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::{Csch, CschAssign, PowerOf2};
use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::basic::traits::{
    Infinity, NaN, NegativeInfinity, NegativeZero, One, Zero,
};
use malachite_base::num::conversion::traits::{ExactFrom, RoundingFrom};
use malachite_base::num::float::NiceFloat;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_base::rounding_modes::RoundingMode::{self, *};
use malachite_base::rounding_modes::exhaustive::exhaustive_rounding_modes;
use malachite_base::test_util::generators::{
    primitive_float_gen, unsigned_rounding_mode_pair_gen_var_3,
};
use malachite_float::float::arithmetic::csch::{
    primitive_float_csch, primitive_float_csch_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::csch::{
    rug_csch, rug_csch_prec, rug_csch_prec_round, rug_csch_rational_prec,
    rug_csch_rational_prec_round, rug_csch_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_csch_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().csch_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.csch_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.csch_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_csch_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, "Infinity", "Infinity", Equal);
    test(
        "-0.0",
        "-0x0.0",
        1,
        Nearest,
        "-Infinity",
        "-Infinity",
        Equal,
    );
    test("0.0", "0x0.0", 10, Nearest, "Infinity", "Infinity", Equal);
    // - the first Ziv iteration of 1 / sinh(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, "1.0", "0x1.0#1", Greater);
    // - the first Ziv iteration of 1 / sinh(x) rounds
    test("1.0", "0x1.0#1", 10, Floor, "0.85059", "0x0.d9c#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        10,
        Ceiling,
        "0.85156",
        "0x0.da0#10",
        Greater,
    );
    test("1.0", "0x1.0#1", 10, Nearest, "0.85059", "0x0.d9c#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        100,
        Floor,
        "0.85091812823932154513384276328642",
        "0x0.d9d5c53c5c86070b36fe901df#100",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Ceiling,
        "0.85091812823932154513384276328721",
        "0x0.d9d5c53c5c86070b36fe901e0#100",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Nearest,
        "0.85091812823932154513384276328721",
        "0x0.d9d5c53c5c86070b36fe901e0#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Floor,
        "-0.85156",
        "-0x0.da0#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Ceiling,
        "-0.85059",
        "-0x0.d9c#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Nearest,
        "-0.85059",
        "-0x0.d9c#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Down,
        "-0.85059",
        "-0x0.d9c#10",
        Greater,
    );
    test("-1.0", "-0x1.0#1", 10, Up, "-0.85156", "-0x0.da0#10", Less);
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Floor,
        "-0.85091812823932154513384276328721",
        "-0x0.d9d5c53c5c86070b36fe901e0#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Ceiling,
        "-0.85091812823932154513384276328642",
        "-0x0.d9d5c53c5c86070b36fe901df#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Nearest,
        "-0.85091812823932154513384276328721",
        "-0x0.d9d5c53c5c86070b36fe901e0#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Down,
        "-0.85091812823932154513384276328642",
        "-0x0.d9d5c53c5c86070b36fe901df#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Up,
        "-0.85091812823932154513384276328721",
        "-0x0.d9d5c53c5c86070b36fe901e0#100",
        Less,
    );
    test("0.50", "0x0.8#1", 10, Floor, "1.9180", "0x1.eb0#10", Less);
    test(
        "0.50",
        "0x0.8#1",
        10,
        Ceiling,
        "1.9199",
        "0x1.eb8#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        10,
        Nearest,
        "1.9199",
        "0x1.eb8#10",
        Greater,
    );
    test("0.50", "0x0.8#1", 10, Down, "1.9180", "0x1.eb0#10", Less);
    test("0.50", "0x0.8#1", 10, Up, "1.9199", "0x1.eb8#10", Greater);
    test(
        "0.50",
        "0x0.8#1",
        100,
        Floor,
        "1.9190347513349437194922028787267",
        "0x1.eb45dc88defecfc84d1dc4fd0#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Ceiling,
        "1.9190347513349437194922028787282",
        "0x1.eb45dc88defecfc84d1dc4fd2#100",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Nearest,
        "1.9190347513349437194922028787267",
        "0x1.eb45dc88defecfc84d1dc4fd0#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Down,
        "1.9190347513349437194922028787267",
        "0x1.eb45dc88defecfc84d1dc4fd0#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Up,
        "1.9190347513349437194922028787282",
        "0x1.eb45dc88defecfc84d1dc4fd2#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Floor,
        "2.9414",
        "0x2.f1#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Ceiling,
        "2.9453",
        "0x2.f2#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Nearest,
        "2.9453",
        "0x2.f2#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Down,
        "2.9414",
        "0x2.f1#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Up,
        "2.9453",
        "0x2.f2#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Floor,
        "2.9451562666948143476455860034919",
        "0x2.f1f5c2d7104d708fac22e7c68#100",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Ceiling,
        "2.9451562666948143476455860034951",
        "0x2.f1f5c2d7104d708fac22e7c6c#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Nearest,
        "2.9451562666948143476455860034951",
        "0x2.f1f5c2d7104d708fac22e7c6c#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Down,
        "2.9451562666948143476455860034919",
        "0x2.f1f5c2d7104d708fac22e7c68#100",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Up,
        "2.9451562666948143476455860034951",
        "0x2.f1f5c2d7104d708fac22e7c6c#100",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Floor, "0.27539", "0x0.468#10", Less);
    test(
        "2.0",
        "0x2.0#2",
        10,
        Ceiling,
        "0.27588",
        "0x0.46a#10",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#2",
        10,
        Nearest,
        "0.27588",
        "0x0.46a#10",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Down, "0.27539", "0x0.468#10", Less);
    test("2.0", "0x2.0#2", 10, Up, "0.27588", "0x0.46a#10", Greater);
    test(
        "2.0",
        "0x2.0#2",
        100,
        Floor,
        "0.27572056477178320775835148216293",
        "0x0.46959f78878a98f9a7d213a2d8#100",
        Less,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Ceiling,
        "0.27572056477178320775835148216332",
        "0x0.46959f78878a98f9a7d213a2e0#100",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Nearest,
        "0.27572056477178320775835148216293",
        "0x0.46959f78878a98f9a7d213a2d8#100",
        Less,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Down,
        "0.27572056477178320775835148216293",
        "0x0.46959f78878a98f9a7d213a2d8#100",
        Less,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Up,
        "0.27572056477178320775835148216332",
        "0x0.46959f78878a98f9a7d213a2e0#100",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Floor,
        "-0.000090837",
        "-0x0.0005f4#10",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Ceiling,
        "-0.000090718",
        "-0x0.0005f2#10",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Nearest,
        "-0.000090837",
        "-0x0.0005f4#10",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Down,
        "-0.000090718",
        "-0x0.0005f2#10",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        10,
        Up,
        "-0.000090837",
        "-0x0.0005f4#10",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Floor,
        "-0.000090799859712122162833736493607358",
        "-0x0.0005f35e6d8dcce82e421fdc56470#100",
        Less,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Ceiling,
        "-0.000090799859712122162833736493607262",
        "-0x0.0005f35e6d8dcce82e421fdc56468#100",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Nearest,
        "-0.000090799859712122162833736493607262",
        "-0x0.0005f35e6d8dcce82e421fdc56468#100",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Down,
