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::{PowerOf2, Sech, SechAssign};
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::sech::{
    primitive_float_sech, primitive_float_sech_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::sech::{
    rug_sech, rug_sech_prec, rug_sech_prec_round, rug_sech_rational_prec,
    rug_sech_rational_prec_round, rug_sech_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_sech_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().sech_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.sech_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.sech_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_sech_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, "0.0", "0x0.0", Equal);
    test("-Infinity", "-Infinity", 1, Nearest, "0.0", "0x0.0", Equal);
    test("0.0", "0x0.0", 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("-0.0", "-0x0.0", 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("0.0", "0x0.0", 10, Nearest, "1.0000", "0x1.000#10", Equal);
    // - the first Ziv iteration of 1 / cosh(x) cannot round, so the loop retries
    test("1.0", "0x1.0#1", 1, Floor, "0.50", "0x0.8#1", Less);
    test("1.0", "0x1.0#1", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("1.0", "0x1.0#1", 1, Nearest, "0.50", "0x0.8#1", Less);
    test("1.0", "0x1.0#1", 10, Floor, "0.64746", "0x0.a5c#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        10,
        Ceiling,
        "0.64844",
        "0x0.a60#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        10,
        Nearest,
        "0.64844",
        "0x0.a60#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Floor,
        "0.64805427366388539957497735322564",
        "0x0.a5e6e2876b5f3b99e515f5ceb#100",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Ceiling,
        "0.64805427366388539957497735322643",
        "0x0.a5e6e2876b5f3b99e515f5cec#100",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Nearest,
        "0.64805427366388539957497735322643",
        "0x0.a5e6e2876b5f3b99e515f5cec#100",
        Greater,
    );
    test("-1.0", "-0x1.0#1", 10, Floor, "0.64746", "0x0.a5c#10", Less);
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Ceiling,
        "0.64844",
        "0x0.a60#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Nearest,
        "0.64844",
        "0x0.a60#10",
        Greater,
    );
    test("-1.0", "-0x1.0#1", 10, Down, "0.64746", "0x0.a5c#10", Less);
    test("-1.0", "-0x1.0#1", 10, Up, "0.64844", "0x0.a60#10", Greater);
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Floor,
        "0.64805427366388539957497735322564",
        "0x0.a5e6e2876b5f3b99e515f5ceb#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Ceiling,
        "0.64805427366388539957497735322643",
        "0x0.a5e6e2876b5f3b99e515f5cec#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Nearest,
        "0.64805427366388539957497735322643",
        "0x0.a5e6e2876b5f3b99e515f5cec#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Down,
        "0.64805427366388539957497735322564",
        "0x0.a5e6e2876b5f3b99e515f5ceb#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Up,
        "0.64805427366388539957497735322643",
        "0x0.a5e6e2876b5f3b99e515f5cec#100",
        Greater,
    );
    test("0.50", "0x0.8#1", 10, Floor, "0.88672", "0x0.e30#10", Less);
    test(
        "0.50",
        "0x0.8#1",
        10,
        Ceiling,
        "0.88770",
        "0x0.e34#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        10,
        Nearest,
        "0.88672",
        "0x0.e30#10",
        Less,
    );
    test("0.50", "0x0.8#1", 10, Down, "0.88672", "0x0.e30#10", Less);
    test("0.50", "0x0.8#1", 10, Up, "0.88770", "0x0.e34#10", Greater);
    test(
        "0.50",
        "0x0.8#1",
        100,
        Floor,
        "0.88681888397007390865889779778288",
        "0x0.e3068ff8206e7fbc254fca8dd#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Ceiling,
        "0.88681888397007390865889779778367",
        "0x0.e3068ff8206e7fbc254fca8de#100",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Nearest,
        "0.88681888397007390865889779778367",
        "0x0.e3068ff8206e7fbc254fca8de#100",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Down,
        "0.88681888397007390865889779778288",
        "0x0.e3068ff8206e7fbc254fca8dd#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Up,
        "0.88681888397007390865889779778367",
        "0x0.e3068ff8206e7fbc254fca8de#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Floor,
        "0.94629",
        "0x0.f24#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Ceiling,
        "0.94727",
        "0x0.f28#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Nearest,
        "0.94727",
        "0x0.f28#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Down,
        "0.94629",
        "0x0.f24#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Up,
        "0.94727",
        "0x0.f28#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Floor,
        "0.94690525376349792655895228013934",
        "0x0.f26861f95326637981841f9c9#100",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Ceiling,
        "0.94690525376349792655895228014013",
        "0x0.f26861f95326637981841f9ca#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Nearest,
        "0.94690525376349792655895228014013",
        "0x0.f26861f95326637981841f9ca#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Down,
        "0.94690525376349792655895228013934",
        "0x0.f26861f95326637981841f9c9#100",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Up,
        "0.94690525376349792655895228014013",
        "0x0.f26861f95326637981841f9ca#100",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Floor, "0.26562", "0x0.440#10", Less);
    test(
        "2.0",
        "0x2.0#2",
        10,
        Ceiling,
        "0.26611",
        "0x0.442#10",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Nearest, "0.26562", "0x0.440#10", Less);
    test("2.0", "0x2.0#2", 10, Down, "0.26562", "0x0.440#10", Less);
    test("2.0", "0x2.0#2", 10, Up, "0.26611", "0x0.442#10", Greater);
    test(
        "2.0",
        "0x2.0#2",
        100,
        Floor,
        "0.26580222883407969212086273981965",
        "0x0.440b9d680bd909be0bba5faa30#100",
        Less,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Ceiling,
        "0.26580222883407969212086273982004",
        "0x0.440b9d680bd909be0bba5faa38#100",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Nearest,
        "0.26580222883407969212086273982004",
        "0x0.440b9d680bd909be0bba5faa38#100",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Down,
        "0.26580222883407969212086273981965",
        "0x0.440b9d680bd909be0bba5faa30#100",
        Less,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Up,
        "0.26580222883407969212086273982004",
        "0x0.440b9d680bd909be0bba5faa38#100",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Floor,
        "0.000090718",
        "0x0.0005f2#10",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Ceiling,
        "0.000090837",
        "0x0.0005f4#10",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Nearest,
        "0.000090837",
        "0x0.0005f4#10",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Down,
        "0.000090718",
        "0x0.0005f2#10",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Up,
        "0.000090837",
        "0x0.0005f4#10",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Floor,
        "0.000090799859337817244080129507820451",
        "0x0.0005f35e6d24716523902208e1c68#100",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Ceiling,
        "0.000090799859337817244080129507820547",
        "0x0.0005f35e6d24716523902208e1c70#100",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Nearest,
        "0.000090799859337817244080129507820451",
        "0x0.0005f35e6d24716523902208e1c68#100",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Down,
        "0.000090799859337817244080129507820451",
        "0x0.0005f35e6d24716523902208e1c68#100",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Up,
        "0.000090799859337817244080129507820547",
        "0x0.0005f35e6d24716523902208e1c70#100",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Floor,
        "0.086182",
        "0x0.1610#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Ceiling,
        "0.086304",
        "0x0.1618#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Nearest,
        "0.086304",
        "0x0.1618#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Down,
        "0.086182",
        "0x0.1610#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Up,
        "0.086304",
        "0x0.1618#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Floor,
        "0.086266738334054414692242558742055",
        "0x0.161593b3e09a38b7e026782e56#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Ceiling,
        "0.086266738334054414692242558742154",
        "0x0.161593b3e09a38b7e026782e58#100",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Nearest,
