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, Sinh, SinhAssign};
use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::basic::traits::{
    Infinity, NaN, NegativeInfinity, NegativeZero, One, Zero,
};
use malachite_base::num::comparison::traits::PartialOrdAbs;
use malachite_base::num::conversion::traits::{ExactFrom, RoundingFrom};
use malachite_base::num::float::NiceFloat;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_base::rounding_modes::RoundingMode::{self, *};
use malachite_base::rounding_modes::exhaustive::exhaustive_rounding_modes;
use malachite_base::test_util::generators::{
    primitive_float_gen, unsigned_rounding_mode_pair_gen_var_3,
};
use malachite_float::float::arithmetic::sinh::{
    primitive_float_sinh, primitive_float_sinh_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::sinh::{
    rug_sinh, rug_sinh_prec, rug_sinh_prec_round, rug_sinh_rational_prec,
    rug_sinh_rational_prec_round, rug_sinh_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_sinh_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().sinh_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.sinh_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.sinh_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_sinh_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, "Infinity", "Infinity", Equal,
    );
    test(
        "-Infinity",
        "-Infinity",
        1,
        Nearest,
        "-Infinity",
        "-Infinity",
        Equal,
    );
    test("0.0", "0x0.0", 1, Nearest, "0.0", "0x0.0", Equal);
    test("-0.0", "-0x0.0", 1, Nearest, "-0.0", "-0x0.0", Equal);
    test("0.0", "0x0.0", 10, Nearest, "0.0", "0x0.0", Equal);
    // - general path; the first Ziv iteration cannot round, 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);
    test("1.0", "0x1.0#1", 10, Floor, "1.1738", "0x1.2c8#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        10,
        Ceiling,
        "1.1758",
        "0x1.2d0#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        10,
        Nearest,
        "1.1758",
        "0x1.2d0#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Floor,
        "1.1752011936438014568823818505953",
        "0x1.2cd9fc44eb9825a80249487f0#100",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Ceiling,
        "1.1752011936438014568823818505969",
        "0x1.2cd9fc44eb9825a80249487f2#100",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Nearest,
        "1.1752011936438014568823818505953",
        "0x1.2cd9fc44eb9825a80249487f0#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Floor,
        "-1.1758",
        "-0x1.2d0#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Ceiling,
        "-1.1738",
        "-0x1.2c8#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Nearest,
        "-1.1758",
        "-0x1.2d0#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Floor,
        "-1.1752011936438014568823818505969",
        "-0x1.2cd9fc44eb9825a80249487f2#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Ceiling,
        "-1.1752011936438014568823818505953",
        "-0x1.2cd9fc44eb9825a80249487f0#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Nearest,
        "-1.1752011936438014568823818505953",
        "-0x1.2cd9fc44eb9825a80249487f0#100",
        Greater,
    );
    test("0.50", "0x0.8#1", 10, Floor, "0.52051", "0x0.854#10", Less);
    test(
        "0.50",
        "0x0.8#1",
        10,
        Ceiling,
        "0.52148",
        "0x0.858#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        10,
        Nearest,
        "0.52148",
        "0x0.858#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Floor,
        "0.52109530549374736162242562641114",
        "0x0.8566807f31dcb651abc4abb0d#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Ceiling,
        "0.52109530549374736162242562641193",
        "0x0.8566807f31dcb651abc4abb0e#100",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Nearest,
        "0.52109530549374736162242562641114",
        "0x0.8566807f31dcb651abc4abb0d#100",
        Less,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        10,
        Floor,
        "-0.52148",
        "-0x0.858#10",
        Less,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        10,
        Ceiling,
        "-0.52051",
        "-0x0.854#10",
        Greater,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        10,
        Nearest,
        "-0.52148",
        "-0x0.858#10",
        Less,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        100,
        Floor,
        "-0.52109530549374736162242562641193",
        "-0x0.8566807f31dcb651abc4abb0e#100",
        Less,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        100,
        Ceiling,
        "-0.52109530549374736162242562641114",
        "-0x0.8566807f31dcb651abc4abb0d#100",
        Greater,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        100,
        Nearest,
        "-0.52109530549374736162242562641114",
        "-0x0.8566807f31dcb651abc4abb0d#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Floor,
        "0.33936",
        "0x0.56e#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Ceiling,
        "0.33984",
        "0x0.570#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Nearest,
        "0.33936",
        "0x0.56e#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Floor,
        "0.33954055725615013910126061133846",
        "0x0.56ec214514ae05405cea1145d0#100",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Ceiling,
        "0.33954055725615013910126061133886",
        "0x0.56ec214514ae05405cea1145d8#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Nearest,
        "0.33954055725615013910126061133886",
        "0x0.56ec214514ae05405cea1145d8#100",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Floor, "3.6250", "0x3.a0#10", Less);
    test(
        "2.0",
        "0x2.0#2",
        10,
        Ceiling,
        "3.6289",
        "0x3.a1#10",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Nearest, "3.6250", "0x3.a0#10", Less);
    test(
        "2.0",
        "0x2.0#2",
        100,
        Floor,
        "3.6268604078470187676682139828013",
        "0x3.a079ec76dc33ede69900592c4#100",
        Less,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Ceiling,
        "3.6268604078470187676682139828044",
        "0x3.a079ec76dc33ede69900592c8#100",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Nearest,
        "3.6268604078470187676682139828013",
        "0x3.a079ec76dc33ede69900592c4#100",
        Less,
    );
    test(
        "10.0",
        "0xa.0#4",
        10,
        Floor,
        "11008.0",
        "0x2.b0E+3#10",
        Less,
    );
    test(
        "10.0",
        "0xa.0#4",
        10,
        Ceiling,
        "11024.0",
        "0x2.b1E+3#10",
        Greater,
    );
    test(
        "10.0",
        "0xa.0#4",
        10,
        Nearest,
        "11008.0",
        "0x2.b0E+3#10",
        Less,
    );
    test(
        "10.0",
        "0xa.0#4",
        100,
        Floor,
        "11013.232874703393377236524554834",
        "0x2b05.3b9dad3323e7c80b6e4524#100",
        Less,
    );
    test(
        "10.0",
        "0xa.0#4",
        100,
        Ceiling,
        "11013.232874703393377236524554847",
        "0x2b05.3b9dad3323e7c80b6e4528#100",
        Greater,
    );
    test(
        "10.0",
        "0xa.0#4",
        100,
        Nearest,
        "11013.232874703393377236524554847",
        "0x2b05.3b9dad3323e7c80b6e4528#100",
        Greater,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        10,
        Floor,
        "-1.3459e43",
        "-0x9.a8E+35#10",
        Less,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        10,
        Ceiling,
        "-1.3437e43",
        "-0x9.a4E+35#10",
        Greater,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        10,
        Nearest,
        "-1.3437e43",
        "-0x9.a4E+35#10",
        Greater,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        100,
        Floor,
        "-1.3440585709080677242063127757915e43",
        "-0x9.a4a54d8b8dfa566112849992E+35#100",
        Less,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        100,
        Ceiling,
        "-1.3440585709080677242063127757898e43",
        "-0x9.a4a54d8b8dfa566112849991E+35#100",
        Greater,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        100,
        Nearest,
        "-1.3440585709080677242063127757898e43",
        "-0x9.a4a54d8b8dfa566112849991E+35#100",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Floor,
        "9.8398e433",
        "0x3.3cE+360#10",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Ceiling,
        "9.8516e433",
        "0x3.3dE+360#10",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Nearest,
        "9.8516e433",
        "0x3.3dE+360#10",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Floor,
        "9.8503555700852349694443967612105e433",
        "0x3.3ce46f35dae75b00ac567f544E+360#100",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Ceiling,
        "9.8503555700852349694443967612201e433",
        "0x3.3ce46f35dae75b00ac567f548E+360#100",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Nearest,
        "9.8503555700852349694443967612201e433",
        "0x3.3ce46f35dae75b00ac567f548E+360#100",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Floor,
        "11.547",
        "0xb.8c#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Ceiling,
        "11.562",
        "0xb.90#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Nearest,
        "11.547",
        "0xb.8c#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Floor,
        "11.548739357257748378558851329885",
        "0xb.8c7a2eb97339113d35fcbd32#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Ceiling,
        "11.548739357257748378558851329897",
        "0xb.8c7a2eb97339113d35fcbd33#100",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Nearest,
        "11.548739357257748378558851329885",
        "0xb.8c7a2eb97339113d35fcbd32#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Floor,
        "1.5145e434294",
        "0x4.1cE+360673#10",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Ceiling,
        "1.5174e434294",
        "0x4.1eE+360673#10",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Nearest,
        "1.5174e434294",
        "0x4.1eE+360673#10",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Floor,
        "1.5166076984010437725432010707070e434294",
        "0x4.1d6ffdeb8a9180f8c69cf6168E+360673#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Ceiling,
        "1.5166076984010437725432010707093e434294",
        "0x4.1d6ffdeb8a9180f8c69cf6170E+360673#100",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Nearest,
        "1.5166076984010437725432010707093e434294",
        "0x4.1d6ffdeb8a9180f8c69cf6170E+360673#100",