        "-0.000090799859712122162833736493607262",
        "-0x0.0005f35e6d8dcce82e421fdc56468#100",
        Greater,
    );
    test(
        "-10.0",
        "-0xa.0#4",
        100,
        Up,
        "-0.000090799859712122162833736493607358",
        "-0x0.0005f35e6d8dcce82e421fdc56470#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Floor,
        "0.086548",
        "0x0.1628#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Ceiling,
        "0.086670",
        "0x0.1630#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Nearest,
        "0.086548",
        "0x0.1628#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Down,
        "0.086548",
        "0x0.1628#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Up,
        "0.086670",
        "0x0.1630#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Floor,
        "0.086589537530046941824099701714064",
        "0x0.162abb5fde086fc5c9e34a86f4#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Ceiling,
        "0.086589537530046941824099701714162",
        "0x0.162abb5fde086fc5c9e34a86f6#100",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Nearest,
        "0.086589537530046941824099701714162",
        "0x0.162abb5fde086fc5c9e34a86f6#100",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Down,
        "0.086589537530046941824099701714064",
        "0x0.162abb5fde086fc5c9e34a86f4#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Up,
        "0.086589537530046941824099701714162",
        "0x0.162abb5fde086fc5c9e34a86f6#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,
    );
    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,
    );
    // - x <= -2^29: the scaled path, with a negative result
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Floor,
        "-7.5107e-323228497",
        "-0x3.27E-268435456#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Ceiling,
        "-7.5014e-323228497",
        "-0x3.26E-268435456#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Nearest,
        "-7.5107e-323228497",
        "-0x3.27E-268435456#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Down,
        "-7.5014e-323228497",
        "-0x3.26E-268435456#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Up,
        "-7.5107e-323228497",
        "-0x3.27E-268435456#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Floor,
        "-7.5098673083218467310380527281592e-323228497",
        "-0x3.26ea18e02da8f8a2632086efcE-268435456#100",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Ceiling,
        "-7.5098673083218467310380527281516e-323228497",
        "-0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Nearest,
        "-7.5098673083218467310380527281516e-323228497",
        "-0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Down,
        "-7.5098673083218467310380527281516e-323228497",
        "-0x3.26ea18e02da8f8a2632086ef8E-268435456#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Up,
        "-7.5098673083218467310380527281592e-323228497",
        "-0x3.26ea18e02da8f8a2632086efcE-268435456#100",
        Less,
    );
    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,
    );
    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,
        "-2.3826e-323228497",
        "-0x1.000E-268435456#10",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Ceiling,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Nearest,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Down,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        10,
        Up,
        "-2.3826e-323228497",
        "-0x1.000E-268435456#10",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Floor,
        "-2.3825649048879510732161697817327e-323228497",
        "-0x1.0000000000000000000000000E-268435456#100",
        Less,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Ceiling,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Nearest,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Down,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "-744261119.59961",
        "-0x2c5c85ff.998#40",
        100,
        Up,
        "-2.3825649048879510732161697817327e-323228497",
        "-0x1.0000000000000000000000000E-268435456#100",
        Less,
    );
    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: |csch(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,
        "1023.0",
        "0x3ff.0#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Floor,
        "-1024.0",
        "-0x400.0#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Ceiling,
        "1024.0",
        "0x400.0#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Ceiling,
        "-1023.0",
        "-0x3ff.0#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Nearest,
        "1024.0",
        "0x400.0#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Nearest,
        "-1024.0",
        "-0x400.0#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Down,
        "1023.0",
        "0x3ff.0#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Down,
        "-1023.0",
        "-0x3ff.0#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Up,
        "1024.0",
        "0x400.0#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Up,
        "-1024.0",
        "-0x400.0#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Floor,
        "1023.9998372396014423815743004207",
        "0x3ff.fff55555693e93c7a725540#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Floor,
        "-1023.9998372396014423815743004215",
        "-0x3ff.fff55555693e93c7a725544#100",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Ceiling,
        "1023.9998372396014423815743004215",
        "0x3ff.fff55555693e93c7a725544#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Ceiling,
        "-1023.9998372396014423815743004207",
        "-0x3ff.fff55555693e93c7a725540#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Nearest,
        "1023.9998372396014423815743004207",
        "0x3ff.fff55555693e93c7a725540#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Nearest,
        "-1023.9998372396014423815743004207",
        "-0x3ff.fff55555693e93c7a725540#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Down,
        "1023.9998372396014423815743004207",
        "0x3ff.fff55555693e93c7a725540#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Down,
        "-1023.9998372396014423815743004207",
        "-0x3ff.fff55555693e93c7a725540#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Up,
        "1023.9998372396014423815743004215",
        "0x3ff.fff55555693e93c7a725544#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Up,
        "-1023.9998372396014423815743004215",
        "-0x3ff.fff55555693e93c7a725544#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Floor,
        "1125899906842623.9999999999999991",
        "0x3ffffffffffff.ffffffffffffc#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Floor,
        "-1125899906842624.0000000000000000",
        "-0x4000000000000.0000000000000#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Ceiling,
        "1125899906842624.0000000000000000",
        "0x4000000000000.0000000000000#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Ceiling,
        "-1125899906842623.9999999999999991",
        "-0x3ffffffffffff.ffffffffffffc#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Nearest,
        "1125899906842624.0000000000000000",
        "0x4000000000000.0000000000000#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Nearest,
        "-1125899906842624.0000000000000000",
        "-0x4000000000000.0000000000000#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Down,
        "1125899906842623.9999999999999991",
        "0x3ffffffffffff.ffffffffffffc#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Down,
        "-1125899906842623.9999999999999991",
        "-0x3ffffffffffff.ffffffffffffc#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Up,
        "1125899906842624.0000000000000000",
        "0x4000000000000.0000000000000#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Up,
        "-1125899906842624.0000000000000000",
        "-0x4000000000000.0000000000000#100",
        Less,
    );
    // - x is tiny and 1/x is exact: csch(x) rounds to the predecessor of 1/x
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Floor,
        "1.2664e30",
        "0xf.fcE+24#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Floor,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Less,
    );