        "0.086266738334054414692242558742055",
        "0x0.161593b3e09a38b7e026782e56#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Down,
        "0.086266738334054414692242558742055",
        "0x0.161593b3e09a38b7e026782e56#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Up,
        "0.086266738334054414692242558742154",
        "0x0.161593b3e09a38b7e026782e58#100",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Floor,
        "1.0144e-434",
        "0x4.f0E-361#10",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Ceiling,
        "1.0160e-434",
        "0x4.f2E-361#10",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Nearest,
        "1.0160e-434",
        "0x4.f2E-361#10",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Down,
        "1.0144e-434",
        "0x4.f0E-361#10",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Up,
        "1.0160e-434",
        "0x4.f2E-361#10",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Floor,
        "1.0151917795098913530583618959146e-434",
        "0x4.f1086790625503cc93d1b9e50E-361#100",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Ceiling,
        "1.0151917795098913530583618959159e-434",
        "0x4.f1086790625503cc93d1b9e58E-361#100",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Nearest,
        "1.0151917795098913530583618959146e-434",
        "0x4.f1086790625503cc93d1b9e50E-361#100",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Down,
        "1.0151917795098913530583618959146e-434",
        "0x4.f1086790625503cc93d1b9e50E-361#100",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Up,
        "1.0151917795098913530583618959159e-434",
        "0x4.f1086790625503cc93d1b9e58E-361#100",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Floor,
        "6.5911e-434295",
        "0x3.e3E-360674#10",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Ceiling,
        "6.5977e-434295",
        "0x3.e4E-360674#10",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Nearest,
        "6.5911e-434295",
        "0x3.e3E-360674#10",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Down,
        "6.5911e-434295",
        "0x3.e3E-360674#10",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Up,
        "6.5977e-434295",
        "0x3.e4E-360674#10",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Floor,
        "6.5936629561771171579378159382151e-434295",
        "0x3.e362986bdaa297eea886313f4E-360674#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Ceiling,
        "6.5936629561771171579378159382204e-434295",
        "0x3.e362986bdaa297eea886313f8E-360674#100",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Nearest,
        "6.5936629561771171579378159382151e-434295",
        "0x3.e362986bdaa297eea886313f4E-360674#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Down,
        "6.5936629561771171579378159382151e-434295",
        "0x3.e362986bdaa297eea886313f4E-360674#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Up,
        "6.5936629561771171579378159382204e-434295",
        "0x3.e362986bdaa297eea886313f8E-360674#100",
        Greater,
    );
    // - x >= 2^29: the scaled path
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Floor,
        "5.3094e-233160075",
        "0x6.52E-193635251#10",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Ceiling,
        "5.3159e-233160075",
        "0x6.54E-193635251#10",
        Greater,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Nearest,
        "5.3094e-233160075",
        "0x6.52E-193635251#10",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Down,
        "5.3094e-233160075",
        "0x6.52E-193635251#10",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        10,
        Up,
        "5.3159e-233160075",
        "0x6.54E-193635251#10",
        Greater,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Floor,
        "5.3096230646839805874289616336017e-233160075",
        "0x6.5213d1f51096f677b1bdae508E-193635251#100",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Ceiling,
        "5.3096230646839805874289616336070e-233160075",
        "0x6.5213d1f51096f677b1bdae510E-193635251#100",
        Greater,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Nearest,
        "5.3096230646839805874289616336070e-233160075",
        "0x6.5213d1f51096f677b1bdae510E-193635251#100",
        Greater,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Down,
        "5.3096230646839805874289616336017e-233160075",
        "0x6.5213d1f51096f677b1bdae508E-193635251#100",
        Less,
    );
    test(
        "5.4e8",
        "0x2.0E+7#1",
        100,
        Up,
        "5.3096230646839805874289616336070e-233160075",
        "0x6.5213d1f51096f677b1bdae510E-193635251#100",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Floor,
        "9.3025e-304006138",
        "0x1.4c8E-252471632#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Ceiling,
        "9.3165e-304006138",
        "0x1.4d0E-252471632#10",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Nearest,
        "9.3025e-304006138",
        "0x1.4c8E-252471632#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Down,
        "9.3025e-304006138",
        "0x1.4c8E-252471632#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Up,
        "9.3165e-304006138",
        "0x1.4d0E-252471632#10",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Floor,
        "9.3058000397652234489131203297804e-304006138",
        "0x1.4c9e6550bdb38bcdec64deb32E-252471632#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Ceiling,
        "9.3058000397652234489131203297917e-304006138",
        "0x1.4c9e6550bdb38bcdec64deb34E-252471632#100",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Nearest,
        "9.3058000397652234489131203297917e-304006138",
        "0x1.4c9e6550bdb38bcdec64deb34E-252471632#100",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Down,
        "9.3058000397652234489131203297804e-304006138",
        "0x1.4c9e6550bdb38bcdec64deb32E-252471632#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Up,
        "9.3058000397652234489131203297917e-304006138",
        "0x1.4c9e6550bdb38bcdec64deb34E-252471632#100",
        Greater,
    );
    // - cosh(x) overflows, but sech(x) is representable: the scaled path
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Floor,
        "7.5014e-323228497",
        "0x3.26E-268435456#10",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Ceiling,
        "7.5107e-323228497",
        "0x3.27E-268435456#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Nearest,
        "7.5107e-323228497",
        "0x3.27E-268435456#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Down,
        "7.5014e-323228497",
        "0x3.26E-268435456#10",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Up,
        "7.5107e-323228497",
        "0x3.27E-268435456#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Floor,
        "7.5098673083218467310380527281516e-323228497",
        "0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Ceiling,
        "7.5098673083218467310380527281592e-323228497",
        "0x3.26ea18e02da8f8a2632086efcE-268435456#100",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Nearest,
        "7.5098673083218467310380527281516e-323228497",
        "0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Down,
        "7.5098673083218467310380527281516e-323228497",
        "0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Up,
        "7.5098673083218467310380527281592e-323228497",
        "0x3.26ea18e02da8f8a2632086efcE-268435456#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Floor,
        "7.5014e-323228497",
        "0x3.26E-268435456#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Ceiling,
        "7.5107e-323228497",
        "0x3.27E-268435456#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Nearest,
        "7.5107e-323228497",
        "0x3.27E-268435456#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Down,
        "7.5014e-323228497",
        "0x3.26E-268435456#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Up,
        "7.5107e-323228497",
        "0x3.27E-268435456#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Floor,
        "7.5098673083218467310380527281516e-323228497",
        "0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Ceiling,
        "7.5098673083218467310380527281592e-323228497",
        "0x3.26ea18e02da8f8a2632086efcE-268435456#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Nearest,
        "7.5098673083218467310380527281516e-323228497",
        "0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Down,
        "7.5098673083218467310380527281516e-323228497",
        "0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Up,
        "7.5098673083218467310380527281592e-323228497",
        "0x3.26ea18e02da8f8a2632086efcE-268435456#100",
        Greater,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Floor,
        "2.7595e-323228497",
        "0x1.288E-268435456#10",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Ceiling,
        "2.7641e-323228497",
        "0x1.290E-268435456#10",