        Greater,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        10,
        Floor,
        "-7.7564e43429447",
        "-0x8.84E+36067375#10",
        Less,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        10,
        Ceiling,
        "-7.7422e43429447",
        "-0x8.80E+36067375#10",
        Greater,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        10,
        Nearest,
        "-7.7564e43429447",
        "-0x8.84E+36067375#10",
        Less,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        100,
        Floor,
        "-7.7498837332421325220922927166788e43429447",
        "-0x8.8229c7cd3e3c8988ae5d5230E+36067375#100",
        Less,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        100,
        Ceiling,
        "-7.7498837332421325220922927166673e43429447",
        "-0x8.8229c7cd3e3c8988ae5d522fE+36067375#100",
        Greater,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        100,
        Nearest,
        "-7.7498837332421325220922927166673e43429447",
        "-0x8.8229c7cd3e3c8988ae5d522fE+36067375#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Floor,
        "0.00097656",
        "0x0.00400#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Floor,
        "-0.00097847",
        "-0x0.00402#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Ceiling,
        "0.00097847",
        "0x0.00402#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Ceiling,
        "-0.00097656",
        "-0x0.00400#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Nearest,
        "0.00097656",
        "0x0.00400#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Nearest,
        "-0.00097656",
        "-0x0.00400#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Down,
        "0.00097656",
        "0x0.00400#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Down,
        "-0.00097656",
        "-0x0.00400#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Up,
        "0.00097847",
        "0x0.00402#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Up,
        "-0.00097847",
        "-0x0.00402#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Floor,
        "0.00097656265522043650406675150063800",
        "0x0.00400000aaaaab33333367367370#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Floor,
        "-0.00097656265522043650406675150063955",
        "-0x0.00400000aaaaab33333367367378#100",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Ceiling,
        "0.00097656265522043650406675150063955",
        "0x0.00400000aaaaab33333367367378#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Ceiling,
        "-0.00097656265522043650406675150063800",
        "-0x0.00400000aaaaab33333367367370#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Nearest,
        "0.00097656265522043650406675150063800",
        "0x0.00400000aaaaab33333367367370#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Nearest,
        "-0.00097656265522043650406675150063800",
        "-0x0.00400000aaaaab33333367367370#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Down,
        "0.00097656265522043650406675150063800",
        "0x0.00400000aaaaab33333367367370#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Down,
        "-0.00097656265522043650406675150063800",
        "-0x0.00400000aaaaab33333367367370#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Up,
        "0.00097656265522043650406675150063955",
        "0x0.00400000aaaaab33333367367378#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Up,
        "-0.00097656265522043650406675150063955",
        "-0x0.00400000aaaaab33333367367378#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Floor,
        "8.8817841970012523233890533447266e-16",
        "0x4.0000000000000000000000000E-13#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Floor,
        "-8.8817841970012523233890533447406e-16",
        "-0x4.0000000000000000000000008E-13#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Ceiling,
        "8.8817841970012523233890533447406e-16",
        "0x4.0000000000000000000000008E-13#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Ceiling,
        "-8.8817841970012523233890533447266e-16",
        "-0x4.0000000000000000000000000E-13#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Nearest,
        "8.8817841970012523233890533447266e-16",
        "0x4.0000000000000000000000000E-13#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Nearest,
        "-8.8817841970012523233890533447266e-16",
        "-0x4.0000000000000000000000000E-13#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Down,
        "8.8817841970012523233890533447266e-16",
        "0x4.0000000000000000000000000E-13#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Down,
        "-8.8817841970012523233890533447266e-16",
        "-0x4.0000000000000000000000000E-13#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Up,
        "8.8817841970012523233890533447406e-16",
        "0x4.0000000000000000000000008E-13#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Up,
        "-8.8817841970012523233890533447406e-16",
        "-0x4.0000000000000000000000008E-13#100",
        Less,
    );
    // - small_input_shortcut returns
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Floor,
        "7.8886e-31",
        "0x1.000E-25#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Floor,
        "-7.9040e-31",
        "-0x1.008E-25#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Ceiling,
        "7.9040e-31",
        "0x1.008E-25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Ceiling,
        "-7.8886e-31",
        "-0x1.000E-25#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Nearest,
        "7.8886e-31",
        "0x1.000E-25#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Nearest,
        "-7.8886e-31",
        "-0x1.000E-25#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Down,
        "7.8886e-31",
        "0x1.000E-25#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Down,
        "-7.8886e-31",
        "-0x1.000E-25#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Up,
        "7.9040e-31",
        "0x1.008E-25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Up,
        "-7.9040e-31",
        "-0x1.008E-25#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Floor,
        "7.888609052210118054117285652827862296732064351090230047702790124822869216287758849295325\
        8285e-31",
        "0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaaaE-25#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Floor,
        "-7.88860905221011805411728565282786229673206435109023004770279012482286921628775884929532\
        58362e-31",
        "-0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaacE-25#300",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Ceiling,
        "7.888609052210118054117285652827862296732064351090230047702790124822869216287758849295325\
        8362e-31",
        "0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaacE-25#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Ceiling,
        "-7.88860905221011805411728565282786229673206435109023004770279012482286921628775884929532\
        58285e-31",
        "-0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaaaE-25#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Nearest,
        "7.888609052210118054117285652827862296732064351090230047702790124822869216287758849295325\
        8285e-31",
        "0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaaaE-25#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Nearest,
        "-7.88860905221011805411728565282786229673206435109023004770279012482286921628775884929532\
        58285e-31",
        "-0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaaaE-25#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Down,
        "7.888609052210118054117285652827862296732064351090230047702790124822869216287758849295325\
        8285e-31",
        "0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaaaE-25#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Down,
        "-7.88860905221011805411728565282786229673206435109023004770279012482286921628775884929532\
        58285e-31",
        "-0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaaaE-25#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Up,
        "7.888609052210118054117285652827862296732064351090230047702790124822869216287758849295325\
        8362e-31",
        "0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaacE-25#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Up,
        "-7.88860905221011805411728565282786229673206435109023004770279012482286921628775884929532\
        58362e-31",
        "-0x1.000000000000000000000000000000000000000000000000002aaaaaaaaaaaaaaaaaaaaaaacE-25#300",
        Less,
    );
    // - a power of 2 stored at a precision above the error bound: the shortcut declines
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Floor,
        "9.0949e-13",
        "0x1.000E-10#10",
        Less,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Floor,
        "-9.1127e-13",
        "-0x1.008E-10#10",
        Less,
    );
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Ceiling,
        "9.1127e-13",
        "0x1.008E-10#10",
        Greater,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Ceiling,
        "-9.0949e-13",
        "-0x1.000E-10#10",
        Greater,
    );
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Nearest,
        "9.0949e-13",
        "0x1.000E-10#10",
        Less,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Nearest,
        "-9.0949e-13",
        "-0x1.000E-10#10",
        Greater,
    );
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Down,
        "9.0949e-13",
        "0x1.000E-10#10",
        Less,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Down,
        "-9.0949e-13",
        "-0x1.000E-10#10",
        Greater,
    );
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Up,
        "9.1127e-13",
        "0x1.008E-10#10",
        Greater,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Up,
        "-9.1127e-13",
        "-0x1.008E-10#10",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Floor,
        "2.38256490488795107322e-323228497",
        "0x1.0000000000000000E-268435456#64",
        Less,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        64,
        Floor,
        "-2.38256490488795107347e-323228497",
        "-0x1.0000000000000002E-268435456#64",
        Less,
    );
    test(
        "1.0e-301030",
        "0x1.0E-250000#1",
        64,
        Floor,
        "1.01003405919803022470e-301030",
        "0x1.0000000000000000E-250000#64",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Ceiling,
        "2.38256490488795107347e-323228497",
        "0x1.0000000000000002E-268435456#64",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        64,