    // - x is tiny and 1/x is exact: csch(x) rounds to 1/x
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Ceiling,
        "1.2677e30",
        "0x1.000E+25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Ceiling,
        "-1.2664e30",
        "-0xf.fcE+24#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Nearest,
        "1.2677e30",
        "0x1.000E+25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Nearest,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Down,
        "1.2664e30",
        "0xf.fcE+24#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Down,
        "-1.2664e30",
        "-0xf.fcE+24#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Up,
        "1.2677e30",
        "0x1.000E+25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Up,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Floor,
        "1267650600228229401496703205375.9999999999999999999999999999998685231824631646990980452391\
        193",
        "0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555555#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Floor,
        "-1267650600228229401496703205375.999999999999999999999999999999868523182463164699098045239\
        1200",
        "-0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555556#300",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Ceiling,
        "1267650600228229401496703205375.9999999999999999999999999999998685231824631646990980452391\
        200",
        "0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555556#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Ceiling,
        "-1267650600228229401496703205375.999999999999999999999999999999868523182463164699098045239\
        1193",
        "-0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555555#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Nearest,
        "1267650600228229401496703205375.9999999999999999999999999999998685231824631646990980452391\
        193",
        "0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555555#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Nearest,
        "-1267650600228229401496703205375.999999999999999999999999999999868523182463164699098045239\
        1193",
        "-0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555555#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Down,
        "1267650600228229401496703205375.9999999999999999999999999999998685231824631646990980452391\
        193",
        "0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555555#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Down,
        "-1267650600228229401496703205375.999999999999999999999999999999868523182463164699098045239\
        1193",
        "-0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555555#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Up,
        "1267650600228229401496703205375.9999999999999999999999999999998685231824631646990980452391\
        200",
        "0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555556#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Up,
        "-1267650600228229401496703205375.999999999999999999999999999999868523182463164699098045239\
        1200",
        "-0xfffffffffffffffffffffffff.fffffffffffffffffffffffffd555555555555555555555556#300",
        Less,
    );
    // - x is tiny and 1/x is inexact: rounding 1/x settles csch(x)
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Floor,
        "2.09857871646738769229e323228496",
        "0x7.fffffffffffffff8E+268435455#64",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Down,
        "2.09857871646738769229e323228496",
        "0x7.fffffffffffffff8E+268435455#64",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    // - an end of the scaled bracket is exact after rounding
    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(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Floor,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Ceiling,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Down,
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Up,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        10,
        Nearest,
        "Infinity",
        "Infinity",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Floor,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Ceiling,
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Down,
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Up,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Nearest,
        "-Infinity",
        "-Infinity",
        Less,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Floor,
        "1.0483e323228496",
        "0x3.ffE+268435455#10",
        Less,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Ceiling,
        "1.0493e323228496",
        "0x4.00E+268435455#10",
        Greater,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Down,
        "1.0483e323228496",
        "0x3.ffE+268435455#10",
        Less,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Up,
        "1.0493e323228496",
        "0x4.00E+268435455#10",
        Greater,
    );
    test(
        "9.5e-323228497",
        "0x4.0E-268435456#1",
        10,
        Nearest,
        "1.0493e323228496",
        "0x4.00E+268435455#10",
        Greater,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Floor,
        "-1.0493e323228496",
        "-0x4.00E+268435455#10",
        Less,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Ceiling,
        "-1.0483e323228496",
        "-0x3.ffE+268435455#10",
        Greater,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Down,
        "-1.0483e323228496",
        "-0x3.ffE+268435455#10",
        Greater,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Up,
        "-1.0493e323228496",
        "-0x4.00E+268435455#10",
        Less,
    );
    test(
        "-9.5e-323228497",
        "-0x4.0E-268435456#1",
        10,
        Nearest,
        "-1.0493e323228496",
        "-0x4.00E+268435455#10",
        Less,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Floor,
        "-2.3826e-323228497",
        "-0x1.000E-268435456#10",
        Less,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Ceiling,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Down,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Up,
        "-2.3826e-323228497",
        "-0x1.000E-268435456#10",
        Less,
    );
    test(
        "-744261120.00",
        "-0x2c5c8600.0#32",
        10,
        Nearest,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "2.4e-30",
        "0x3.0E-25#2",
        10,
        Floor,
        "4.2214e29",
        "0x5.54E+24#10",
        Less,
    );
    test(
        "0.000976562500000000000000",
        "0x0.0040000000000000000#64",
        10,
        Floor,
        "1023.0",
        "0x3ff.0#10",
        Less,
    );
    test(
        "-0.000976562500000000000000",
        "-0x0.0040000000000000000#64",
        10,
        Floor,
        "-1024.0",
        "-0x400.0#10",
        Less,
    );
    test(
        "2.4e-30",
        "0x3.0E-25#2",
        10,
        Ceiling,
        "4.2276e29",
        "0x5.56E+24#10",
        Greater,
    );
    test(
        "0.000976562500000000000000",
        "0x0.0040000000000000000#64",
        10,
        Ceiling,
        "1024.0",
        "0x400.0#10",
        Greater,
    );
    test(
        "-0.000976562500000000000000",
        "-0x0.0040000000000000000#64",
        10,
        Ceiling,
        "-1023.0",
        "-0x3ff.0#10",
        Greater,
    );
    test(
        "2.4e-30",
        "0x3.0E-25#2",
        10,
        Nearest,
        "4.2276e29",
        "0x5.56E+24#10",
        Greater,
    );
    test(
        "0.000976562500000000000000",
        "0x0.0040000000000000000#64",
        10,
        Nearest,
        "1024.0",
        "0x400.0#10",
        Greater,
    );
    test(
        "-0.000976562500000000000000",
        "-0x0.0040000000000000000#64",
        10,
        Nearest,
        "-1024.0",
        "-0x400.0#10",
        Less,
    );
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#[test]
fn csch_prec_properties() {
    float_unsigned_pair_gen_var_1().test_properties(|(x, prec)| {
        let (c, o) = x.clone().csch_prec(prec);
        assert!(c.is_valid());
        let (c_alt, o_alt) = x.csch_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.csch_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.csch_prec_round_ref(prec, Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