        Greater,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Nearest,
        "2.7641e-323228497",
        "0x1.290E-268435456#10",
        Greater,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Down,
        "2.7595e-323228497",
        "0x1.288E-268435456#10",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        10,
        Up,
        "2.7641e-323228497",
        "0x1.290E-268435456#10",
        Greater,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Floor,
        "2.7627257886571247097149806987996e-323228497",
        "0x1.28d8e45434c7216121ffbfc56E-268435456#100",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Ceiling,
        "2.7627257886571247097149806988033e-323228497",
        "0x1.28d8e45434c7216121ffbfc58E-268435456#100",
        Greater,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Nearest,
        "2.7627257886571247097149806988033e-323228497",
        "0x1.28d8e45434c7216121ffbfc58E-268435456#100",
        Greater,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Down,
        "2.7627257886571247097149806987996e-323228497",
        "0x1.28d8e45434c7216121ffbfc56E-268435456#100",
        Less,
    );
    test(
        "744261118.50",
        "0x2c5c85fe.8#31",
        100,
        Up,
        "2.7627257886571247097149806988033e-323228497",
        "0x1.28d8e45434c7216121ffbfc58E-268435456#100",
        Greater,
    );
    // - sech(x) rounds with the underflow rules in the scaled path
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Nearest,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        10,
        Up,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Nearest,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.00000",
        "0x2c5c85ff.000#40",
        100,
        Up,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Nearest,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        10,
        Up,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Nearest,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.29980",
        "0x2c5c85ff.4cc#40",
        100,
        Up,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Nearest,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Up,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Nearest,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Up,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Nearest,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        10,
        Up,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Nearest,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261119.90039",
        "0x2c5c85ff.e68#40",
        100,
        Up,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    // - |x| >= 744261120: sech(x) is below half the smallest positive Float
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Nearest,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        10,
        Up,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Nearest,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "744261120.00",
        "0x2c5c8600.0#30",
        100,
        Up,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Nearest,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Up,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Nearest,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Up,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Down,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Down,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Up,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Up,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Floor,
        "0.99999952316303127486438457454987",
        "0x0.fffff80000355553fa4fadc57#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Floor,
        "0.99999952316303127486438457454987",
        "0x0.fffff80000355553fa4fadc57#100",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Ceiling,
        "0.99999952316303127486438457455066",
        "0x0.fffff80000355553fa4fadc58#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Ceiling,
        "0.99999952316303127486438457455066",
        "0x0.fffff80000355553fa4fadc58#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Nearest,
        "0.99999952316303127486438457455066",
        "0x0.fffff80000355553fa4fadc58#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Nearest,
        "0.99999952316303127486438457455066",
        "0x0.fffff80000355553fa4fadc58#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Down,
        "0.99999952316303127486438457454987",
        "0x0.fffff80000355553fa4fadc57#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Down,
        "0.99999952316303127486438457454987",
        "0x0.fffff80000355553fa4fadc57#100",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Up,
        "0.99999952316303127486438457455066",
        "0x0.fffff80000355553fa4fadc58#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Up,
        "0.99999952316303127486438457455066",
        "0x0.fffff80000355553fa4fadc58#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Floor,
        "0.99999999999999999999999999999921",
        "0x0.fffffffffffffffffffffffff#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Floor,
        "0.99999999999999999999999999999921",
        "0x0.fffffffffffffffffffffffff#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Ceiling,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Ceiling,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Down,
        "0.99999999999999999999999999999921",
        "0x0.fffffffffffffffffffffffff#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Down,
        "0.99999999999999999999999999999921",
        "0x0.fffffffffffffffffffffffff#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Up,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Up,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    // - small_input_shortcut returns
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Down,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Down,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Up,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Up,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Floor,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31099",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000000#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Floor,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31099",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000000#300",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Ceiling,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31148",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000001#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Ceiling,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31148",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000001#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Nearest,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31099",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000000#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Nearest,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31099",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000000#300",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Down,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31099",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000000#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Down,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31099",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000000#300",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Up,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31148",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000001#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Up,
        "0.999999999999999999999999999999999999999999999999999999999999688849236106942914642796797\
        31148",
        "0x0.ffffffffffffffffffffffffffffffffffffffffffffffffff8000000000000000000000001#300",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Floor,
        "0.999999999999999999946",
        "0x0.ffffffffffffffff#64",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Ceiling,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Nearest,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Down,
        "0.999999999999999999946",
        "0x0.ffffffffffffffff#64",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Up,
        "1.00000000000000000000",
        "0x1.0000000000000000#64",
        Greater,
    );
    // - for a large x, the first scaled bracket cannot round, so the working precision grows
    test(
        "623740651.00",
        "0x252d86eb.0#30",
        1,
        Floor,
        "2.7e-270887123",
        "0x2.0E-224966886#1",
        Less,
    );
    test(
        "623740651.00",
        "0x252d86eb.0#30",
        1,
        Ceiling,
        "5.4e-270887123",
        "0x4.0E-224966886#1",
        Greater,
    );
    test(
        "623740651.00",
        "0x252d86eb.0#30",
        1,
        Nearest,
        "2.7e-270887123",
        "0x2.0E-224966886#1",
        Less,
    );
}