        Ceiling,
        "-2.38256490488795107322e-323228497",
        "-0x1.0000000000000000E-268435456#64",
        Greater,
    );
    test(
        "1.0e-301030",
        "0x1.0E-250000#1",
        64,
        Ceiling,
        "1.01003405919803022481e-301030",
        "0x1.0000000000000002E-250000#64",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Nearest,
        "2.38256490488795107322e-323228497",
        "0x1.0000000000000000E-268435456#64",
        Less,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        64,
        Nearest,
        "-2.38256490488795107322e-323228497",
        "-0x1.0000000000000000E-268435456#64",
        Greater,
    );
    test(
        "1.0e-301030",
        "0x1.0E-250000#1",
        64,
        Nearest,
        "1.01003405919803022470e-301030",
        "0x1.0000000000000000E-250000#64",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Floor,
        "1.0744e304006137",
        "0xc.50E+252471631#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Ceiling,
        "1.0758e304006137",
        "0xc.54E+252471631#10",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Nearest,
        "1.0744e304006137",
        "0xc.50E+252471631#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Down,
        "1.0744e304006137",
        "0xc.50E+252471631#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Up,
        "1.0758e304006137",
        "0xc.54E+252471631#10",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Floor,
        "1.0745986328169899684213985210251e304006137",
        "0xc.507c7e17bca36323b1e8bc08E+252471631#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Ceiling,
        "1.0745986328169899684213985210262e304006137",
        "0xc.507c7e17bca36323b1e8bc09E+252471631#100",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Nearest,
        "1.0745986328169899684213985210251e304006137",
        "0xc.507c7e17bca36323b1e8bc08E+252471631#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Down,
        "1.0745986328169899684213985210251e304006137",
        "0xc.507c7e17bca36323b1e8bc08E+252471631#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Up,
        "1.0745986328169899684213985210262e304006137",
        "0xc.507c7e17bca36323b1e8bc09E+252471631#100",
        Greater,
    );
    // - exp(x) reaches the top binade but sinh(x) does not overflow: h = u * (u / 2), u = exp(x /
    //   2)
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Floor,
        "1.3301e323228496",
        "0x5.12E+268435455#10",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Ceiling,
        "1.3321e323228496",
        "0x5.14E+268435455#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Nearest,
        "1.3321e323228496",
        "0x5.14E+268435455#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Down,
        "1.3301e323228496",
        "0x5.12E+268435455#10",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Up,
        "1.3321e323228496",
        "0x5.14E+268435455#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Floor,
        "1.3315814500369112065268344141958e323228496",
        "0x5.137d0b40cdfb4457d4a570f10E+268435455#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Ceiling,
        "1.3315814500369112065268344141975e323228496",
        "0x5.137d0b40cdfb4457d4a570f18E+268435455#100",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Nearest,
        "1.3315814500369112065268344141975e323228496",
        "0x5.137d0b40cdfb4457d4a570f18E+268435455#100",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Down,
        "1.3315814500369112065268344141958e323228496",
        "0x5.137d0b40cdfb4457d4a570f10E+268435455#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Up,
        "1.3315814500369112065268344141975e323228496",
        "0x5.137d0b40cdfb4457d4a570f18E+268435455#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Floor,
        "-1.3321e323228496",
        "-0x5.14E+268435455#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Ceiling,
        "-1.3301e323228496",
        "-0x5.12E+268435455#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Nearest,
        "-1.3321e323228496",
        "-0x5.14E+268435455#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Down,
        "-1.3301e323228496",
        "-0x5.12E+268435455#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Up,
        "-1.3321e323228496",
        "-0x5.14E+268435455#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Floor,
        "-1.3315814500369112065268344141975e323228496",
        "-0x5.137d0b40cdfb4457d4a570f18E+268435455#100",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Ceiling,
        "-1.3315814500369112065268344141958e323228496",
        "-0x5.137d0b40cdfb4457d4a570f10E+268435455#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Nearest,
        "-1.3315814500369112065268344141975e323228496",
        "-0x5.137d0b40cdfb4457d4a570f18E+268435455#100",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Down,
        "-1.3315814500369112065268344141958e323228496",
        "-0x5.137d0b40cdfb4457d4a570f10E+268435455#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Up,
        "-1.3315814500369112065268344141975e323228496",
        "-0x5.137d0b40cdfb4457d4a570f18E+268435455#100",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Floor,
        "1.9859e323228496",
        "0x7.92E+268435455#10",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Ceiling,
        "1.9879e323228496",
        "0x7.94E+268435455#10",
        Greater,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Nearest,
        "1.9879e323228496",
        "0x7.94E+268435455#10",
        Greater,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Down,
        "1.9859e323228496",
        "0x7.92E+268435455#10",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Up,
        "1.9879e323228496",
        "0x7.94E+268435455#10",
        Greater,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Floor,
        "1.9872622167931390381615986861180e323228496",
        "0x7.935dcb7045691ebed3cf12138E+268435455#100",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Ceiling,
        "1.9872622167931390381615986861197e323228496",
        "0x7.935dcb7045691ebed3cf12140E+268435455#100",
        Greater,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Nearest,
        "1.9872622167931390381615986861180e323228496",
        "0x7.935dcb7045691ebed3cf12138E+268435455#100",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Down,
        "1.9872622167931390381615986861180e323228496",
        "0x7.935dcb7045691ebed3cf12138E+268435455#100",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Up,
        "1.9872622167931390381615986861197e323228496",
        "0x7.935dcb7045691ebed3cf12140E+268435455#100",
        Greater,
    );
    // - h = u * (u / 2) saturates, so sinh(x) overflows
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Floor,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Down,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Floor,
        "2.0985787164673876924043581168822e323228496",
        "0x7.ffffffffffffffffffffffff8E+268435455#100",
        Less,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Down,
        "2.0985787164673876924043581168822e323228496",
        "0x7.ffffffffffffffffffffffff8E+268435455#100",
        Less,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Floor,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Ceiling,
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Nearest,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Down,
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Up,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Floor,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Ceiling,
        "-2.0985787164673876924043581168822e323228496",
        "-0x7.ffffffffffffffffffffffff8E+268435455#100",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Nearest,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Down,
        "-2.0985787164673876924043581168822e323228496",
        "-0x7.ffffffffffffffffffffffff8E+268435455#100",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Up,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Floor,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Down,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Floor,
        "2.0985787164673876924043581168822e323228496",
        "0x7.ffffffffffffffffffffffff8E+268435455#100",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Down,
        "2.0985787164673876924043581168822e323228496",
        "0x7.ffffffffffffffffffffffff8E+268435455#100",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    // - exp(x / 2) reaches the top binade, so sinh(x) overflows
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Floor,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Down,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Floor,
        "2.0985787164673876924043581168822e323228496",
        "0x7.ffffffffffffffffffffffff8E+268435455#100",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Down,
        "2.0985787164673876924043581168822e323228496",
        "0x7.ffffffffffffffffffffffff8E+268435455#100",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Floor,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Ceiling,
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Nearest,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Down,
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Up,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Floor,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Ceiling,
        "-2.0985787164673876924043581168822e323228496",
        "-0x7.ffffffffffffffffffffffff8E+268435455#100",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Nearest,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Down,
        "-2.0985787164673876924043581168822e323228496",
        "-0x7.ffffffffffffffffffffffff8E+268435455#100",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Up,
        "-Infinity",
        "-Infinity",
        Less,
    );
    // - near the overflow threshold, the first Ziv iteration cannot round
    test(
        "744261117.29980",
        "0x2c5c85fd.4cc#40",
        105,
        Floor,
        "1.08999377317323357831214151177440e323228496",
        "0x4.27b92f7e5b053dc703b866e7b0E+268435455#105",
        Less,
    );
    test(
        "744261117.29980",
        "0x2c5c85fd.4cc#40",
        105,
        Ceiling,
        "1.08999377317323357831214151177446e323228496",
        "0x4.27b92f7e5b053dc703b866e7b4E+268435455#105",
        Greater,
    );
    test(
        "744261117.29980",
        "0x2c5c85fd.4cc#40",
        105,
        Nearest,
        "1.08999377317323357831214151177446e323228496",
        "0x4.27b92f7e5b053dc703b866e7b4E+268435455#105",
        Greater,
    );
}

