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::{Asinh, AsinhAssign, PowerOf2};
use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::basic::traits::{
    Infinity, NaN, NegativeInfinity, NegativeZero, One, Zero,
};
use malachite_base::num::comparison::traits::PartialOrdAbs;
use malachite_base::num::conversion::traits::{ExactFrom, RoundingFrom};
use malachite_base::num::float::NiceFloat;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_base::rounding_modes::RoundingMode::{self, *};
use malachite_base::rounding_modes::exhaustive::exhaustive_rounding_modes;
use malachite_base::test_util::generators::{
    primitive_float_gen, unsigned_rounding_mode_pair_gen_var_3,
};
use malachite_float::float::arithmetic::asinh::{
    primitive_float_asinh, primitive_float_asinh_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::asinh::{
    rug_asinh, rug_asinh_prec, rug_asinh_prec_round, rug_asinh_rational_prec,
    rug_asinh_rational_prec_round, rug_asinh_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_asinh_prec_round() {
    let test = |s: &str,
                s_hex: &str,
                prec: u64,
                rm: RoundingMode,
                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().asinh_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.asinh_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.asinh_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_asinh_prec_round(&rug::Float::exact_from(&x), prec, rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    };
    test("NaN", "NaN", 1, Nearest, "NaN", "NaN", Equal);
    test(
        "Infinity", "Infinity", 1, Nearest, "Infinity", "Infinity", Equal,
    );
    test(
        "-Infinity",
        "-Infinity",
        1,
        Nearest,
        "-Infinity",
        "-Infinity",
        Equal,
    );
    test("0.0", "0x0.0", 1, Nearest, "0.0", "0x0.0", Equal);
    test("-0.0", "-0x0.0", 1, Nearest, "-0.0", "-0x0.0", Equal);
    test("0.0", "0x0.0", 10, Nearest, "0.0", "0x0.0", Equal);
    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);
    test("1.0", "0x1.0#1", 10, Floor, "0.88086", "0x0.e18#10", Less);
    test(
        "1.0",
        "0x1.0#1",
        10,
        Ceiling,
        "0.88184",
        "0x0.e1c#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        10,
        Nearest,
        "0.88184",
        "0x0.e1c#10",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Floor,
        "0.88137358701954302523260932497968",
        "0x0.e1a1b30bcea13660d8f99e8dd#100",
        Less,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Ceiling,
        "0.88137358701954302523260932498047",
        "0x0.e1a1b30bcea13660d8f99e8de#100",
        Greater,
    );
    test(
        "1.0",
        "0x1.0#1",
        100,
        Nearest,
        "0.88137358701954302523260932497968",
        "0x0.e1a1b30bcea13660d8f99e8dd#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Floor,
        "-0.88184",
        "-0x0.e1c#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Ceiling,
        "-0.88086",
        "-0x0.e18#10",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        10,
        Nearest,
        "-0.88184",
        "-0x0.e1c#10",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Floor,
        "-0.88137358701954302523260932498047",
        "-0x0.e1a1b30bcea13660d8f99e8de#100",
        Less,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Ceiling,
        "-0.88137358701954302523260932497968",
        "-0x0.e1a1b30bcea13660d8f99e8dd#100",
        Greater,
    );
    test(
        "-1.0",
        "-0x1.0#1",
        100,
        Nearest,
        "-0.88137358701954302523260932497968",
        "-0x0.e1a1b30bcea13660d8f99e8dd#100",
        Greater,
    );
    test("0.50", "0x0.8#1", 10, Floor, "0.48096", "0x0.7b2#10", Less);
    test(
        "0.50",
        "0x0.8#1",
        10,
        Ceiling,
        "0.48145",
        "0x0.7b4#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        10,
        Nearest,
        "0.48145",
        "0x0.7b4#10",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Floor,
        "0.48121182505960344749775891342426",
        "0x0.7b30b2bb14582652f810812a58#100",
        Less,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Ceiling,
        "0.48121182505960344749775891342465",
        "0x0.7b30b2bb14582652f810812a60#100",
        Greater,
    );
    test(
        "0.50",
        "0x0.8#1",
        100,
        Nearest,
        "0.48121182505960344749775891342426",
        "0x0.7b30b2bb14582652f810812a58#100",
        Less,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        10,
        Floor,
        "-0.48145",
        "-0x0.7b4#10",
        Less,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        10,
        Ceiling,
        "-0.48096",
        "-0x0.7b2#10",
        Greater,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        10,
        Nearest,
        "-0.48145",
        "-0x0.7b4#10",
        Less,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        100,
        Floor,
        "-0.48121182505960344749775891342465",
        "-0x0.7b30b2bb14582652f810812a60#100",
        Less,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        100,
        Ceiling,
        "-0.48121182505960344749775891342426",
        "-0x0.7b30b2bb14582652f810812a58#100",
        Greater,
    );
    test(
        "-0.50",
        "-0x0.8#1",
        100,
        Nearest,
        "-0.48121182505960344749775891342426",
        "-0x0.7b30b2bb14582652f810812a58#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Floor,
        "0.32715",
        "0x0.53c#10",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Ceiling,
        "0.32764",
        "0x0.53e#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        10,
        Nearest,
        "0.32764",
        "0x0.53e#10",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Floor,
        "0.32745015023725844332253525998813",
        "0x0.53d3c5e656dd20ec63b484c7e8#100",
        Less,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Ceiling,
        "0.32745015023725844332253525998852",
        "0x0.53d3c5e656dd20ec63b484c7f0#100",
        Greater,
    );
    test(
        "0.33333333333333333333333333333346",
        "0x0.55555555555555555555555558#100",
        100,
        Nearest,
        "0.32745015023725844332253525998852",
        "0x0.53d3c5e656dd20ec63b484c7f0#100",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Floor, "1.4434", "0x1.718#10", Less);
    test(
        "2.0",
        "0x2.0#2",
        10,
        Ceiling,
        "1.4453",
        "0x1.720#10",
        Greater,
    );