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

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

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

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

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

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

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

    // 0 <= sech x <= 1
    if !x.is_nan() {
        assert!((0u32..=1u32).contains(&c));
        assert!(c.is_sign_positive());
    }
    if c.is_normal() {
        assert_eq!(c.get_prec(), Some(prec));
    }

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

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

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

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

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

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

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

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

#[test]
fn sech_prec_properties() {
    float_unsigned_pair_gen_var_1().test_properties(|(x, prec)| {
        let (c, o) = x.clone().sech_prec(prec);
        assert!(c.is_valid());
        let (c_alt, o_alt) = x.sech_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.sech_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.sech_prec_round_ref(prec, Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

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

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

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

        let c_alt = x.sech_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_sech(
                &rug::Float::exact_from(&x)
            ))),
            ComparableFloatRef(&c)
        );

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

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_sech() {
    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_sech(x)), NiceFloat(out));
    }
    test::<f32>(f32::NAN, f32::NAN);
    test::<f32>(f32::INFINITY, 0.0);
    test::<f32>(f32::NEGATIVE_INFINITY, 0.0);
    test::<f32>(0.0, 1.0);
    test::<f32>(-0.0, 1.0);
    test::<f32>(1.0, 0.6480543);
    test::<f32>(-1.0, 0.6480543);
    test::<f32>(0.5, 0.8868189);
    test::<f32>(2.0, 0.26580223);
    test::<f32>(10.0, 0.00009079986);
    test::<f32>(88.0, 1.2109204e-38);
    test::<f32>(89.0, 4.454728e-39);
    test::<f32>(95.0, 1.1042e-41);
    test::<f32>(100.0, 7.4e-44);
    test::<f32>(104.0, 1.0e-45);
    test::<f32>(1.0e-20, 1.0);
    test::<f32>(1.0e-45, 1.0);
    test::<f32>(3.4028235e38, 0.0);

    test::<f64>(f64::NAN, f64::NAN);
    test::<f64>(f64::INFINITY, 0.0);
    test::<f64>(f64::NEGATIVE_INFINITY, 0.0);
    test::<f64>(0.0, 1.0);
    test::<f64>(-0.0, 1.0);
    test::<f64>(1.0, 0.6480542736638853);
    test::<f64>(-1.0, 0.6480542736638853);
    test::<f64>(0.5, 0.8868188839700739);
    test::<f64>(2.0, 0.26580222883407967);
    test::<f64>(10.0, 0.00009079985933781725);
    test::<f64>(700.0, 1.971935308751954e-304);
    test::<f64>(710.0, 8.95257245135026e-309);
    test::<f64>(720.0, 4.06446160484e-313);
    test::<f64>(744.0, 1.5e-323);
    test::<f64>(745.0, 5.0e-324);
    test::<f64>(746.0, 0.0);
    test::<f64>(1.0e-200, 1.0);
    test::<f64>(5.0e-324, 1.0);
    test::<f64>(1.7976931348623157e308, 0.0);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_sech_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_sech(x);
        // sech is NaN exactly for NaN inputs, and otherwise lies in [0, 1]
        assert_eq!(c.is_nan(), x.is_nan());
        if !x.is_nan() {
            assert!(c >= T::ZERO && c <= T::ONE);
            assert!(c.is_sign_positive());
            // sech is even
            assert_eq!(NiceFloat(primitive_float_sech(-x)), NiceFloat(c));
        }
        if x.is_finite() {
            // the result is the correctly rounded hyperbolic secant 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_sech_prec(&rug::Float::exact_from(&Float::from(x)), p).0,
                )
            });
            assert_eq!(NiceFloat(rug_c), NiceFloat(c));
        }
    });
}

