfway between two `T`s, so the spare bits must also resolve that gap.
        let spare = if x == 0u32 {
            64
        } else {
            64 + (x.floor_log_base_2_abs().unsigned_abs() << 1)
        };
        let rug_c = rug_coth_rational_prec(&x, T::MANTISSA_WIDTH + spare).0;
        let rug_c: T = T::rounding_from(&<Float as From<&rug::Float>>::from(&rug_c), Nearest).0;
        assert_eq!(NiceFloat(rug_c), NiceFloat(c));
    });

    primitive_float_gen::<T>().test_properties(|x| {
        // The hyperbolic cotangent of a finite nonzero primitive float, taken through the
        // `Rational` path, matches the direct primitive-float hyperbolic cotangent. (Zero is
        // excluded, since a `Rational` has no negative zero.)
        if x.is_finite() && x != T::ZERO {
            assert_eq!(
                NiceFloat(primitive_float_coth_rational::<T>(&Rational::exact_from(x))),
                NiceFloat(primitive_float_coth(x))
            );
        }
    });
}

#[test]
fn primitive_float_coth_rational_properties() {
    apply_fn_to_primitive_floats!(primitive_float_coth_rational_properties_helper);
}