    test("2.0", "0x2.0#2", 10, Nearest, "1.4434", "0x1.718#10", Less);
    test(
        "2.0",
        "0x2.0#2",
        100,
        Floor,
        "1.4436354751788103424932767402724",
        "0x1.719218313d0872f8e831837f0#100",
        Less,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Ceiling,
        "1.4436354751788103424932767402740",
        "0x1.719218313d0872f8e831837f2#100",
        Greater,
    );
    test(
        "2.0",
        "0x2.0#2",
        100,
        Nearest,
        "1.4436354751788103424932767402724",
        "0x1.719218313d0872f8e831837f0#100",
        Less,
    );
    test("10.0", "0xa.0#4", 10, Floor, "2.9961", "0x2.ff#10", Less);
    test(
        "10.0",
        "0xa.0#4",
        10,
        Ceiling,
        "3.0000",
        "0x3.00#10",
        Greater,
    );
    test(
        "10.0",
        "0xa.0#4",
        10,
        Nearest,
        "3.0000",
        "0x3.00#10",
        Greater,
    );
    test(
        "10.0",
        "0xa.0#4",
        100,
        Floor,
        "2.9982229502979697388465955375953",
        "0x2.ff8b8a0da57b5aa38395e9070#100",
        Less,
    );
    test(
        "10.0",
        "0xa.0#4",
        100,
        Ceiling,
        "2.9982229502979697388465955375985",
        "0x2.ff8b8a0da57b5aa38395e9074#100",
        Greater,
    );
    test(
        "10.0",
        "0xa.0#4",
        100,
        Nearest,
        "2.9982229502979697388465955375953",
        "0x2.ff8b8a0da57b5aa38395e9070#100",
        Less,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        10,
        Floor,
        "-5.3047",
        "-0x5.4e#10",
        Less,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        10,
        Ceiling,
        "-5.2969",
        "-0x5.4c#10",
        Greater,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        10,
        Nearest,
        "-5.2969",
        "-0x5.4c#10",
        Greater,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        100,
        Floor,
        "-5.2983423656105887573688256891151",
        "-0x5.4c602a4f4f0a7cedac9045f40#100",
        Less,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        100,
        Ceiling,
        "-5.2983423656105887573688256891088",
        "-0x5.4c602a4f4f0a7cedac9045f38#100",
        Greater,
    );
    test(
        "-100.0",
        "-0x64.0#7",
        100,
        Nearest,
        "-5.2983423656105887573688256891151",
        "-0x5.4c602a4f4f0a7cedac9045f40#100",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Floor,
        "7.5938",
        "0x7.98#10",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Ceiling,
        "7.6016",
        "0x7.9a#10",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        10,
        Nearest,
        "7.6016",
        "0x7.9a#10",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Floor,
        "7.6009027095419886115232897846635",
        "0x7.99d4c28d8f8554d4dd7364140#100",
        Less,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Ceiling,
        "7.6009027095419886115232897846698",
        "0x7.99d4c28d8f8554d4dd7364148#100",
        Greater,
    );
    test(
        "1000.0",
        "0x3e8.0#10",
        100,
        Nearest,
        "7.6009027095419886115232897846635",
        "0x7.99d4c28d8f8554d4dd7364140#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Floor,
        "1.8613",
        "0x1.dc8#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Ceiling,
        "1.8633",
        "0x1.dd0#10",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        10,
        Nearest,
        "1.8613",
        "0x1.dc8#10",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Floor,
        "1.8622957433108482199035772703700",
        "0x1.dcbf69f10006ce973ebb7a636#100",
        Less,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Ceiling,
        "1.8622957433108482199035772703716",
        "0x1.dcbf69f10006ce973ebb7a638#100",
        Greater,
    );
    test(
        "3.14159265358979323851",
        "0x3.243f6a8885a308d4#64",
        100,
        Nearest,
        "1.8622957433108482199035772703700",
        "0x1.dcbf69f10006ce973ebb7a636#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Floor,
        "14.500",
        "0xe.80#10",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Ceiling,
        "14.516",
        "0xe.84#10",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        10,
        Nearest,
        "14.516",
        "0xe.84#10",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Floor,
        "14.508657738524469413525180755814",
        "0xe.823764bfd1e5fa37c6bf52ed#100",
        Less,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Ceiling,
        "14.508657738524469413525180755826",
        "0xe.823764bfd1e5fa37c6bf52ee#100",
        Greater,
    );
    test(
        "1000000.0",
        "0xf4240.0#20",
        100,
        Nearest,
        "14.508657738524469413525180755814",
        "0xe.823764bfd1e5fa37c6bf52ed#100",
        Less,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        10,
        Floor,
        "-19.125",
        "-0x13.20#10",
        Less,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        10,
        Ceiling,
        "-19.094",
        "-0x13.18#10",
        Greater,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        10,
        Nearest,
        "-19.125",
        "-0x13.20#10",
        Less,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        100,
        Floor,
        "-19.113827924512310806561163758946",
        "-0x13.1d23d3ad26e4fe563fe7f692#100",
        Less,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        100,
        Ceiling,
        "-19.113827924512310806561163758921",
        "-0x13.1d23d3ad26e4fe563fe7f690#100",
        Greater,
    );
    test(
        "-100000000.0",
        "-0x5f5e100.0#27",
        100,
        Nearest,
        "-19.113827924512310806561163758921",
        "-0x13.1d23d3ad26e4fe563fe7f690#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Floor,
        "0.00097561",
        "0x0.003ff#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Floor,
        "-0.00097656",
        "-0x0.00400#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Ceiling,
        "0.00097656",
        "0x0.00400#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Ceiling,
        "-0.00097561",
        "-0x0.003ff#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Nearest,
        "0.00097656",
        "0x0.00400#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Nearest,
        "-0.00097656",
        "-0x0.00400#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Down,
        "0.00097561",
        "0x0.003ff#10",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Down,