#[test]
fn primitive_float_sech_properties() {
    apply_fn_to_primitive_floats!(primitive_float_sech_properties_helper);
}

#[test]
fn test_sech_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::sech_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::sech_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_sech_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, "1.0", "0x1.0#1", Equal);
    test("0", 10, Down, "1.0000", "0x1.000#10", Equal);
    test("0", 1, Up, "1.0", "0x1.0#1", Equal);
    test("0", 10, Up, "1.0000", "0x1.000#10", Equal);
    test("0", 1, Floor, "1.0", "0x1.0#1", Equal);
    test("0", 10, Floor, "1.0000", "0x1.000#10", Equal);
    test("0", 1, Ceiling, "1.0", "0x1.0#1", Equal);
    test("0", 10, Ceiling, "1.0000", "0x1.000#10", Equal);
    test("0", 1, Nearest, "1.0", "0x1.0#1", Equal);
    test("0", 10, Nearest, "1.0000", "0x1.000#10", Equal);
    test("0", 1, Exact, "1.0", "0x1.0#1", Equal);
    test("0", 10, Exact, "1.0000", "0x1.000#10", Equal);
    // - the first bracket of |x| rounds the same way at both ends
    test("3/5", 1, Floor, "0.50", "0x0.8#1", Less);
    test("3/5", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("3/5", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("3/5", 10, Floor, "0.84277", "0x0.d7c#10", Less);
    test("3/5", 10, Ceiling, "0.84375", "0x0.d80#10", Greater);
    test("3/5", 10, Nearest, "0.84375", "0x0.d80#10", Greater);
    test(
        "3/5",
        100,
        Floor,
        "0.84355068762180664157749873109046",
        "0x0.d7f2f017da9de104a6d765766#100",
        Less,
    );
    test(
        "3/5",
        100,
        Ceiling,
        "0.84355068762180664157749873109125",
        "0x0.d7f2f017da9de104a6d765767#100",
        Greater,
    );
    test(
        "3/5",
        100,
        Nearest,
        "0.84355068762180664157749873109125",
        "0x0.d7f2f017da9de104a6d765767#100",
        Greater,
    );
    test("-3/5", 1, Floor, "0.50", "0x0.8#1", Less);
    test("-3/5", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("-3/5", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("-3/5", 10, Floor, "0.84277", "0x0.d7c#10", Less);
    test("-3/5", 10, Ceiling, "0.84375", "0x0.d80#10", Greater);
    test("-3/5", 10, Nearest, "0.84375", "0x0.d80#10", Greater);
    test(
        "-3/5",
        100,
        Floor,
        "0.84355068762180664157749873109046",
        "0x0.d7f2f017da9de104a6d765766#100",
        Less,
    );
    test(
        "-3/5",
        100,
        Ceiling,
        "0.84355068762180664157749873109125",
        "0x0.d7f2f017da9de104a6d765767#100",
        Greater,
    );
    test(
        "-3/5",
        100,
        Nearest,
        "0.84355068762180664157749873109125",
        "0x0.d7f2f017da9de104a6d765767#100",
        Greater,
    );
    test("1/3", 1, Floor, "0.50", "0x0.8#1", Less);
    test("1/3", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("1/3", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("1/3", 10, Floor, "0.94629", "0x0.f24#10", Less);
    test("1/3", 10, Ceiling, "0.94727", "0x0.f28#10", Greater);
    test("1/3", 10, Nearest, "0.94727", "0x0.f28#10", Greater);
    test(
        "1/3",
        100,
        Floor,
        "0.94690525376349792655895228013934",
        "0x0.f26861f95326637981841f9c9#100",
        Less,
    );
    test(
        "1/3",
        100,
        Ceiling,
        "0.94690525376349792655895228014013",
        "0x0.f26861f95326637981841f9ca#100",
        Greater,
    );
    test(
        "1/3",
        100,
        Nearest,
        "0.94690525376349792655895228014013",
        "0x0.f26861f95326637981841f9ca#100",
        Greater,
    );
    test("22/7", 1, Floor, "0.062", "0x0.1#1", Less);
    test("22/7", 1, Ceiling, "0.12", "0x0.2#1", Greater);
    test("22/7", 1, Nearest, "0.062", "0x0.1#1", Less);
    test("22/7", 10, Floor, "0.086060", "0x0.1608#10", Less);
    test("22/7", 10, Ceiling, "0.086182", "0x0.1610#10", Greater);
    test("22/7", 10, Nearest, "0.086182", "0x0.1610#10", Greater);
    test(
        "22/7",
        100,
        Floor,
        "0.086158129536979492276196616870947",
        "0x0.160e758ca556fc438352ae2a42#100",
        Less,
    );
    test(
        "22/7",
        100,
        Ceiling,
        "0.086158129536979492276196616871046",
        "0x0.160e758ca556fc438352ae2a44#100",
        Greater,
    );
    test(
        "22/7",
        100,
        Nearest,
        "0.086158129536979492276196616870947",
        "0x0.160e758ca556fc438352ae2a42#100",
        Less,
    );
    // - |x| is exactly representable at the working precision
    test("100", 1, Floor, "4.5e-44", "0x1.0E-36#1", Less);
    test("100", 1, Ceiling, "9.0e-44", "0x2.0E-36#1", Greater);
    test("100", 1, Nearest, "9.0e-44", "0x2.0E-36#1", Greater);
    test("100", 10, Floor, "7.4356e-44", "0x1.a88E-36#10", Less);
    test("100", 10, Ceiling, "7.4444e-44", "0x1.a90E-36#10", Greater);
    test("100", 10, Nearest, "7.4444e-44", "0x1.a90E-36#10", Greater);
    test(
        "100",
        100,
        Floor,
        "7.4401519520416719259193916077216e-44",
        "0x1.a8c1f14e2af5caf3dd91375c6E-36#100",
        Less,
    );
    test(
        "100",
        100,
        Ceiling,
        "7.4401519520416719259193916077287e-44",
        "0x1.a8c1f14e2af5caf3dd91375c8E-36#100",
        Greater,
    );
    test(
        "100",
        100,
        Nearest,
        "7.4401519520416719259193916077287e-44",
        "0x1.a8c1f14e2af5caf3dd91375c8E-36#100",
        Greater,
    );
    test("-100", 1, Floor, "4.5e-44", "0x1.0E-36#1", Less);
    test("-100", 1, Ceiling, "9.0e-44", "0x2.0E-36#1", Greater);
    test("-100", 1, Nearest, "9.0e-44", "0x2.0E-36#1", Greater);
    test("-100", 10, Floor, "7.4356e-44", "0x1.a88E-36#10", Less);