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

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

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

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

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

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

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

    // |sinh x| >= |x|, and sinh x has the sign of x
    if !x.is_nan() {
        assert!(c.ge_abs(&x) || !c.is_finite() || c.get_prec() < x.get_prec());
        assert_eq!(c.is_sign_positive(), x.is_sign_positive());
    }
    if c.is_normal() {
        assert_eq!(c.get_prec(), Some(prec));
    }

    if o == Equal {
        // sinh 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.sinh_prec_round_ref(prec, rm2);
            assert_eq!(ComparableFloat(c2), ComparableFloat(c.clone()));
            assert_eq!(o2, Equal);
        }
    } else {
        assert_panic!(x.sinh_prec_round_ref(prec, Exact));
    }
}

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

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

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

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

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

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

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

#[test]
fn sinh_prec_properties() {
    float_unsigned_pair_gen_var_1().test_properties(|(x, prec)| {
        let (c, o) = x.clone().sinh_prec(prec);
        assert!(c.is_valid());
        let (c_alt, o_alt) = x.sinh_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.sinh_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.sinh_prec_round_ref(prec, Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

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

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

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

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

        assert_eq!(ComparableFloatRef(&(-&x).sinh()), 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_sinh() {
    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_sinh(x)), NiceFloat(out));
    }
    test::<f32>(f32::NAN, f32::NAN);
    test::<f32>(f32::INFINITY, f32::INFINITY);
    test::<f32>(f32::NEGATIVE_INFINITY, f32::NEGATIVE_INFINITY);
    test::<f32>(0.0, 0.0);
    test::<f32>(-0.0, -0.0);
    test::<f32>(1.0, 1.1752012);
    test::<f32>(-1.0, -1.1752012);
    test::<f32>(0.5, 0.5210953);
    test::<f32>(-0.5, -0.5210953);
    test::<f32>(2.0, 3.6268604);
    test::<f32>(10.0, 11013.232);
    test::<f32>(core::f32::consts::PI, 11.54874);
    test::<f32>(88.0, 8.2581813e37);
    test::<f32>(89.0, 2.2448064e38);
    test::<f32>(89.5, f32::INFINITY);
    test::<f32>(-89.5, f32::NEGATIVE_INFINITY);
    test::<f32>(90.0, f32::INFINITY);
    test::<f32>(1.0e-20, 1.0e-20);
    test::<f32>(1.0e-45, 1.0e-45);
    test::<f32>(3.4028235e38, f32::INFINITY);

    test::<f64>(f64::NAN, f64::NAN);
    test::<f64>(f64::INFINITY, f64::INFINITY);
    test::<f64>(f64::NEGATIVE_INFINITY, f64::NEGATIVE_INFINITY);
    test::<f64>(0.0, 0.0);
    test::<f64>(-0.0, -0.0);
    test::<f64>(1.0, 1.1752011936438014);
    test::<f64>(-1.0, -1.1752011936438014);
    test::<f64>(0.5, 0.5210953054937474);
    test::<f64>(-0.5, -0.5210953054937474);
    test::<f64>(2.0, 3.6268604078470186);
    test::<f64>(10.0, 11013.232874703393);
    test::<f64>(core::f64::consts::PI, 11.548739357257746);
    test::<f64>(709.0, 4.109203730777486e307);
    test::<f64>(710.0, 1.1169973830808555e308);
    test::<f64>(710.4, 1.6663642832806496e308);
    test::<f64>(-710.4, -1.6663642832806496e308);
    test::<f64>(711.0, f64::INFINITY);
    test::<f64>(1.0e-200, 1.0e-200);
    test::<f64>(5.0e-324, 5.0e-324);
    test::<f64>(1.7976931348623157e308, f64::INFINITY);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_sinh_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_sinh(x);
        // sinh is NaN exactly for NaN inputs, and otherwise has the sign of x and |sinh x| >= |x|.
        assert_eq!(c.is_nan(), x.is_nan());
        if !x.is_nan() {
            assert_eq!(c.is_sign_positive(), x.is_sign_positive());
            assert!(c.abs() >= x.abs());
            // sinh is odd
            assert_eq!(NiceFloat(primitive_float_sinh(-x)), NiceFloat(-c));
        }
        if x.is_finite() {
            // the result is the correctly rounded hyperbolic cosine, as computed by MPFR at the
            // same precision. MPFR's exponent range is wider than T's, so a result beyond T's
            // largest finite value overflows to infinity.
            let rug_x = rug::Float::with_val(
                u32::exact_from(T::MANTISSA_WIDTH + 1),
                &rug::Float::exact_from(&Float::from(x)),
            );
            let rug_c = <Float as From<&rug::Float>>::from(&rug_x.sinh());
            let expected = if rug_c > T::MAX_FINITE {
                T::INFINITY
            } else if rug_c < -T::MAX_FINITE {
                T::NEGATIVE_INFINITY
            } else {
                T::exact_from(&rug_c)
            };
            assert_eq!(NiceFloat(expected), NiceFloat(c));
        }
    });
}