        "-0.00097561",
        "-0x0.003ff#10",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        10,
        Up,
        "0.00097656",
        "0x0.00400#10",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        10,
        Up,
        "-0.00097656",
        "-0x0.00400#10",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Floor,
        "0.00097656234477963751076391095890807",
        "0x0.003fffff55555a2221f46b48a630#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Floor,
        "-0.00097656234477963751076391095890884",
        "-0x0.003fffff55555a2221f46b48a634#100",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Ceiling,
        "0.00097656234477963751076391095890884",
        "0x0.003fffff55555a2221f46b48a634#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Ceiling,
        "-0.00097656234477963751076391095890807",
        "-0x0.003fffff55555a2221f46b48a630#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Nearest,
        "0.00097656234477963751076391095890884",
        "0x0.003fffff55555a2221f46b48a634#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Nearest,
        "-0.00097656234477963751076391095890884",
        "-0x0.003fffff55555a2221f46b48a634#100",
        Less,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Down,
        "0.00097656234477963751076391095890807",
        "0x0.003fffff55555a2221f46b48a630#100",
        Less,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Down,
        "-0.00097656234477963751076391095890807",
        "-0x0.003fffff55555a2221f46b48a630#100",
        Greater,
    );
    test(
        "0.00098",
        "0x0.004#1",
        100,
        Up,
        "0.00097656234477963751076391095890884",
        "0x0.003fffff55555a2221f46b48a634#100",
        Greater,
    );
    test(
        "-0.00098",
        "-0x0.004#1",
        100,
        Up,
        "-0.00097656234477963751076391095890884",
        "-0x0.003fffff55555a2221f46b48a634#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Floor,
        "8.8817841970012523233890533447196e-16",
        "0x3.ffffffffffffffffffffffffcE-13#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Floor,
        "-8.8817841970012523233890533447266e-16",
        "-0x4.0000000000000000000000000E-13#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Ceiling,
        "8.8817841970012523233890533447266e-16",
        "0x4.0000000000000000000000000E-13#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Ceiling,
        "-8.8817841970012523233890533447196e-16",
        "-0x3.ffffffffffffffffffffffffcE-13#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Nearest,
        "8.8817841970012523233890533447266e-16",
        "0x4.0000000000000000000000000E-13#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Nearest,
        "-8.8817841970012523233890533447266e-16",
        "-0x4.0000000000000000000000000E-13#100",
        Less,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Down,
        "8.8817841970012523233890533447196e-16",
        "0x3.ffffffffffffffffffffffffcE-13#100",
        Less,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Down,
        "-8.8817841970012523233890533447196e-16",
        "-0x3.ffffffffffffffffffffffffcE-13#100",
        Greater,
    );
    test(
        "8.9e-16",
        "0x4.0E-13#1",
        100,
        Up,
        "8.8817841970012523233890533447266e-16",
        "0x4.0000000000000000000000000E-13#100",
        Greater,
    );
    test(
        "-8.9e-16",
        "-0x4.0E-13#1",
        100,
        Up,
        "-8.8817841970012523233890533447266e-16",
        "-0x4.0000000000000000000000000E-13#100",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Floor,
        "7.8809e-31",
        "0xf.fcE-26#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Floor,
        "-7.8886e-31",
        "-0x1.000E-25#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Ceiling,
        "7.8886e-31",
        "0x1.000E-25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Ceiling,
        "-7.8809e-31",
        "-0xf.fcE-26#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Nearest,
        "7.8886e-31",
        "0x1.000E-25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Nearest,
        "-7.8886e-31",
        "-0x1.000E-25#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Down,
        "7.8809e-31",
        "0xf.fcE-26#10",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Down,
        "-7.8809e-31",
        "-0xf.fcE-26#10",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        10,
        Up,
        "7.8886e-31",
        "0x1.000E-25#10",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        10,
        Up,
        "-7.8886e-31",
        "-0x1.000E-25#10",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Floor,
        "7.888609052210118054117285652827862296732064351090230047702788488458380783712241150704674\
        1677e-31",
        "0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555555E-26#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Floor,
        "-7.88860905221011805411728565282786229673206435109023004770278848845838078371224115070467\
        41715e-31",
        "-0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555556E-26#300",
        Less,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Ceiling,
        "7.888609052210118054117285652827862296732064351090230047702788488458380783712241150704674\
        1715e-31",
        "0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555556E-26#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Ceiling,
        "-7.88860905221011805411728565282786229673206435109023004770278848845838078371224115070467\
        41677e-31",
        "-0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555555E-26#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Nearest,
        "7.888609052210118054117285652827862296732064351090230047702788488458380783712241150704674\
        1677e-31",
        "0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555555E-26#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Nearest,
        "-7.88860905221011805411728565282786229673206435109023004770278848845838078371224115070467\
        41677e-31",
        "-0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555555E-26#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Down,
        "7.888609052210118054117285652827862296732064351090230047702788488458380783712241150704674\
        1677e-31",
        "0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555555E-26#300",
        Less,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Down,