    test("-100", 10, Ceiling, "7.4444e-44", "0x1.a90E-36#10", Greater);
    test("-100", 10, Nearest, "7.4444e-44", "0x1.a90E-36#10", Greater);
    test(
        "-100",
        100,
        Floor,
        "7.4401519520416719259193916077216e-44",
        "0x1.a8c1f14e2af5caf3dd91375c6E-36#100",
        Less,
    );
    test(
        "-100",
        100,
        Ceiling,
        "7.4401519520416719259193916077287e-44",
        "0x1.a8c1f14e2af5caf3dd91375c8E-36#100",
        Greater,
    );
    test(
        "-100",
        100,
        Nearest,
        "7.4401519520416719259193916077287e-44",
        "0x1.a8c1f14e2af5caf3dd91375c8E-36#100",
        Greater,
    );
    test("1/1000", 1, Floor, "0.50", "0x0.8#1", Less);
    test("1/1000", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("1/1000", 1, Nearest, "1.0", "0x1.0#1", Greater);
    // - tiny x: sech(x) rounds to 1 or its predecessor
    test("1/1000", 10, Floor, "0.99902", "0x0.ffc#10", Less);
    test("1/1000", 10, Ceiling, "1.0000", "0x1.000#10", Greater);
    test("1/1000", 10, Nearest, "1.0000", "0x1.000#10", Greater);
    // - small x: bracketed by series bounds on cosh(x)
    test(
        "1/1000",
        100,
        Floor,
        "0.99999950000020833324861114546071",
        "0x0.fffff79c846a490757e6daafb#100",
        Less,
    );
    test(
        "1/1000",
        100,
        Ceiling,
        "0.99999950000020833324861114546150",
        "0x0.fffff79c846a490757e6daafc#100",
        Greater,
    );
    test(
        "1/1000",
        100,
        Nearest,
        "0.99999950000020833324861114546150",
        "0x0.fffff79c846a490757e6daafc#100",
        Greater,
    );
    test("-1/1000000", 1, Floor, "0.50", "0x0.8#1", Less);
    test("-1/1000000", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("-1/1000000", 1, Nearest, "1.0", "0x1.0#1", Greater);
    test("-1/1000000", 10, Floor, "0.99902", "0x0.ffc#10", Less);
    test("-1/1000000", 10, Ceiling, "1.0000", "0x1.000#10", Greater);
    test("-1/1000000", 10, Nearest, "1.0000", "0x1.000#10", Greater);
    test(
        "-1/1000000",
        100,
        Floor,
        "0.99999999999950000000000020833323",
        "0x0.ffffffffff734333f690eff11#100",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Ceiling,
        "0.99999999999950000000000020833402",
        "0x0.ffffffffff734333f690eff12#100",
        Greater,
    );
    test(
        "-1/1000000",
        100,
        Nearest,
        "0.99999999999950000000000020833323",
        "0x0.ffffffffff734333f690eff11#100",
        Less,
    );
    test("1/100000000000000000000", 1, Floor, "0.50", "0x0.8#1", Less);
    test(
        "1/100000000000000000000",
        1,
        Ceiling,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1/100000000000000000000",
        1,
        Nearest,
        "1.0",
        "0x1.0#1",
        Greater,
    );
    test(
        "1/100000000000000000000",
        10,
        Floor,
        "0.99902",
        "0x0.ffc#10",
        Less,
    );
    test(
        "1/100000000000000000000",
        10,
        Ceiling,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        10,
        Nearest,
        "1.0000",
        "0x1.000#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Floor,
        "0.99999999999999999999999999999921",
        "0x0.fffffffffffffffffffffffff#100",
        Less,
    );
    test(
        "1/100000000000000000000",
        100,
        Ceiling,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Nearest,
        "1.0000000000000000000000000000000",
        "0x1.0000000000000000000000000#100",
        Greater,
    );
    // - the bracket ends round differently, so the working precision grows
    test(
        "1488522235/2",
        1,
        Floor,
        "4.8e-323228497",
        "0x2.0E-268435456#1",
        Less,
    );
    test(
        "1488522235/2",
        1,
        Ceiling,
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        Greater,
    );
    test(
        "1488522235/2",
        1,
        Nearest,
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        Greater,
    );
    test(
        "1488522235/2",
        10,
        Floor,
        "7.5014e-323228497",
        "0x3.26E-268435456#10",
        Less,
    );
    test(
        "1488522235/2",
        10,
        Ceiling,
        "7.5107e-323228497",
        "0x3.27E-268435456#10",
        Greater,
    );
    test(
        "1488522235/2",
        10,
        Nearest,
        "7.5107e-323228497",
        "0x3.27E-268435456#10",
        Greater,
    );
    test(
        "1488522235/2",
        100,
        Floor,
        "7.5098673083218467310380527281516e-323228497",
        "0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Less,
    );
    test(
        "1488522235/2",
        100,
        Ceiling,
        "7.5098673083218467310380527281592e-323228497",
        "0x3.26ea18e02da8f8a2632086efcE-268435456#100",
        Greater,
    );
    test(
        "1488522235/2",
        100,
        Nearest,
        "7.5098673083218467310380527281516e-323228497",
        "0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Less,
    );
    test(
        "7442611177/10",
        1,
        Floor,
        "4.8e-323228497",
        "0x2.0E-268435456#1",
        Less,
    );
    test(
        "7442611177/10",
        1,
        Ceiling,
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        Greater,
    );
    test(
        "7442611177/10",
        1,
        Nearest,
        "4.8e-323228497",
        "0x2.0E-268435456#1",
        Less,
    );
    test(
        "7442611177/10",
        10,
        Floor,
        "6.1426e-323228497",
        "0x2.94E-268435456#10",
        Less,
    );
    test(
        "7442611177/10",
        10,
        Ceiling,
        "6.1519e-323228497",
        "0x2.95E-268435456#10",
        Greater,