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

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

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

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

        assert_eq!(ComparableFloatRef(&(-&x).csch()), 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_csch() {
    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_csch(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, f32::INFINITY);
    test::<f32>(-0.0, f32::NEGATIVE_INFINITY);
    test::<f32>(1.0, 0.8509181);
    test::<f32>(-1.0, -0.8509181);
    test::<f32>(0.5, 1.9190347);
    test::<f32>(2.0, 0.27572057);
    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, 1.0e20);
    test::<f32>(1.0e-38, 1.0000001e38);
    test::<f32>(3.0e-39, 3.3333327e38);
    test::<f32>(1.0e-45, f32::INFINITY);
    test::<f32>(3.4028235e38, 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, f64::INFINITY);
    test::<f64>(-0.0, f64::NEGATIVE_INFINITY);
    test::<f64>(1.0, 0.8509181282393216);
    test::<f64>(-1.0, -0.8509181282393216);
    test::<f64>(0.5, 1.9190347513349437);
    test::<f64>(2.0, 0.2757205647717832);
    test::<f64>(10.0, 0.00009079985971212217);
    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, 1.0e200);
    test::<f64>(1.0e-308, 1.0e308);
    test::<f64>(5.0e-309, f64::INFINITY);
    test::<f64>(5.0e-324, f64::INFINITY);
    test::<f64>(1.7976931348623157e308, 0.0);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_csch_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_csch(x);
        // csch is NaN exactly for NaN inputs, and otherwise has the sign of its input
        assert_eq!(c.is_nan(), x.is_nan());
        if !x.is_nan() {
            assert_eq!(c.is_sign_positive(), x.is_sign_positive());
            // csch is odd
            assert_eq!(NiceFloat(primitive_float_csch(-x)), NiceFloat(-c));
        }
        if x.is_finite() {
            // the result is the correctly rounded hyperbolic cosecant 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_csch_prec(&rug::Float::exact_from(&Float::from(x)), p).0,
                )
            });
            assert_eq!(NiceFloat(rug_c), NiceFloat(c));
        }
    });
}

#[test]
fn primitive_float_csch_properties() {
    apply_fn_to_primitive_floats!(primitive_float_csch_properties_helper);
}