        "-7.88860905221011805411728565282786229673206435109023004770278848845838078371224115070467\
        41677e-31",
        "-0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555555E-26#300",
        Greater,
    );
    test(
        "7.9e-31",
        "0x1.0E-25#1",
        300,
        Up,
        "7.888609052210118054117285652827862296732064351090230047702788488458380783712241150704674\
        1715e-31",
        "0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555556E-26#300",
        Greater,
    );
    test(
        "-7.9e-31",
        "-0x1.0E-25#1",
        300,
        Up,
        "-7.88860905221011805411728565282786229673206435109023004770278848845838078371224115070467\
        41715e-31",
        "-0xf.fffffffffffffffffffffffffffffffffffffffffffffffffd555555555555555555555556E-26#300",
        Less,
    );
    // - the shortcut cannot decide, and t is zero at the first working precision, so the loop
    //   retries
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Floor,
        "9.0861e-13",
        "0xf.fcE-11#10",
        Less,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Floor,
        "-9.0949e-13",
        "-0x1.000E-10#10",
        Less,
    );
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Ceiling,
        "9.0949e-13",
        "0x1.000E-10#10",
        Greater,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Ceiling,
        "-9.0861e-13",
        "-0xf.fcE-11#10",
        Greater,
    );
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Nearest,
        "9.0949e-13",
        "0x1.000E-10#10",
        Greater,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Nearest,
        "-9.0949e-13",
        "-0x1.000E-10#10",
        Less,
    );
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Down,
        "9.0861e-13",
        "0xf.fcE-11#10",
        Less,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Down,
        "-9.0861e-13",
        "-0xf.fcE-11#10",
        Greater,
    );
    test(
        "9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Up,
        "9.0949e-13",
        "0x1.000E-10#10",
        Greater,
    );
    test(
        "-9.0949470177292823791503906250000000000000000000000000000000000e-13",
        "-0x1.00000000000000000000000000000000000000000000000000E-10#200",
        10,
        Up,
        "-9.0949e-13",
        "-0x1.000E-10#10",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        64,
        Floor,
        "-2.38256490488795107322e-323228497",
        "-0x1.0000000000000000E-268435456#64",
        Less,
    );
    test(
        "1.0e-301030",
        "0x1.0E-250000#1",
        64,
        Floor,
        "1.01003405919803022465e-301030",
        "0xf.fffffffffffffffE-250001#64",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Ceiling,
        "2.38256490488795107322e-323228497",
        "0x1.0000000000000000E-268435456#64",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        64,
        Ceiling,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "1.0e-301030",
        "0x1.0E-250000#1",
        64,
        Ceiling,
        "1.01003405919803022470e-301030",
        "0x1.0000000000000000E-250000#64",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        64,
        Nearest,
        "2.38256490488795107322e-323228497",
        "0x1.0000000000000000E-268435456#64",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        64,
        Nearest,
        "-2.38256490488795107322e-323228497",
        "-0x1.0000000000000000E-268435456#64",
        Less,
    );
    test(
        "1.0e-301030",
        "0x1.0E-250000#1",
        64,
        Nearest,
        "1.01003405919803022470e-301030",
        "0x1.0000000000000000E-250000#64",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Floor,
        "21.031",
        "0x15.08#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Ceiling,
        "21.062",
        "0x15.10#10",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Nearest,
        "21.062",
        "0x15.10#10",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Down,
        "21.031",
        "0x15.08#10",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        10,
        Up,
        "21.062",
        "0x15.10#10",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Floor,
        "21.059738073567624087176720584002",
        "0x15.0f4afe904c8a71d974b1f30e#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Ceiling,
        "21.059738073567624087176720584027",
        "0x15.0f4afe904c8a71d974b1f310#100",
        Greater,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Nearest,
        "21.059738073567624087176720584002",
        "0x15.0f4afe904c8a71d974b1f30e#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Down,
        "21.059738073567624087176720584002",
        "0x15.0f4afe904c8a71d974b1f30e#100",
        Less,
    );
    test(
        "700000000.00",
        "0x29b92700.0#30",
        100,
        Up,
        "21.059738073567624087176720584027",
        "0x15.0f4afe904c8a71d974b1f310#100",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Floor,
        "21.094",
        "0x15.18#10",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Ceiling,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Nearest,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Down,
        "21.094",
        "0x15.18#10",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        10,
        Up,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Floor,
        "21.121049676165439428678979107033",
        "0x15.1efd1c90526b838dc390cdf8#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Ceiling,
        "21.121049676165439428678979107058",
        "0x15.1efd1c90526b838dc390cdfa#100",
        Greater,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Nearest,
        "21.121049676165439428678979107033",
        "0x15.1efd1c90526b838dc390cdf8#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Down,
        "21.121049676165439428678979107033",
        "0x15.1efd1c90526b838dc390cdf8#100",
        Less,
    );
    test(
        "744261117.50",
        "0x2c5c85fd.8#31",
        100,
        Up,
        "21.121049676165439428678979107058",
        "0x15.1efd1c90526b838dc390cdfa#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Floor,
        "-21.125",
        "-0x15.20#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Ceiling,
        "-21.094",
        "-0x15.18#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Nearest,
        "-21.125",
        "-0x15.20#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Down,
        "-21.094",
        "-0x15.18#10",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        10,
        Up,
        "-21.125",