#[test]
fn primitive_float_sinh_properties() {
    apply_fn_to_primitive_floats!(primitive_float_sinh_properties_helper);
}

#[test]
fn test_sinh_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::sinh_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::sinh_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_sinh_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, "0.0", "0x0.0", Equal);
    test("0", 10, Down, "0.0", "0x0.0", Equal);
    test("0", 1, Up, "0.0", "0x0.0", Equal);
    test("0", 10, Up, "0.0", "0x0.0", Equal);
    test("0", 1, Floor, "0.0", "0x0.0", Equal);
    test("0", 10, Floor, "0.0", "0x0.0", Equal);
    test("0", 1, Ceiling, "0.0", "0x0.0", Equal);
    test("0", 10, Ceiling, "0.0", "0x0.0", Equal);
    test("0", 1, Nearest, "0.0", "0x0.0", Equal);
    test("0", 10, Nearest, "0.0", "0x0.0", Equal);
    test("0", 1, Exact, "0.0", "0x0.0", Equal);
    test("0", 10, Exact, "0.0", "0x0.0", 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, "0.50", "0x0.8#1", Less);
    test("3/5", 10, Floor, "0.63574", "0x0.a2c#10", Less);
    test("3/5", 10, Ceiling, "0.63672", "0x0.a30#10", Greater);
    test("3/5", 10, Nearest, "0.63672", "0x0.a30#10", Greater);
    test(
        "3/5",
        100,
        Floor,
        "0.63665358214824127112345437546503",
        "0x0.a2fbbaaa353beda5841b49fd2#100",
        Less,
    );
    test(
        "3/5",
        100,
        Ceiling,
        "0.63665358214824127112345437546582",
        "0x0.a2fbbaaa353beda5841b49fd3#100",
        Greater,
    );
    test(
        "3/5",
        100,
        Nearest,
        "0.63665358214824127112345437546503",
        "0x0.a2fbbaaa353beda5841b49fd2#100",
        Less,
    );
    test("-3/5", 1, Floor, "-1.0", "-0x1.0#1", Less);
    test("-3/5", 1, Ceiling, "-0.50", "-0x0.8#1", Greater);
    test("-3/5", 1, Nearest, "-0.50", "-0x0.8#1", Greater);
    test("-3/5", 10, Floor, "-0.63672", "-0x0.a30#10", Less);
    test("-3/5", 10, Ceiling, "-0.63574", "-0x0.a2c#10", Greater);
    test("-3/5", 10, Nearest, "-0.63672", "-0x0.a30#10", Less);
    test(
        "-3/5",
        100,
        Floor,
        "-0.63665358214824127112345437546582",
        "-0x0.a2fbbaaa353beda5841b49fd3#100",
        Less,
    );
    test(
        "-3/5",
        100,
        Ceiling,
        "-0.63665358214824127112345437546503",
        "-0x0.a2fbbaaa353beda5841b49fd2#100",
        Greater,
    );
    test(
        "-3/5",
        100,
        Nearest,
        "-0.63665358214824127112345437546503",
        "-0x0.a2fbbaaa353beda5841b49fd2#100",
        Greater,
    );
    test("1/3", 1, Floor, "0.25", "0x0.4#1", Less);
    test("1/3", 1, Ceiling, "0.50", "0x0.8#1", Greater);
    test("1/3", 1, Nearest, "0.25", "0x0.4#1", Less);
    test("1/3", 10, Floor, "0.33936", "0x0.56e#10", Less);
    test("1/3", 10, Ceiling, "0.33984", "0x0.570#10", Greater);
    test("1/3", 10, Nearest, "0.33936", "0x0.56e#10", Less);
    test(
        "1/3",
        100,
        Floor,
        "0.33954055725615013910126061133846",
        "0x0.56ec214514ae05405cea1145d0#100",
        Less,
    );
    test(
        "1/3",
        100,
        Ceiling,
        "0.33954055725615013910126061133886",
        "0x0.56ec214514ae05405cea1145d8#100",
        Greater,
    );
    test(
        "1/3",
        100,
        Nearest,
        "0.33954055725615013910126061133846",
        "0x0.56ec214514ae05405cea1145d0#100",
        Less,
    );
    test("22/7", 1, Floor, "8.0", "0x8.0#1", Less);
    test("22/7", 1, Ceiling, "16.0", "0x1.0E+1#1", Greater);
    test("22/7", 1, Nearest, "8.0", "0x8.0#1", Less);
    test("22/7", 10, Floor, "11.562", "0xb.90#10", Less);
    test("22/7", 10, Ceiling, "11.578", "0xb.94#10", Greater);
    test("22/7", 10, Nearest, "11.562", "0xb.90#10", Less);
    test(
        "22/7",
        100,
        Floor,
        "11.563406494500513816416460850606",
        "0xb.903b68743bd476d7129c12b8#100",
        Less,
    );
    test(
        "22/7",
        100,
        Ceiling,
        "11.563406494500513816416460850618",
        "0xb.903b68743bd476d7129c12b9#100",
        Greater,
    );
    test(
        "22/7",
        100,
        Nearest,
        "11.563406494500513816416460850618",
        "0xb.903b68743bd476d7129c12b9#100",
        Greater,
    );
    test("-22/7", 1, Floor, "-16.0", "-0x1.0E+1#1", Less);
    test("-22/7", 1, Ceiling, "-8.0", "-0x8.0#1", Greater);
    test("-22/7", 1, Nearest, "-8.0", "-0x8.0#1", Greater);
    test("-22/7", 10, Floor, "-11.578", "-0xb.94#10", Less);
    test("-22/7", 10, Ceiling, "-11.562", "-0xb.90#10", Greater);
    test("-22/7", 10, Nearest, "-11.562", "-0xb.90#10", Greater);
    test(
        "-22/7",
        100,
        Floor,
        "-11.563406494500513816416460850618",
        "-0xb.903b68743bd476d7129c12b9#100",
        Less,
    );
    test(
        "-22/7",
        100,
        Ceiling,
        "-11.563406494500513816416460850606",
        "-0xb.903b68743bd476d7129c12b8#100",
        Greater,
    );
    test(
        "-22/7",
        100,
        Nearest,
        "-11.563406494500513816416460850618",
        "-0xb.903b68743bd476d7129c12b9#100",
        Less,
    );
    test("100", 1, Floor, "1.1e43", "0x8.0E+35#1", Less);
    test("100", 1, Ceiling, "2.2e43", "0x1.0E+36#1", Greater);
    test("100", 1, Nearest, "1.1e43", "0x8.0E+35#1", Less);
    test("100", 10, Floor, "1.3437e43", "0x9.a4E+35#10", Less);
    test("100", 10, Ceiling, "1.3459e43", "0x9.a8E+35#10", Greater);
    test("100", 10, Nearest, "1.3437e43", "0x9.a4E+35#10", Less);
    test(
        "100",
        100,
        Floor,
        "1.3440585709080677242063127757898e43",
        "0x9.a4a54d8b8dfa566112849991E+35#100",
        Less,
    );
    test(
        "100",
        100,
        Ceiling,
        "1.3440585709080677242063127757915e43",
        "0x9.a4a54d8b8dfa566112849992E+35#100",
        Greater,
    );
    test(
        "100",
        100,
        Nearest,
        "1.3440585709080677242063127757898e43",
        "0x9.a4a54d8b8dfa566112849991E+35#100",
        Less,
    );
    test("-100", 1, Floor, "-2.2e43", "-0x1.0E+36#1", Less);
    test("-100", 1, Ceiling, "-1.1e43", "-0x8.0E+35#1", Greater);
    test("-100", 1, Nearest, "-1.1e43", "-0x8.0E+35#1", Greater);
    test("-100", 10, Floor, "-1.3459e43", "-0x9.a8E+35#10", Less);
    test("-100", 10, Ceiling, "-1.3437e43", "-0x9.a4E+35#10", Greater);
    test("-100", 10, Nearest, "-1.3437e43", "-0x9.a4E+35#10", Greater);
    test(
        "-100",
        100,
        Floor,
        "-1.3440585709080677242063127757915e43",
        "-0x9.a4a54d8b8dfa566112849992E+35#100",
        Less,
    );
    test(
        "-100",
        100,
        Ceiling,
        "-1.3440585709080677242063127757898e43",
        "-0x9.a4a54d8b8dfa566112849991E+35#100",
        Greater,
    );
    test(
        "-100",
        100,
        Nearest,
        "-1.3440585709080677242063127757898e43",
        "-0x9.a4a54d8b8dfa566112849991E+35#100",
        Greater,
    );
    test("1/1000", 1, Floor, "0.00098", "0x0.004#1", Less);
    test("1/1000", 1, Ceiling, "0.0020", "0x0.008#1", Greater);
    test("1/1000", 1, Nearest, "0.00098", "0x0.004#1", Less);
    test("1/1000", 10, Floor, "0.00099945", "0x0.00418#10", Less);
    test("1/1000", 10, Ceiling, "0.0010014", "0x0.0041a#10", Greater);
    test("1/1000", 10, Nearest, "0.00099945", "0x0.00418#10", Less);
    // - small x: bracketed by its series, with several terms
    test(
        "1/1000",
        100,
        Floor,
        "0.0010000001666666750000001984127008",
        "0x0.004189380307278af506711800d0#100",
        Less,
    );
    test(
        "1/1000",
        100,
        Ceiling,
        "0.0010000001666666750000001984127023",
        "0x0.004189380307278af506711800d8#100",
        Greater,
    );
    test(
        "1/1000",
        100,
        Nearest,
        "0.0010000001666666750000001984127008",
        "0x0.004189380307278af506711800d0#100",
        Less,
    );
    test("-1/1000000", 1, Floor, "-1.9e-6", "-0x0.00002#1", Less);
    test("-1/1000000", 1, Ceiling, "-9.5e-7", "-0x0.00001#1", Greater);
    test("-1/1000000", 1, Nearest, "-9.5e-7", "-0x0.00001#1", Greater);
    test(
        "-1/1000000",
        10,
        Floor,
        "-1.0002e-6",
        "-0x0.000010c8#10",
        Less,
    );
    test(
        "-1/1000000",
        10,
        Ceiling,
        "-9.9838e-7",
        "-0x0.000010c0#10",
        Greater,
    );
    test(
        "-1/1000000",
        10,
        Nearest,
        "-1.0002e-6",
        "-0x0.000010c8#10",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Floor,
        "-1.0000000000001666666666666750015e-6",
        "-0x0.000010c6f7a0b5f0a04657c054111a#100",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Ceiling,
        "-1.0000000000001666666666666750000e-6",
        "-0x0.000010c6f7a0b5f0a04657c0541118#100",
        Greater,
    );
    test(
        "-1/1000000",
        100,
        Nearest,
        "-1.0000000000001666666666666750000e-6",
        "-0x0.000010c6f7a0b5f0a04657c0541118#100",
        Greater,
    );
    test(
        "1/100000000000000000000",
        1,
        Floor,
        "6.8e-21",
        "0x2.0E-17#1",
        Less,
    );
    test(
        "1/100000000000000000000",
        1,
        Ceiling,
        "1.4e-20",
        "0x4.0E-17#1",
        Greater,
    );
    test(
        "1/100000000000000000000",
        1,
        Nearest,
        "6.8e-21",
        "0x2.0E-17#1",
        Less,
    );
    test(
        "1/100000000000000000000",
        10,
        Floor,
        "9.9923e-21",
        "0x2.f3E-17#10",
        Less,
    );
    test(
        "1/100000000000000000000",
        10,
        Ceiling,
        "1.0006e-20",