#[test]
fn test_csch_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::csch_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::csch_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_csch_rational_prec_round(&x, prec, rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    };
    test("0", 1, Down, "Infinity", "Infinity", Equal);
    test("0", 10, Down, "Infinity", "Infinity", Equal);
    test("0", 1, Up, "Infinity", "Infinity", Equal);
    test("0", 10, Up, "Infinity", "Infinity", Equal);
    test("0", 1, Floor, "Infinity", "Infinity", Equal);
    test("0", 10, Floor, "Infinity", "Infinity", Equal);
    test("0", 1, Ceiling, "Infinity", "Infinity", Equal);
    test("0", 10, Ceiling, "Infinity", "Infinity", Equal);
    test("0", 1, Nearest, "Infinity", "Infinity", Equal);
    test("0", 10, Nearest, "Infinity", "Infinity", Equal);
    test("0", 1, Exact, "Infinity", "Infinity", Equal);
    test("0", 10, Exact, "Infinity", "Infinity", Equal);
    // - the first bracket of x rounds the same way at both ends
    test("3/5", 1, Floor, "1.0", "0x1.0#1", Less);
    test("3/5", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("3/5", 1, Nearest, "2.0", "0x2.0#1", Greater);
    test("3/5", 10, Floor, "1.5703", "0x1.920#10", Less);
    test("3/5", 10, Ceiling, "1.5723", "0x1.928#10", Greater);
    test("3/5", 10, Nearest, "1.5703", "0x1.920#10", Less);
    test(
        "3/5",
        100,
        Floor,
        "1.5707129089350753418197932853841",
        "0x1.921a3dbf47fb12065464e2540#100",
        Less,
    );
    test(
        "3/5",
        100,
        Ceiling,
        "1.5707129089350753418197932853856",
        "0x1.921a3dbf47fb12065464e2542#100",
        Greater,
    );
    test(
        "3/5",
        100,
        Nearest,
        "1.5707129089350753418197932853856",
        "0x1.921a3dbf47fb12065464e2542#100",
        Greater,
    );
    test("-3/5", 1, Floor, "-2.0", "-0x2.0#1", Less);
    test("-3/5", 1, Ceiling, "-1.0", "-0x1.0#1", Greater);
    test("-3/5", 1, Nearest, "-2.0", "-0x2.0#1", Less);
    test("-3/5", 10, Floor, "-1.5723", "-0x1.928#10", Less);
    test("-3/5", 10, Ceiling, "-1.5703", "-0x1.920#10", Greater);
    test("-3/5", 10, Nearest, "-1.5703", "-0x1.920#10", Greater);
    test(
        "-3/5",
        100,
        Floor,
        "-1.5707129089350753418197932853856",
        "-0x1.921a3dbf47fb12065464e2542#100",
        Less,
    );
    test(
        "-3/5",
        100,
        Ceiling,
        "-1.5707129089350753418197932853841",
        "-0x1.921a3dbf47fb12065464e2540#100",
        Greater,
    );
    test(
        "-3/5",
        100,
        Nearest,
        "-1.5707129089350753418197932853856",
        "-0x1.921a3dbf47fb12065464e2542#100",
        Less,
    );
    test("1/3", 1, Floor, "2.0", "0x2.0#1", Less);
    test("1/3", 1, Ceiling, "4.0", "0x4.0#1", Greater);
    test("1/3", 1, Nearest, "2.0", "0x2.0#1", Less);
    test("1/3", 10, Floor, "2.9414", "0x2.f1#10", Less);
    test("1/3", 10, Ceiling, "2.9453", "0x2.f2#10", Greater);
    test("1/3", 10, Nearest, "2.9453", "0x2.f2#10", Greater);
    test(
        "1/3",
        100,
        Floor,
        "2.9451562666948143476455860034951",
        "0x2.f1f5c2d7104d708fac22e7c6c#100",
        Less,
    );
    test(
        "1/3",
        100,
        Ceiling,
        "2.9451562666948143476455860034982",
        "0x2.f1f5c2d7104d708fac22e7c70#100",
        Greater,
    );
    test(
        "1/3",
        100,
        Nearest,
        "2.9451562666948143476455860034951",
        "0x2.f1f5c2d7104d708fac22e7c6c#100",
        Less,
    );
    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, "0.086426", "0x0.1620#10", Less);
    test("22/7", 10, Ceiling, "0.086548", "0x0.1628#10", Greater);
    test("22/7", 10, Nearest, "0.086426", "0x0.1620#10", Less);
    test(
        "22/7",
        100,
        Floor,
        "0.086479706518627875891032052705382",
        "0x0.162388b743e325b1326cd6dab8#100",
        Less,
    );
    test(
        "22/7",
        100,
        Ceiling,
        "0.086479706518627875891032052705481",
        "0x0.162388b743e325b1326cd6daba#100",
        Greater,
    );
    test(
        "22/7",
        100,
        Nearest,
        "0.086479706518627875891032052705382",
        "0x0.162388b743e325b1326cd6dab8#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, "-9.0e-44", "-0x2.0E-36#1", Less);
    test("-100", 1, Ceiling, "-4.5e-44", "-0x1.0E-36#1", Greater);
    test("-100", 1, Nearest, "-9.0e-44", "-0x2.0E-36#1", Less);
    test("-100", 10, Floor, "-7.4444e-44", "-0x1.a90E-36#10", Less);
    test(
        "-100",
        10,
        Ceiling,
        "-7.4356e-44",
        "-0x1.a88E-36#10",
        Greater,
    );
    test("-100", 10, Nearest, "-7.4444e-44", "-0x1.a90E-36#10", Less);
    test(
        "-100",
        100,
        Floor,
        "-7.4401519520416719259193916077287e-44",
        "-0x1.a8c1f14e2af5caf3dd91375c8E-36#100",
        Less,
    );
    test(
        "-100",
        100,
        Ceiling,
        "-7.4401519520416719259193916077216e-44",
        "-0x1.a8c1f14e2af5caf3dd91375c6E-36#100",
        Greater,
    );
    test(
        "-100",
        100,
        Nearest,
        "-7.4401519520416719259193916077287e-44",
        "-0x1.a8c1f14e2af5caf3dd91375c8E-36#100",
        Less,
    );
    // - tiny x: the rounding of 1/x, nudged toward zero
    test("1/1000", 1, Floor, "5.1e2", "0x2.0E+2#1", Less);
    test("1/1000", 1, Ceiling, "1.0e3", "0x4.0E+2#1", Greater);
    test("1/1000", 1, Nearest, "1.0e3", "0x4.0E+2#1", Greater);
    // - tiny x with 1/x exactly representable: the result steps toward zero
    test("1/1000", 10, Floor, "999.00", "0x3e7.0#10", Less);
    test("1/1000", 10, Ceiling, "1000.0", "0x3e8.0#10", Greater);
    test("1/1000", 10, Nearest, "1000.0", "0x3e8.0#10", Greater);