        "-0x15.20#10",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Floor,
        "-21.121049676165439428678979107058",
        "-0x15.1efd1c90526b838dc390cdfa#100",
        Less,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Ceiling,
        "-21.121049676165439428678979107033",
        "-0x15.1efd1c90526b838dc390cdf8#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Nearest,
        "-21.121049676165439428678979107033",
        "-0x15.1efd1c90526b838dc390cdf8#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Down,
        "-21.121049676165439428678979107033",
        "-0x15.1efd1c90526b838dc390cdf8#100",
        Greater,
    );
    test(
        "-744261117.50",
        "-0x2c5c85fd.8#31",
        100,
        Up,
        "-21.121049676165439428678979107058",
        "-0x15.1efd1c90526b838dc390cdfa#100",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Floor,
        "21.094",
        "0x15.18#10",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Ceiling,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Nearest,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Down,
        "21.094",
        "0x15.18#10",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        10,
        Up,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Floor,
        "21.121049676703410062207743023070",
        "0x15.1efd1c92a1ecc911a3f30740#100",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Ceiling,
        "21.121049676703410062207743023095",
        "0x15.1efd1c92a1ecc911a3f30742#100",
        Greater,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Nearest,
        "21.121049676703410062207743023095",
        "0x15.1efd1c92a1ecc911a3f30742#100",
        Greater,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Down,
        "21.121049676703410062207743023070",
        "0x15.1efd1c92a1ecc911a3f30740#100",
        Less,
    );
    test(
        "744261117.90039",
        "0x2c5c85fd.e68#40",
        100,
        Up,
        "21.121049676703410062207743023095",
        "0x15.1efd1c92a1ecc911a3f30742#100",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Floor,
        "21.094",
        "0x15.18#10",
        Less,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Ceiling,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Nearest,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Down,
        "21.094",
        "0x15.18#10",
        Less,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        10,
        Up,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Floor,
        "21.121049676837246658796771995816",
        "0x15.1efd1c93351470369d535cce#100",
        Less,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Ceiling,
        "21.121049676837246658796771995841",
        "0x15.1efd1c93351470369d535cd0#100",
        Greater,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Nearest,
        "21.121049676837246658796771995816",
        "0x15.1efd1c93351470369d535cce#100",
        Less,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Down,
        "21.121049676837246658796771995816",
        "0x15.1efd1c93351470369d535cce#100",
        Less,
    );
    test(
        "744261118.00",
        "0x2c5c85fe.0#30",
        100,
        Up,
        "21.121049676837246658796771995841",
        "0x15.1efd1c93351470369d535cd0#100",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Floor,
        "-21.125",
        "-0x15.20#10",
        Less,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Ceiling,
        "-21.094",
        "-0x15.18#10",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Nearest,
        "-21.125",
        "-0x15.20#10",
        Less,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Down,
        "-21.094",
        "-0x15.18#10",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        10,
        Up,
        "-21.125",
        "-0x15.20#10",
        Less,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Floor,
        "-21.121049676837246658796771995841",
        "-0x15.1efd1c93351470369d535cd0#100",
        Less,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Ceiling,
        "-21.121049676837246658796771995816",
        "-0x15.1efd1c93351470369d535cce#100",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Nearest,
        "-21.121049676837246658796771995816",
        "-0x15.1efd1c93351470369d535cce#100",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Down,
        "-21.121049676837246658796771995816",
        "-0x15.1efd1c93351470369d535cce#100",
        Greater,
    );
    test(
        "-744261118.00",
        "-0x2c5c85fe.0#30",
        100,
        Up,
        "-21.121049676837246658796771995841",
        "-0x15.1efd1c93351470369d535cd0#100",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Floor,
        "21.406",
        "0x15.68#10",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Ceiling,
        "21.438",
        "0x15.70#10",
        Greater,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Nearest,
        "21.406",
        "0x15.68#10",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Down,
        "21.406",
        "0x15.68#10",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        10,
        Up,
        "21.438",
        "0x15.70#10",
        Greater,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Floor,
        "21.416413017506356465829155213605",
        "0x15.6a9a0b23d187ace95ab1462a#100",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Ceiling,
        "21.416413017506356465829155213630",
        "0x15.6a9a0b23d187ace95ab1462c#100",
        Greater,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Nearest,
        "21.416413017506356465829155213605",
        "0x15.6a9a0b23d187ace95ab1462a#100",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Down,
        "21.416413017506356465829155213605",
        "0x15.6a9a0b23d187ace95ab1462a#100",
        Less,
    );
    test(
        "1000000000.0",
        "0x3b9aca00.0#30",
        100,
        Up,
        "21.416413017506356465829155213630",
        "0x15.6a9a0b23d187ace95ab1462c#100",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Floor,
        "7.4344e8",
        "0x2.c5E+7#10",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Ceiling,
        "7.4449e8",
        "0x2.c6E+7#10",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Nearest,
        "7.4449e8",
        "0x2.c6E+7#10",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Down,
        "7.4344e8",
        "0x2.c5E+7#10",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        10,
        Up,
        "7.4449e8",
        "0x2.c6E+7#10",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Floor,