        "0x2.f4E-17#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        10,
        Nearest,
        "1.0006e-20",
        "0x2.f4E-17#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Floor,
        "9.9999999999999999999999999999955e-21",
        "0x2.f394219248446baa23d2ec728E-17#100",
        Less,
    );
    test(
        "1/100000000000000000000",
        100,
        Ceiling,
        "1.0000000000000000000000000000006e-20",
        "0x2.f394219248446baa23d2ec72cE-17#100",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Nearest,
        "9.9999999999999999999999999999955e-21",
        "0x2.f394219248446baa23d2ec728E-17#100",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        1,
        Floor,
        "-3.2e-30",
        "-0x4.0E-25#1",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        1,
        Ceiling,
        "-1.6e-30",
        "-0x2.0E-25#1",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        1,
        Nearest,
        "-3.2e-30",
        "-0x4.0E-25#1",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        10,
        Floor,
        "-2.3697e-30",
        "-0x3.01E-25#10",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        10,
        Ceiling,
        "-2.3666e-30",
        "-0x3.00E-25#10",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        10,
        Nearest,
        "-2.3666e-30",
        "-0x3.00E-25#10",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Floor,
        "-2.3665827156630354162351856958508e-30",
        "-0x3.0000000000000000000000004E-25#100",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Ceiling,
        "-2.3665827156630354162351856958484e-30",
        "-0x3.0000000000000000000000000E-25#100",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Nearest,
        "-2.3665827156630354162351856958484e-30",
        "-0x3.0000000000000000000000000E-25#100",
        Greater,
    );
    test(
        "1488522235/2",
        1,
        Floor,
        "1.0e323228496",
        "0x4.0E+268435455#1",
        Less,
    );
    test("1488522235/2", 1, Ceiling, "Infinity", "Infinity", Greater);
    test(
        "1488522235/2",
        1,
        Nearest,
        "1.0e323228496",
        "0x4.0E+268435455#1",
        Less,
    );
    test(
        "1488522235/2",
        10,
        Floor,
        "1.3301e323228496",
        "0x5.12E+268435455#10",
        Less,
    );
    test(
        "1488522235/2",
        10,
        Ceiling,
        "1.3321e323228496",
        "0x5.14E+268435455#10",
        Greater,
    );
    test(
        "1488522235/2",
        10,
        Nearest,
        "1.3321e323228496",
        "0x5.14E+268435455#10",
        Greater,
    );
    // - x is exactly representable at the working precision
    test(
        "1488522235/2",
        100,
        Floor,
        "1.3315814500369112065268344141958e323228496",
        "0x5.137d0b40cdfb4457d4a570f10E+268435455#100",
        Less,
    );
    test(
        "1488522235/2",
        100,
        Ceiling,
        "1.3315814500369112065268344141975e323228496",
        "0x5.137d0b40cdfb4457d4a570f18E+268435455#100",
        Greater,
    );
    test(
        "1488522235/2",
        100,
        Nearest,
        "1.3315814500369112065268344141975e323228496",
        "0x5.137d0b40cdfb4457d4a570f18E+268435455#100",
        Greater,
    );
    test(
        "7442611177/10",
        1,
        Floor,
        "1.0e323228496",
        "0x4.0E+268435455#1",
        Less,
    );
    test("7442611177/10", 1, Ceiling, "Infinity", "Infinity", Greater);
    test("7442611177/10", 1, Nearest, "Infinity", "Infinity", Greater);
    test(
        "7442611177/10",
        10,
        Floor,
        "1.6252e323228496",
        "0x6.32E+268435455#10",
        Less,
    );
    test(
        "7442611177/10",
        10,
        Ceiling,
        "1.6272e323228496",
        "0x6.34E+268435455#10",
        Greater,
    );
    test(
        "7442611177/10",
        10,
        Nearest,
        "1.6272e323228496",
        "0x6.34E+268435455#10",
        Greater,
    );
    test(
        "7442611177/10",
        100,
        Floor,
        "1.6263972557900017291577754485045e323228496",
        "0x6.3332e349c3b727aba6fa728b0E+268435455#100",
        Less,
    );
    test(
        "7442611177/10",
        100,
        Ceiling,
        "1.6263972557900017291577754485062e323228496",
        "0x6.3332e349c3b727aba6fa728b8E+268435455#100",
        Greater,
    );
    test(
        "7442611177/10",
        100,
        Nearest,
        "1.6263972557900017291577754485062e323228496",
        "0x6.3332e349c3b727aba6fa728b8E+268435455#100",
        Greater,
    );
    // - the bracket ends round differently, so the working precision grows
    test("-7442611177/10", 1, Floor, "-Infinity", "-Infinity", Less);
    test(
        "-7442611177/10",
        1,
        Ceiling,
        "-1.0e323228496",
        "-0x4.0E+268435455#1",
        Greater,
    );
    test("-7442611177/10", 1, Nearest, "-Infinity", "-Infinity", Less);
    test(
        "-7442611177/10",
        10,
        Floor,
        "-1.6272e323228496",
        "-0x6.34E+268435455#10",
        Less,
    );
    test(
        "-7442611177/10",
        10,
        Ceiling,
        "-1.6252e323228496",
        "-0x6.32E+268435455#10",
        Greater,
    );
    test(
        "-7442611177/10",
        10,
        Nearest,
        "-1.6272e323228496",
        "-0x6.34E+268435455#10",
        Less,
    );
    test(
        "-7442611177/10",
        100,
        Floor,
        "-1.6263972557900017291577754485062e323228496",
        "-0x6.3332e349c3b727aba6fa728b8E+268435455#100",
        Less,
    );
    test(
        "-7442611177/10",
        100,
        Ceiling,
        "-1.6263972557900017291577754485045e323228496",
        "-0x6.3332e349c3b727aba6fa728b0E+268435455#100",
        Greater,
    );
    test(
        "-7442611177/10",
        100,
        Nearest,
        "-1.6263972557900017291577754485062e323228496",
        "-0x6.3332e349c3b727aba6fa728b8E+268435455#100",
        Less,
    );
    test(
        "744261118",
        1,
        Floor,
        "1.0e323228496",
        "0x4.0E+268435455#1",
        Less,
    );
    test("744261118", 1, Ceiling, "Infinity", "Infinity", Greater);
    test("744261118", 1, Nearest, "Infinity", "Infinity", Greater);
    test(
        "744261118",
        10,
        Floor,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test("744261118", 10, Ceiling, "Infinity", "Infinity", Greater);
    test("744261118", 10, Nearest, "Infinity", "Infinity", Greater);
    test(
        "744261118",
        100,
        Floor,
        "2.0985787164673876924043581168822e323228496",
        "0x7.ffffffffffffffffffffffff8E+268435455#100",
        Less,
    );
    test("744261118", 100, Ceiling, "Infinity", "Infinity", Greater);
    test("744261118", 100, Nearest, "Infinity", "Infinity", Greater);
    test("-744261118", 1, Floor, "-Infinity", "-Infinity", Less);
    test(
        "-744261118",
        1,
        Ceiling,
        "-1.0e323228496",
        "-0x4.0E+268435455#1",
        Greater,
    );
    test("-744261118", 1, Nearest, "-Infinity", "-Infinity", Less);
    test("-744261118", 10, Floor, "-Infinity", "-Infinity", Less);
    test(
        "-744261118",
        10,
        Ceiling,
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        Greater,
    );
    test("-744261118", 10, Nearest, "-Infinity", "-Infinity", Less);
    test("-744261118", 100, Floor, "-Infinity", "-Infinity", Less);
    test(
        "-744261118",
        100,
        Ceiling,
        "-2.0985787164673876924043581168822e323228496",
        "-0x7.ffffffffffffffffffffffff8E+268435455#100",
        Greater,
    );
    test("-744261118", 100, Nearest, "-Infinity", "-Infinity", Less);
    test(
        "10000000000",
        1,
        Floor,
        "1.0e323228496",
        "0x4.0E+268435455#1",
        Less,
    );
    test("10000000000", 1, Ceiling, "Infinity", "Infinity", Greater);
    test("10000000000", 1, Nearest, "Infinity", "Infinity", Greater);
    test(
        "10000000000",
        10,
        Floor,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test("10000000000", 10, Ceiling, "Infinity", "Infinity", Greater);
    test("10000000000", 10, Nearest, "Infinity", "Infinity", Greater);
    test(
        "10000000000",
        100,
        Floor,
        "2.0985787164673876924043581168822e323228496",
        "0x7.ffffffffffffffffffffffff8E+268435455#100",
        Less,
    );
    test("10000000000", 100, Ceiling, "Infinity", "Infinity", Greater);
    test("10000000000", 100, Nearest, "Infinity", "Infinity", Greater);
    test(
        "1/1000",
        100,
        Down,
        "0.0010000001666666750000001984127008",
        "0x0.004189380307278af506711800d0#100",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Down,
        "-2.3665827156630354162351856958484e-30",
        "-0x3.0000000000000000000000000E-25#100",
        Greater,
    );
    test(
        "1/1000",
        100,
        Up,
        "0.0010000001666666750000001984127023",
        "0x0.004189380307278af506711800d8#100",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Up,
        "-2.3665827156630354162351856958508e-30",
        "-0x3.0000000000000000000000004E-25#100",
        Less,
    );
    // - the first series bracket straddles a rounding boundary, so the series is refined
    test("1/65537", 2, Floor, "0.000011", "0x0.0000c#2", Less);
    test("1/65537", 2, Ceiling, "0.000015", "0x0.00010#2", Greater);
    test("1/65537", 2, Nearest, "0.000015", "0x0.00010#2", Greater);
    test("8/4194311", 2, Up, "1.9e-6", "0x0.00002#2", Greater);
    test("-8/4194311", 2, Up, "-1.9e-6", "-0x0.00002#2", Less);
}