    );
    test(
        "7442611177/10",
        10,
        Nearest,
        "6.1519e-323228497",
        "0x2.95E-268435456#10",
        Greater,
    );
    test(
        "7442611177/10",
        100,
        Floor,
        "6.1485593168580621515208966267134e-323228497",
        "0x2.94a54a8d64062c460adda8654E-268435456#100",
        Less,
    );
    test(
        "7442611177/10",
        100,
        Ceiling,
        "6.1485593168580621515208966267209e-323228497",
        "0x2.94a54a8d64062c460adda8658E-268435456#100",
        Greater,
    );
    test(
        "7442611177/10",
        100,
        Nearest,
        "6.1485593168580621515208966267134e-323228497",
        "0x2.94a54a8d64062c460adda8654E-268435456#100",
        Less,
    );
    test(
        "-7442611185/10",
        1,
        Floor,
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        Less,
    );
    test(
        "-7442611185/10",
        1,
        Ceiling,
        "4.8e-323228497",
        "0x2.0E-268435456#1",
        Greater,
    );
    test(
        "-7442611185/10",
        1,
        Nearest,
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        Less,
    );
    test(
        "-7442611185/10",
        10,
        Floor,
        "2.7595e-323228497",
        "0x1.288E-268435456#10",
        Less,
    );
    test(
        "-7442611185/10",
        10,
        Ceiling,
        "2.7641e-323228497",
        "0x1.290E-268435456#10",
        Greater,
    );
    test(
        "-7442611185/10",
        10,
        Nearest,
        "2.7641e-323228497",
        "0x1.290E-268435456#10",
        Greater,
    );
    test(
        "-7442611185/10",
        100,
        Floor,
        "2.7627257886571247097149806987996e-323228497",
        "0x1.28d8e45434c7216121ffbfc56E-268435456#100",
        Less,
    );
    test(
        "-7442611185/10",
        100,
        Ceiling,
        "2.7627257886571247097149806988033e-323228497",
        "0x1.28d8e45434c7216121ffbfc58E-268435456#100",
        Greater,
    );
    test(
        "-7442611185/10",
        100,
        Nearest,
        "2.7627257886571247097149806988033e-323228497",
        "0x1.28d8e45434c7216121ffbfc58E-268435456#100",
        Greater,
    );
    test("744261119", 1, Floor, "0.0", "0x0.0", Less);
    test(
        "744261119",
        1,
        Ceiling,
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        Greater,
    );
    test(
        "744261119",
        1,
        Nearest,
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        Greater,
    );
    test("744261119", 10, Floor, "0.0", "0x0.0", Less);
    test(
        "744261119",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "744261119",
        10,
        Nearest,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test("744261119", 100, Floor, "0.0", "0x0.0", Less);
    test(
        "744261119",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "744261119",
        100,
        Nearest,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test("7442611196/10", 1, Floor, "0.0", "0x0.0", Less);
    test(
        "7442611196/10",
        1,
        Ceiling,
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        Greater,
    );
    test("7442611196/10", 1, Nearest, "0.0", "0x0.0", Less);
    test("7442611196/10", 10, Floor, "0.0", "0x0.0", Less);
    test(
        "7442611196/10",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test("7442611196/10", 10, Nearest, "0.0", "0x0.0", Less);
    test("7442611196/10", 100, Floor, "0.0", "0x0.0", Less);
    test(
        "7442611196/10",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test("7442611196/10", 100, Nearest, "0.0", "0x0.0", Less);
    // - |x| >= 744261120: sech(x) is below half the smallest positive Float
    test("744261120", 1, Floor, "0.0", "0x0.0", Less);
    test(
        "744261120",
        1,
        Ceiling,
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        Greater,
    );
    test("744261120", 1, Nearest, "0.0", "0x0.0", Less);
    test("744261120", 10, Floor, "0.0", "0x0.0", Less);
    test(
        "744261120",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test("744261120", 10, Nearest, "0.0", "0x0.0", Less);
    test("744261120", 100, Floor, "0.0", "0x0.0", Less);
    test(
        "744261120",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test("744261120", 100, Nearest, "0.0", "0x0.0", Less);
    test("10000000000", 1, Floor, "0.0", "0x0.0", Less);
    test(
        "10000000000",
        1,
        Ceiling,
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        Greater,
    );
    test("10000000000", 1, Nearest, "0.0", "0x0.0", Less);
    test("10000000000", 10, Floor, "0.0", "0x0.0", Less);
    test(
        "10000000000",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test("10000000000", 10, Nearest, "0.0", "0x0.0", Less);
    test("10000000000", 100, Floor, "0.0", "0x0.0", Less);
    test(
        "10000000000",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test("10000000000", 100, Nearest, "0.0", "0x0.0", Less);
    test(
        "1/1000",
        100,
        Down,
        "0.99999950000020833324861114546071",
        "0x0.fffff79c846a490757e6daafb#100",
        Less,
    );
    test("744261119", 100, Down, "0.0", "0x0.0", Less);
    test(
        "1/1000",
        100,
        Up,
        "0.99999950000020833324861114546150",
        "0x0.fffff79c846a490757e6daafc#100",
        Greater,
    );
    test(
        "744261119",
        100,
        Up,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    // - the first series bracket straddles a rounding boundary, so the series is refined
    test("2/13", 7, Floor, "0.9844", "0x0.fc#7", Less);
    test("2/13", 7, Ceiling, "0.9922", "0x0.fe#7", Greater);
    test("2/13", 7, Nearest, "0.9922", "0x0.fe#7", Greater);
}