        "744261117.95391597822607658233916",
        "0x2c5c85fd.f433d6699ce38ac130#100",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Ceiling,
        "744261117.95391597822607658234001",
        "0x2c5c85fd.f433d6699ce38ac134#100",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Nearest,
        "744261117.95391597822607658234001",
        "0x2c5c85fd.f433d6699ce38ac134#100",
        Greater,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Down,
        "744261117.95391597822607658233916",
        "0x2c5c85fd.f433d6699ce38ac130#100",
        Less,
    );
    test(
        "2.0965e323228496",
        "0x7.feE+268435455#10",
        100,
        Up,
        "744261117.95391597822607658234001",
        "0x2c5c85fd.f433d6699ce38ac134#100",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Floor,
        "-7.4449e8",
        "-0x2.c6E+7#10",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Ceiling,
        "-7.4344e8",
        "-0x2.c5E+7#10",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Nearest,
        "-7.4449e8",
        "-0x2.c6E+7#10",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Down,
        "-7.4344e8",
        "-0x2.c5E+7#10",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        10,
        Up,
        "-7.4449e8",
        "-0x2.c6E+7#10",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Floor,
        "-744261117.95391597822607658234001",
        "-0x2c5c85fd.f433d6699ce38ac134#100",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Ceiling,
        "-744261117.95391597822607658233916",
        "-0x2c5c85fd.f433d6699ce38ac130#100",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Nearest,
        "-744261117.95391597822607658234001",
        "-0x2c5c85fd.f433d6699ce38ac134#100",
        Less,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Down,
        "-744261117.95391597822607658233916",
        "-0x2c5c85fd.f433d6699ce38ac130#100",
        Greater,
    );
    test(
        "-2.0965e323228496",
        "-0x7.feE+268435455#10",
        100,
        Up,
        "-744261117.95391597822607658234001",
        "-0x2c5c85fd.f433d6699ce38ac134#100",
        Less,
    );
    test(
        "744261117.29980",
        "0x2c5c85fd.4cc#40",
        105,
        Floor,
        "21.1210496758964541118060674980227",
        "0x15.1efd1c8f2aaae0c9d2db6539a#105",
        Less,
    );
    test(
        "744261117.29980",
        "0x2c5c85fd.4cc#40",
        105,
        Ceiling,
        "21.1210496758964541118060674980235",
        "0x15.1efd1c8f2aaae0c9d2db6539b#105",
        Greater,
    );
    test(
        "744261117.29980",
        "0x2c5c85fd.4cc#40",
        105,
        Nearest,
        "21.1210496758964541118060674980227",
        "0x15.1efd1c8f2aaae0c9d2db6539a#105",
        Less,
    );
    // - the largest x for which x^2 cannot overflow, so the general path is taken
    test(
        "5.1e161614247",
        "0x4.0E+134217727#1",
        1,
        Floor,
        "2.7e8",
        "0x1.0E+7#1",
        Less,
    );
    test(
        "5.1e161614247",
        "0x4.0E+134217727#1",
        1,
        Ceiling,
        "5.4e8",
        "0x2.0E+7#1",
        Greater,
    );
    test(
        "5.1e161614247",
        "0x4.0E+134217727#1",
        1,
        Nearest,
        "2.7e8",
        "0x1.0E+7#1",
        Less,
    );
    test(
        "5.1e161614247",
        "0x4.0E+134217727#1",
        10,
        Floor,
        "3.7172e8",
        "0x1.628E+7#10",
        Less,
    );
    test(
        "5.1e161614247",
        "0x4.0E+134217727#1",
        10,
        Ceiling,
        "3.7224e8",
        "0x1.630E+7#10",
        Greater,
    );
    test(
        "5.1e161614247",
        "0x4.0E+134217727#1",
        10,
        Nearest,
        "3.7224e8",
        "0x1.630E+7#10",
        Greater,
    );
    test(
        "5.1e161614247",
        "0x4.0E+134217727#1",
        100,
        Floor,
        "372130558.28429932837700628814559",
        "0x162e42fe.48c7d73da76cfcc736#100",
        Less,
    );
    test(
        "5.1e161614247",
        "0x4.0E+134217727#1",
        100,
        Ceiling,
        "372130558.28429932837700628814601",
        "0x162e42fe.48c7d73da76cfcc738#100",
        Greater,
    );
    test(
        "5.1e161614247",
        "0x4.0E+134217727#1",
        100,
        Nearest,
        "372130558.28429932837700628814559",
        "0x162e42fe.48c7d73da76cfcc736#100",
        Less,
    );
    test(
        "1.016e161614248",
        "0x7.fE+134217727#7",
        20,
        Down,
        "3.7213030e8",
        "0x1.62e42E+7#20",
        Less,
    );
    test(
        "1.016e161614248",
        "0x7.fE+134217727#7",
        20,
        Up,
        "3.7213082e8",
        "0x1.62e44E+7#20",
        Greater,
    );
    test(
        "1.016e161614248",
        "0x7.fE+134217727#7",
        20,
        Nearest,
        "3.7213030e8",
        "0x1.62e42E+7#20",
        Less,
    );
    // - x^2 would overflow, so asinh(|x|) is computed as ln(|x|) + ln 2; at precision 1 with
    //   Nearest the first iteration cannot round
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        1,
        Floor,
        "2.7e8",
        "0x1.0E+7#1",
        Less,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        1,
        Ceiling,
        "5.4e8",
        "0x2.0E+7#1",
        Greater,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        1,
        Nearest,
        "2.7e8",
        "0x1.0E+7#1",
        Less,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        10,
        Floor,
        "3.7172e8",
        "0x1.628E+7#10",
        Less,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        10,
        Ceiling,
        "3.7224e8",
        "0x1.630E+7#10",
        Greater,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        10,
        Nearest,
        "3.7224e8",
        "0x1.630E+7#10",
        Greater,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        100,
        Floor,
        "372130558.97744650893695159756284",
        "0x162e42fe.fa39ef35793c767300#100",
        Less,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        100,
        Ceiling,
        "372130558.97744650893695159756327",
        "0x162e42fe.fa39ef35793c767302#100",
        Greater,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        100,
        Nearest,
        "372130558.97744650893695159756284",
        "0x162e42fe.fa39ef35793c767300#100",
        Less,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        200,
        Floor,
        "372130558.97744650893695159756294602395972384199011277483256122",
        "0x162e42fe.fa39ef35793c7673007e5ed5e81e6864ce5316c5b14#200",