    // - small x: bracketed by the reciprocals of series bounds on sinh(x)
    test(
        "1/1000",
        100,
        Floor,
        "999.99983333335277777572751343712",
        "0x3e7.fff513cc336aae69e615430#100",
        Less,
    );
    test(
        "1/1000",
        100,
        Ceiling,
        "999.99983333335277777572751343793",
        "0x3e7.fff513cc336aae69e615434#100",
        Greater,
    );
    test(
        "1/1000",
        100,
        Nearest,
        "999.99983333335277777572751343712",
        "0x3e7.fff513cc336aae69e615430#100",
        Less,
    );
    test("-1/1000000", 1, Floor, "-1.0e6", "-0x1.0E+5#1", Less);
    test("-1/1000000", 1, Ceiling, "-5.2e5", "-0x8.0E+4#1", Greater);
    test("-1/1000000", 1, Nearest, "-1.0e6", "-0x1.0E+5#1", Less);
    test("-1/1000000", 10, Floor, "-1.0004e6", "-0xf.44E+4#10", Less);
    test(
        "-1/1000000",
        10,
        Ceiling,
        "-9.9942e5",
        "-0xf.40E+4#10",
        Greater,
    );
    test(
        "-1/1000000",
        10,
        Nearest,
        "-1.0004e6",
        "-0xf.44E+4#10",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Floor,
        "-999999.99999983333333333335277852",
        "-0xf423f.fffffd342c0fe1ae19a0#100",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Ceiling,
        "-999999.99999983333333333335277769",
        "-0xf423f.fffffd342c0fe1ae199f#100",
        Greater,
    );
    test(
        "-1/1000000",
        100,
        Nearest,
        "-999999.99999983333333333335277769",
        "-0xf423f.fffffd342c0fe1ae199f#100",
        Greater,
    );
    test(
        "1/100000000000000000000",
        1,
        Floor,
        "7.4e19",
        "0x4.0E+16#1",
        Less,
    );
    test(
        "1/100000000000000000000",
        1,
        Ceiling,
        "1.5e20",
        "0x8.0E+16#1",
        Greater,
    );
    test(
        "1/100000000000000000000",
        1,
        Nearest,
        "7.4e19",
        "0x4.0E+16#1",
        Less,
    );
    test(
        "1/100000000000000000000",
        10,
        Floor,
        "9.9872e19",
        "0x5.6aE+16#10",
        Less,
    );
    test(
        "1/100000000000000000000",
        10,
        Ceiling,
        "1.0002e20",
        "0x5.6cE+16#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        10,
        Nearest,
        "1.0002e20",
        "0x5.6cE+16#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Floor,
        "99999999999999999999.999999999884",
        "0x56bc75e2d630fffff.ffffffff8#100",
        Less,
    );
    test(
        "1/100000000000000000000",
        100,
        Ceiling,
        "100000000000000000000.00000000000",
        "0x56bc75e2d63100000.000000000#100",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Nearest,
        "100000000000000000000.00000000000",
        "0x56bc75e2d63100000.000000000#100",
        Greater,
    );
    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,
    );
    // - the bracket ends round differently, so the working precision grows
    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,
        "-4.8e-323228497",
        "-0x2.0E-268435456#1",
        Less,
    );
    test(
        "-7442611185/10",
        1,
        Ceiling,
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        Greater,
    );
    test(
        "-7442611185/10",
        1,
        Nearest,
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        Greater,
    );
    test(
        "-7442611185/10",
        10,
        Floor,
        "-2.7641e-323228497",
        "-0x1.290E-268435456#10",
        Less,
    );
    test(
        "-7442611185/10",
        10,
        Ceiling,
        "-2.7595e-323228497",
        "-0x1.288E-268435456#10",
        Greater,
    );
    test(
        "-7442611185/10",
        10,
        Nearest,
        "-2.7641e-323228497",
        "-0x1.290E-268435456#10",
        Less,
    );
    test(
        "-7442611185/10",
        100,
        Floor,
        "-2.7627257886571247097149806988033e-323228497",
        "-0x1.28d8e45434c7216121ffbfc58E-268435456#100",
        Less,
    );
    test(
        "-7442611185/10",
        100,
        Ceiling,
        "-2.7627257886571247097149806987996e-323228497",
        "-0x1.28d8e45434c7216121ffbfc56E-268435456#100",
        Greater,
    );
    test(
        "-7442611185/10",
        100,
        Nearest,
        "-2.7627257886571247097149806988033e-323228497",
        "-0x1.28d8e45434c7216121ffbfc58E-268435456#100",
        Less,
    );
    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: |csch(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,
        "999.99983333335277777572751343712",
        "0x3e7.fff513cc336aae69e615430#100",
        Less,
    );
    test("744261119", 100, Down, "0.0", "0x0.0", Less);
    test(
        "1/1000",
        100,
        Up,
        "999.99983333335277777572751343793",
        "0x3e7.fff513cc336aae69e615434#100",
        Greater,
    );
    test(
        "744261119",
        100,
        Up,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test("2/13", 7, Floor, "6.438", "0x6.7#7", Less);
    test("2/13", 7, Ceiling, "6.500", "0x6.8#7", Greater);
    test("2/13", 7, Nearest, "6.500", "0x6.8#7", Greater);
    test(
        "1/1267650600228229401496703205376",
        10,
        Floor,
        "1.2664e30",
        "0xf.fcE+24#10",
        Less,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Floor,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Less,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Floor,
        "3.8030e30",
        "0x3.00E+25#10",
        Less,
    );
    test(
        "1/1267650600228229401496703205377",
        100,
        Floor,
        "1267650600228229401496703205376.0",
        "0x10000000000000000000000000.0#100",
        Less,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Floor,
        "-1267650600228229401496703205378.0",