#[test]
fn test_sinh_rational_extreme() {
    // |x| = 2^(-2^30 - 10) is too small to be a `Float`, and sinh(x) underflows
    let x = Rational::power_of_2(-(1i64 << 30) - 10);
    for (rm, out, o_out) in [
        (Floor, Float::ZERO, Less),
        (Down, Float::ZERO, Less),
        (Nearest, Float::ZERO, Less),
        (Ceiling, Float::min_positive_value_prec(10), Greater),
        (Up, Float::min_positive_value_prec(10), Greater),
    ] {
        let (c, o) = Float::sinh_rational_prec_round_ref(&x, 10, rm);
        assert_eq!(ComparableFloat(c.clone()), ComparableFloat(out));
        assert_eq!(o, o_out);
        let (c_neg, o_neg) = Float::sinh_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 sinh(x) overflows
    let x = Rational::power_of_2(1i64 << 30);
    let (c, o) = Float::sinh_rational_prec_round_ref(&x, 10, Nearest);
    assert_eq!(ComparableFloat(c), ComparableFloat(Float::INFINITY));
    assert_eq!(o, Greater);
    let (c, o) = Float::sinh_rational_prec_round(-x, 10, Ceiling);
    assert_eq!(
        ComparableFloat(c),
        ComparableFloat(-Float::max_finite_value_with_prec(10))
    );
    assert_eq!(o, Greater);
}