        Less,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        200,
        Ceiling,
        "372130558.97744650893695159756294602395972384199011277483256155",
        "0x162e42fe.fa39ef35793c7673007e5ed5e81e6864ce5316c5b16#200",
        Greater,
    );
    test(
        "1.0e161614248",
        "0x8.0E+134217727#1",
        200,
        Nearest,
        "372130558.97744650893695159756294602395972384199011277483256122",
        "0x162e42fe.fa39ef35793c7673007e5ed5e81e6864ce5316c5b14#200",
        Less,
    );
    test(
        "-1.0e161614248",
        "-0x8.0E+134217727#1",
        64,
        Floor,
        "-372130558.977446508943",
        "-0x162e42fe.fa39ef358#64",
        Less,
    );
    test(
        "-1.0e161614248",
        "-0x8.0E+134217727#1",
        64,
        Ceiling,
        "-372130558.977446508914",
        "-0x162e42fe.fa39ef356#64",
        Greater,
    );
    test(
        "-1.0e161614248",
        "-0x8.0E+134217727#1",
        64,
        Down,
        "-372130558.977446508914",
        "-0x162e42fe.fa39ef356#64",
        Greater,
    );
    test(
        "-1.0e161614248",
        "-0x8.0E+134217727#1",
        64,
        Up,
        "-372130558.977446508943",
        "-0x162e42fe.fa39ef358#64",
        Less,
    );
    test(
        "-1.0e161614248",
        "-0x8.0E+134217727#1",
        64,
        Nearest,
        "-372130558.977446508943",
        "-0x162e42fe.fa39ef358#64",
        Less,
    );
    test(
        "2.041e161614248",
        "0xf.fE+134217727#8",
        30,
        Floor,
        "372130559.50",
        "0x162e42ff.8#30",
        Less,
    );
    test(
        "2.041e161614248",
        "0xf.fE+134217727#8",
        30,
        Nearest,
        "372130559.50",
        "0x162e42ff.8#30",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        1,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        1,
        Ceiling,
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        1,
        Nearest,
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        100,
        Floor,
        "0.0",
        "0x0.0",
        Less,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        100,
        Ceiling,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "2.4e-323228497",
        "0x1.0E-268435456#1",
        100,
        Nearest,
        "2.3825649048879510732161697817327e-323228497",
        "0x1.0000000000000000000000000E-268435456#100",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Floor,
        "-2.3826e-323228497",
        "-0x1.000E-268435456#10",
        Less,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Ceiling,
        "-0.0",
        "-0x0.0",
        Greater,
    );
    test(
        "-2.4e-323228497",
        "-0x1.0E-268435456#1",
        10,
        Nearest,
        "-2.3826e-323228497",
        "-0x1.000E-268435456#10",
        Less,
    );
    // - t is so small that the error estimate is nonpositive, so the loop retries rather than
    //   testing whether t can be rounded
    test(
        "4.656612873077392580113e-10",
        "0x2.000000000000000fcE-8#68",
        25,
        Nearest,
        "4.65661287e-10",
        "0x2.000000E-8#25",
        Less,
    );
    test(
        "4.656612873077392580113e-10",
        "0x2.000000000000000fcE-8#68",
        25,
        Floor,
        "4.65661287e-10",
        "0x2.000000E-8#25",
        Less,
    );
    test(
        "4.656612873077392580113e-10",
        "0x2.000000000000000fcE-8#68",
        25,
        Ceiling,
        "4.65661315e-10",
        "0x2.000002E-8#25",
        Greater,
    );
    test(
        "4.6938657760620117187500306e-7",
        "0x7.e000000000000000003eE-6#82",
        7,
        Nearest,
        "4.694e-7",
        "0x7.eE-6#7",
        Greater,
    );
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#[test]
fn asinh_prec_properties() {
    float_unsigned_pair_gen_var_1().test_properties(|(x, prec)| {
        let (c, o) = x.clone().asinh_prec(prec);
        assert!(c.is_valid());
        let (c_alt, o_alt) = x.asinh_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.asinh_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.asinh_prec_round_ref(prec, Nearest);
        assert_eq!(ComparableFloatRef(&c_alt), ComparableFloatRef(&c));
        assert_eq!(o_alt, o);

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

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

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

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

        assert_eq!(ComparableFloatRef(&(-&x).asinh()), 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_asinh() {
    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_asinh(x)), NiceFloat(out));
    }
    test::<f32>(f32::NAN, f32::NAN);
    test::<f32>(f32::INFINITY, f32::INFINITY);
    test::<f32>(f32::NEGATIVE_INFINITY, f32::NEGATIVE_INFINITY);
    test::<f32>(0.0, 0.0);
    test::<f32>(-0.0, -0.0);
    test::<f32>(1.0, 0.8813736);
    test::<f32>(-1.0, -0.8813736);
    test::<f32>(0.5, 0.4812118);
    test::<f32>(-0.5, -0.4812118);
    test::<f32>(2.0, 1.4436355);
    test::<f32>(10.0, 2.998223);
    test::<f32>(core::f32::consts::PI, 1.8622957);
    test::<f32>(88.0, 5.1705165);
    test::<f32>(10000000000.0, 23.718998);
    test::<f32>(1.0e30, 69.7707);
    test::<f32>(3.4028235e38, 89.415985);
    test::<f32>(-3.4028235e38, -89.415985);
    test::<f32>(1.0e-20, 1.0e-20);
    test::<f32>(1.0e-45, 1.0e-45);
    test::<f32>(-1.0e-45, -1.0e-45);

    test::<f64>(f64::NAN, f64::NAN);
    test::<f64>(f64::INFINITY, f64::INFINITY);
    test::<f64>(f64::NEGATIVE_INFINITY, f64::NEGATIVE_INFINITY);
    test::<f64>(0.0, 0.0);
    test::<f64>(-0.0, -0.0);
    test::<f64>(1.0, 0.881373587019543);
    test::<f64>(-1.0, -0.881373587019543);
    test::<f64>(0.5, 0.48121182505960347);
    test::<f64>(-0.5, -0.48121182505960347);
    test::<f64>(2.0, 1.4436354751788103);
    test::<f64>(10.0, 2.99822295029797);
    test::<f64>(core::f64::consts::PI, 1.8622957433108482);
    test::<f64>(709.0, 7.257003204425001);
    test::<f64>(1.0e100, 230.95165647996453);
    test::<f64>(1.0e300, 691.4686750787737);
    test::<f64>(1.7976931348623157e308, 710.475860073944);
    test::<f64>(-1.7976931348623157e308, -710.475860073944);
    test::<f64>(1.0e-200, 1.0e-200);
    test::<f64>(5.0e-324, 5.0e-324);
    test::<f64>(-5.0e-324, -5.0e-324);
}

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_asinh_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_asinh(x);
        // asinh is NaN exactly for NaN inputs, and otherwise has the sign of x and |asinh x| <=
        // |x|.