        "-0x10000000000000000000000002.0#100",
        Less,
    );
    test("-22/7", 20, Floor, "-0.086479783", "-0x0.16238a#20", Less);
    test("-1/1000", 10, Floor, "-1000.0", "-0x3e8.0#10", Less);
    test(
        "-744261120",
        10,
        Floor,
        "-2.3826e-323228497",
        "-0x1.000E-268435456#10",
        Less,
    );
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Ceiling,
        "1.2677e30",
        "0x1.000E+25#10",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Ceiling,
        "-1.2664e30",
        "-0xf.fcE+24#10",
        Greater,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Ceiling,
        "3.8079e30",
        "0x3.01E+25#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205377",
        100,
        Ceiling,
        "1267650600228229401496703205378.0",
        "0x10000000000000000000000002.0#100",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Ceiling,
        "-1267650600228229401496703205376.0",
        "-0x10000000000000000000000000.0#100",
        Greater,
    );
    test(
        "-22/7",
        20,
        Ceiling,
        "-0.086479664",
        "-0x0.162388#20",
        Greater,
    );
    test("-1/1000", 10, Ceiling, "-999.00", "-0x3e7.0#10", Greater);
    test("-744261120", 10, Ceiling, "-0.0", "-0x0.0", Greater);
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Ceiling,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Down,
        "1.2664e30",
        "0xf.fcE+24#10",
        Less,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Down,
        "-1.2664e30",
        "-0xf.fcE+24#10",
        Greater,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Down,
        "3.8030e30",
        "0x3.00E+25#10",
        Less,
    );
    test(
        "1/1267650600228229401496703205377",
        100,
        Down,
        "1267650600228229401496703205376.0",
        "0x10000000000000000000000000.0#100",
        Less,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Down,
        "-1267650600228229401496703205376.0",
        "-0x10000000000000000000000000.0#100",
        Greater,
    );
    test(
        "1/3",
        100,
        Down,
        "2.9451562666948143476455860034951",
        "0x2.f1f5c2d7104d708fac22e7c6c#100",
        Less,
    );
    test("-22/7", 20, Down, "-0.086479664", "-0x0.162388#20", Greater);
    test("1/1000", 10, Down, "999.00", "0x3e7.0#10", Less);
    test("-1/1000", 10, Down, "-999.00", "-0x3e7.0#10", Greater);
    test("744261120", 10, Down, "0.0", "0x0.0", Less);
    test("-744261120", 10, Down, "-0.0", "-0x0.0", Greater);
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Down,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Up,
        "1.2677e30",
        "0x1.000E+25#10",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Up,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Less,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Up,
        "3.8079e30",
        "0x3.01E+25#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205377",
        100,
        Up,
        "1267650600228229401496703205378.0",
        "0x10000000000000000000000002.0#100",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Up,
        "-1267650600228229401496703205378.0",
        "-0x10000000000000000000000002.0#100",
        Less,
    );
    test(
        "1/3",
        100,
        Up,
        "2.9451562666948143476455860034982",
        "0x2.f1f5c2d7104d708fac22e7c70#100",
        Greater,
    );
    test("-22/7", 20, Up, "-0.086479783", "-0x0.16238a#20", Less);
    test("1/1000", 10, Up, "1000.0", "0x3e8.0#10", Greater);
    test("-1/1000", 10, Up, "-1000.0", "-0x3e8.0#10", Less);
    test(
        "744261120",
        10,
        Up,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "-744261120",
        10,
        Up,
        "-2.3826e-323228497",
        "-0x1.000E-268435456#10",
        Less,
    );
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Up,
        "2.3826e-323228497",
        "0x1.000E-268435456#10",
        Greater,
    );
    test(
        "1/1267650600228229401496703205376",
        10,
        Nearest,
        "1.2677e30",
        "0x1.000E+25#10",
        Greater,
    );
    test(
        "-1/1267650600228229401496703205376",
        10,
        Nearest,
        "-1.2677e30",
        "-0x1.000E+25#10",
        Less,
    );
    test(
        "1/3802951800684688204490109616129",
        10,
        Nearest,
        "3.8030e30",
        "0x3.00E+25#10",
        Less,
    );
    // - tiny x with 1/x a Nearest tie: the neighbor toward zero wins
    test(
        "1/1267650600228229401496703205377",
        100,
        Nearest,
        "1267650600228229401496703205376.0",
        "0x10000000000000000000000000.0#100",
        Less,
    );
    test(
        "-1/1267650600228229401496703205377",
        100,
        Nearest,
        "-1267650600228229401496703205376.0",
        "-0x10000000000000000000000000.0#100",
        Greater,
    );
    test(
        "-22/7",
        20,
        Nearest,
        "-0.086479664",
        "-0x0.162388#20",
        Greater,
    );
    test("-1/1000", 10, Nearest, "-1000.0", "-0x3e8.0#10", Less);
    test("-744261120", 10, Nearest, "-0.0", "-0x0.0", Greater);
    test(
        "100000000000000000000000000000000000000000000000000",
        10,
        Nearest,
        "0.0",
        "0x0.0",
        Less,
    );
    // - the first series bracket straddles a rounding boundary, so the series is refined
    test(
        "3/257",
        40,
        Floor,
        "85.664721172303",
        "0x55.aa2b2ab00#40",
        Less,
    );
    test(
        "3/257",
        40,
        Ceiling,
        "85.664721172419",
        "0x55.aa2b2ab08#40",
        Greater,
    );
    test(
        "3/257",
        40,
        Nearest,
        "85.664721172303",
        "0x55.aa2b2ab00#40",
        Less,
    );
}