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

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

#[test]
#[should_panic]
fn sinh_rational_prec_round_fail_1() {
    Float::sinh_rational_prec_round(Rational::ONE, 0, Floor);
}

#[test]
#[should_panic]
fn sinh_rational_prec_round_fail_2() {
    Float::sinh_rational_prec_round(Rational::ONE, 10, Exact);
}

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

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

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

    // sinh is odd (a `Rational` has no negative zero, so x = 0 is excluded)
    if x != 0u32 {
        let (c_neg, o_neg) = Float::sinh_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_sinh_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::sinh_rational_prec_round_ref(&x, prec, rm);
            assert_eq!(ComparableFloatRef(&s), ComparableFloatRef(&c));
            assert_eq!(oo, Equal);
        }
    } else {
        assert_panic!(Float::sinh_rational_prec_round_ref(&x, prec, Exact));
    }
}

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

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

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

    let (c_alt, o_alt) = Float::sinh_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::sinh_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_sinh_rational_prec(&x, prec);
    assert_eq!(
        ComparableFloatRef(&Float::from(&rug_c)),
        ComparableFloatRef(&c)
    );
    assert_eq!(rug_o, o);

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

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

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_sinh_rational() {
    fn test<T: PrimitiveFloat>(x: &Rational, out: T)
    where
        Float: From<T> + PartialOrd<T>,
        for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
    {
        assert_eq!(
            NiceFloat(primitive_float_sinh_rational::<T>(x)),
            NiceFloat(out)
        );
    }
    let test_s = |s: &str| Rational::from_str(s).unwrap();
    test::<f32>(&test_s("0"), 0.0);
    test::<f32>(&test_s("1"), 1.1752012);
    test::<f32>(&test_s("-1"), -1.1752012);
    test::<f32>(&test_s("1/3"), 0.33954057);
    test::<f32>(&test_s("-1/3"), -0.33954057);
    test::<f32>(&test_s("22/7"), 11.563407);
    test::<f32>(&test_s("89"), 2.2448064e38);
    test::<f32>(&test_s("90"), f32::INFINITY);
    test::<f32>(&test_s("-90"), f32::NEGATIVE_INFINITY);
    test::<f32>(&test_s("710"), f32::INFINITY);
    test::<f32>(&test_s("7101/10"), f32::INFINITY);
    test::<f32>(&test_s("711"), f32::INFINITY);
    test::<f32>(&test_s("-711"), f32::NEGATIVE_INFINITY);
    test::<f32>(&test_s("10000"), f32::INFINITY);
    test::<f32>(&test_s("1/100000000000000000000"), 1.0e-20);
    test::<f32>(&test_s("-1/100000000000000000000"), -1.0e-20);
    test::<f32>(
        &test_s("1/10000000000000000000000000000000000000000"),
        1.0e-40,
    );
    test::<f32>(
        &test_s("-1/10000000000000000000000000000000000000000"),
        -1.0e-40,
    );
    test::<f32>(
        &test_s("1/100000000000000000000000000000000000000000000000000"),
        0.0,
    );
    test::<f32>(
        &test_s("-1/100000000000000000000000000000000000000000000000000"),
        -0.0,
    );

    test::<f64>(&test_s("0"), 0.0);
    test::<f64>(&test_s("1"), 1.1752011936438014);
    test::<f64>(&test_s("-1"), -1.1752011936438014);
    test::<f64>(&test_s("1/3"), 0.3395405572561501);
    test::<f64>(&test_s("-1/3"), -0.3395405572561501);
    test::<f64>(&test_s("22/7"), 11.563406494500514);
    test::<f64>(&test_s("89"), 2.2448064095871728e38);
    test::<f64>(&test_s("90"), 6.102016471589204e38);
    test::<f64>(&test_s("-90"), -6.102016471589204e38);
    test::<f64>(&test_s("710"), 1.1169973830808555e308);
    test::<f64>(&test_s("7101/10"), 1.234473023347565e308);
    test::<f64>(&test_s("711"), f64::INFINITY);
    test::<f64>(&test_s("-711"), f64::NEGATIVE_INFINITY);
    test::<f64>(&test_s("10000"), f64::INFINITY);
    test::<f64>(&test_s("1/100000000000000000000"), 1.0e-20);
    test::<f64>(&test_s("-1/100000000000000000000"), -1.0e-20);
    test::<f64>(
        &test_s("1/10000000000000000000000000000000000000000"),
        1.0e-40,
    );
    test::<f64>(
        &test_s("-1/10000000000000000000000000000000000000000"),
        -1.0e-40,
    );
    test::<f64>(
        &test_s("1/100000000000000000000000000000000000000000000000000"),
        1.0e-50,
    );
    test::<f64>(
        &test_s("-1/100000000000000000000000000000000000000000000000000"),
        -1.0e-50,
    );

    // a subnormal f64 result, and results that underflow
    let x = Rational::power_of_2(-1070i64);
    test::<f32>(&x, 0.0);
    test::<f64>(&x, 8.0e-323);
    test::<f32>(&-&x, -0.0);
    test::<f64>(&-x, -8.0e-323);
    let x = Rational::from_unsigneds(1u32, 3) >> 1100u32;
    test::<f32>(&x, 0.0);
    test::<f64>(&x, 0.0);
    test::<f32>(&-&x, -0.0);
    test::<f64>(&-x, -0.0);
    // a subnormal f32 result
    let x = Rational::from_unsigneds(1u32, 3) >> 140u32;
    test::<f32>(&x, 2.4e-43);
    test::<f64>(&x, 2.3915493791143543e-43);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_sinh_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_sinh_rational::<T>(&x);
        // the hyperbolic sine of a rational is never NaN
        assert!(!c.is_nan());
        // sinh is odd (a `Rational` has no negative zero, so x = 0 is excluded)
        if x != 0u32 {
            assert_eq!(
                NiceFloat(primitive_float_sinh_rational::<T>(&-&x)),
                NiceFloat(-c)
            );
        }
        // the result is the correctly rounded hyperbolic sine 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_sinh_rational_prec(&x, p).0)
        });
        assert_eq!(NiceFloat(rug_c), NiceFloat(c));
    });

    primitive_float_gen::<T>().test_properties(|x| {
        // The hyperbolic sine of a finite nonzero primitive float, taken through the `Rational`
        // path, matches the direct primitive-float hyperbolic sine (a `Rational` cannot carry the
        // sign of a zero).
        if x.is_finite() && x != T::ZERO {
            assert_eq!(
                NiceFloat(primitive_float_sinh_rational::<T>(&Rational::exact_from(x))),
                NiceFloat(primitive_float_sinh(x))
            );
        }
    });
}

#[test]
fn primitive_float_sinh_rational_properties() {
    apply_fn_to_primitive_floats!(primitive_float_sinh_rational_properties_helper);
}