#[test]
fn test_sech_rational_extreme() {
    // |x| = 2^(-2^30 - 10) is too small to be a `Float`; sech(x) is within 2^(-2^31) of 1, below it
    let x = Rational::power_of_2(-(1i64 << 30) - 10);
    for (rm, out, o_out) in [
        (Floor, "0.99902", Less),
        (Down, "0.99902", Less),
        (Nearest, "1.0000", Greater),
        (Ceiling, "1.0000", Greater),
        (Up, "1.0000", Greater),
    ] {
        let (c, o) = Float::sech_rational_prec_round_ref(&x, 10, rm);
        assert_eq!(c.to_string(), out);
        assert_eq!(c.get_prec(), Some(10));
        assert_eq!(o, o_out);
        let (c_neg, o_neg) = Float::sech_rational_prec_round(-&x, 10, rm);
        assert_eq!(ComparableFloat(c_neg), ComparableFloat(c));
        assert_eq!(o_neg, o);
    }

    // |x| = 2^(2^30) is too large to be a `Float`, and sech(x) underflows
    let x = Rational::power_of_2(1i64 << 30);
    let (c, o) = Float::sech_rational_prec_round_ref(&x, 10, Nearest);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::ZERO));
    assert_eq!(o, Less);
    let (c, o) = Float::sech_rational_prec_round(-x, 10, Up);
    assert_eq!(
        ComparableFloat(c),
        ComparableFloat(Float::min_positive_value_prec(10))
    );
    assert_eq!(o, Greater);
}

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

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

#[test]
#[should_panic]
fn sech_rational_prec_round_fail_1() {
    Float::sech_rational_prec_round(Rational::ONE, 0, Floor);
}

#[test]
#[should_panic]
fn sech_rational_prec_round_fail_2() {
    Float::sech_rational_prec_round(Rational::ONE, 10, Exact);
}

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

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

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

    // sech x >= 1, and sech is even
    assert!((0u32..=1u32).contains(&c));
    let (c_neg, o_neg) = Float::sech_rational_prec_round(-&x, prec, rm);
    assert_eq!(ComparableFloatRef(&c_neg), ComparableFloatRef(&c));
    assert_eq!(o_neg, o);

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

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

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

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

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

    assert!((0u32..=1u32).contains(&c));

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

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

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

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_sech_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_sech_rational::<T>(&x)),
            NiceFloat(out)
        );
    }
    test::<f32>("0", 1.0);
    test::<f32>("1", 0.6480543);
    test::<f32>("-1", 0.6480543);
    test::<f32>("1/3", 0.94690526);
    test::<f32>("22/7", 0.08615813);
    test::<f32>("95", 1.1042e-41);
    test::<f32>("100", 7.4e-44);
    test::<f32>("104", 1.0e-45);
    test::<f32>("710", 0.0);
    test::<f32>("720", 0.0);
    test::<f32>("-745", 0.0);
    test::<f32>("7451/10", 0.0);
    test::<f32>("746", 0.0);
    test::<f32>("10000", 0.0);
    test::<f32>("1/100000000000000000000", 1.0);

    test::<f64>("0", 1.0);
    test::<f64>("1", 0.6480542736638853);
    test::<f64>("-1", 0.6480542736638853);
    test::<f64>("1/3", 0.9469052537634979);
    test::<f64>("22/7", 0.08615812953697949);
    test::<f64>("95", 1.1042164554057065e-41);
    test::<f64>("100", 7.440151952041672e-44);
    test::<f64>("104", 1.3627113643090597e-45);
    test::<f64>("710", 8.95257245135026e-309);
    test::<f64>("720", 4.06446160484e-313);
    test::<f64>("-745", 5.0e-324);
    test::<f64>("7451/10", 5.0e-324);
    test::<f64>("746", 0.0);
    test::<f64>("10000", 0.0);
    test::<f64>("1/100000000000000000000", 1.0);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_sech_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_sech_rational::<T>(&x);
        // the hyperbolic secant of a rational is never NaN, and lies in [0, 1]
        assert!(c >= T::ZERO && c <= T::ONE);
        // sech is even
        assert_eq!(
            NiceFloat(primitive_float_sech_rational::<T>(&-&x)),
            NiceFloat(c)
        );
        // the result is the correctly rounded hyperbolic secant 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_sech_rational_prec(&x, p).0)
        });
        assert_eq!(NiceFloat(rug_c), NiceFloat(c));
    });

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

#[test]
fn primitive_float_sech_rational_properties() {
    apply_fn_to_primitive_floats!(primitive_float_sech_rational_properties_helper);
}