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

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

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

#[test]
#[should_panic]
fn csch_rational_prec_round_fail_1() {
    Float::csch_rational_prec_round(Rational::ONE, 0, Floor);
}

#[test]
#[should_panic]
fn csch_rational_prec_round_fail_2() {
    Float::csch_rational_prec_round(Rational::ONE, 10, Exact);
}

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

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

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

    if x != 0u32 {
        // csch x has the sign of x, and csch is odd (a `Rational` has no negative zero, so x = 0 is
        // excluded)
        assert_eq!(c.is_sign_positive(), x > 0u32);
        let (c_neg, o_neg) = Float::csch_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_csch_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::csch_rational_prec_round_ref(&x, prec, rm);
            assert_eq!(ComparableFloatRef(&s), ComparableFloatRef(&c));
            assert_eq!(oo, Equal);
        }
    } else {
        assert_panic!(Float::csch_rational_prec_round_ref(&x, prec, Exact));
    }
}

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

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

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

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

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

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

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_csch_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_csch_rational::<T>(&x)),
            NiceFloat(out)
        );
    }
    test::<f32>("0", f32::INFINITY);
    test::<f32>("1", 0.8509181);
    test::<f32>("-1", -0.8509181);
    test::<f32>("1/3", 2.9451563);
    test::<f32>("22/7", 0.08647971);
    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", 1.0e20);
    test::<f32>("1/10000000000000000000000000000000000000000", f32::INFINITY);
    test::<f32>(
        "-1/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
        0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
        0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
        00000000000000000000000000000000000000000000000",
        f32::NEGATIVE_INFINITY,
    );

    test::<f64>("0", f64::INFINITY);
    test::<f64>("1", 0.8509181282393216);
    test::<f64>("-1", -0.8509181282393216);
    test::<f64>("1/3", 2.9451562666948146);
    test::<f64>("22/7", 0.08647970651862788);
    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", 1.0e20);
    test::<f64>("1/10000000000000000000000000000000000000000", 1.0e40);
    test::<f64>(
        "-1/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
        0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
        0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\
        00000000000000000000000000000000000000000000000",
        f64::NEGATIVE_INFINITY,
    );
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_csch_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_csch_rational::<T>(&x);
        // the hyperbolic cosecant of a rational is never NaN
        assert!(!c.is_nan());
        if x != 0u32 {
            // csch x has the sign of x, and csch is odd
            assert_eq!(c.is_sign_positive(), x > 0u32);
            assert_eq!(
                NiceFloat(primitive_float_csch_rational::<T>(&-&x)),
                NiceFloat(-c)
            );
        }
        // the result is the correctly rounded hyperbolic cosecant, as computed by MPFR with bits to
        // spare, so that a subnormal result is rounded once by the conversion rather than twice.
        // For a tiny x, csch x = 1/x - x/6 + ... lies within about x^2 (relatively) of 1/x, which
        // may be exactly halfway between two `T`s, so the spare bits must also resolve that gap.
        let spare = if x == 0u32 {
            64
        } else {
            64 + (x.floor_log_base_2_abs().unsigned_abs() << 1)
        };
        let rug_c = rug_csch_rational_prec(&x, T::MANTISSA_WIDTH + spare).0;
        let rug_c: T = T::rounding_from(&<Float as From<&rug::Float>>::from(&rug_c), Nearest).0;
        assert_eq!(NiceFloat(rug_c), NiceFloat(c));
    });

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

#[test]
fn primitive_float_csch_rational_properties() {
    apply_fn_to_primitive_floats!(primitive_float_csch_rational_properties_helper);
}