        assert_eq!(c.is_nan(), x.is_nan());
        if !x.is_nan() {
            assert_eq!(c.is_sign_positive(), x.is_sign_positive());
            assert!(c.abs() <= x.abs());
            // asinh is odd
            assert_eq!(NiceFloat(primitive_float_asinh(-x)), NiceFloat(-c));
        }
        if x.is_finite() {
            // the result is the correctly rounded inverse hyperbolic sine, as computed by MPFR at
            // the same precision; it never overflows.
            let rug_x = rug::Float::with_val(
                u32::exact_from(T::MANTISSA_WIDTH + 1),
                &rug::Float::exact_from(&Float::from(x)),
            );
            let rug_c = <Float as From<&rug::Float>>::from(&rug_x.asinh());
            let expected = T::exact_from(&rug_c);
            assert_eq!(NiceFloat(expected), NiceFloat(c));
        }
    });
}

#[test]
fn primitive_float_asinh_properties() {
    apply_fn_to_primitive_floats!(primitive_float_asinh_properties_helper);
}

#[test]
fn test_asinh_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::asinh_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::asinh_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_asinh_rational_prec_round(&x, prec, rug_rm);
            assert_eq!(
                ComparableFloatRef(&Float::from(&rug_c)),
                ComparableFloatRef(&c)
            );
            assert_eq!(rug_o, o);
        }
    };
    test("0", 1, Down, "0.0", "0x0.0", Equal);
    test("0", 10, Down, "0.0", "0x0.0", Equal);
    test("0", 1, Up, "0.0", "0x0.0", Equal);
    test("0", 10, Up, "0.0", "0x0.0", Equal);
    test("0", 1, Floor, "0.0", "0x0.0", Equal);
    test("0", 10, Floor, "0.0", "0x0.0", Equal);
    test("0", 1, Ceiling, "0.0", "0x0.0", Equal);
    test("0", 10, Ceiling, "0.0", "0x0.0", Equal);
    test("0", 1, Nearest, "0.0", "0x0.0", Equal);
    test("0", 10, Nearest, "0.0", "0x0.0", Equal);
    test("0", 1, Exact, "0.0", "0x0.0", Equal);
    test("0", 10, Exact, "0.0", "0x0.0", Equal);
    test("3/5", 1, Floor, "0.50", "0x0.8#1", Less);
    test("3/5", 1, Ceiling, "1.0", "0x1.0#1", Greater);
    test("3/5", 1, Nearest, "0.50", "0x0.8#1", Less);
    test("3/5", 10, Floor, "0.56836", "0x0.918#10", Less);
    test("3/5", 10, Ceiling, "0.56934", "0x0.91c#10", Greater);
    test("3/5", 10, Nearest, "0.56836", "0x0.918#10", Less);
    test(
        "3/5",
        100,
        Floor,
        "0.56882489873224753009868833686101",
        "0x0.919e8231349ca195eef163017#100",
        Less,
    );
    test(
        "3/5",
        100,
        Ceiling,
        "0.56882489873224753009868833686180",
        "0x0.919e8231349ca195eef163018#100",
        Greater,
    );
    test(
        "3/5",
        100,
        Nearest,
        "0.56882489873224753009868833686101",
        "0x0.919e8231349ca195eef163017#100",
        Less,
    );
    test("-3/5", 1, Floor, "-1.0", "-0x1.0#1", Less);
    test("-3/5", 1, Ceiling, "-0.50", "-0x0.8#1", Greater);
    test("-3/5", 1, Nearest, "-0.50", "-0x0.8#1", Greater);
    test("-3/5", 10, Floor, "-0.56934", "-0x0.91c#10", Less);
    test("-3/5", 10, Ceiling, "-0.56836", "-0x0.918#10", Greater);
    test("-3/5", 10, Nearest, "-0.56836", "-0x0.918#10", Greater);
    test(
        "-3/5",
        100,
        Floor,
        "-0.56882489873224753009868833686180",
        "-0x0.919e8231349ca195eef163018#100",
        Less,
    );
    test(
        "-3/5",
        100,
        Ceiling,
        "-0.56882489873224753009868833686101",
        "-0x0.919e8231349ca195eef163017#100",
        Greater,
    );
    test(
        "-3/5",
        100,
        Nearest,
        "-0.56882489873224753009868833686101",
        "-0x0.919e8231349ca195eef163017#100",
        Greater,
    );
    test("1/3", 1, Floor, "0.25", "0x0.4#1", Less);
    test("1/3", 1, Ceiling, "0.50", "0x0.8#1", Greater);
    test("1/3", 1, Nearest, "0.25", "0x0.4#1", Less);
    test("1/3", 10, Floor, "0.32715", "0x0.53c#10", Less);
    test("1/3", 10, Ceiling, "0.32764", "0x0.53e#10", Greater);
    test("1/3", 10, Nearest, "0.32764", "0x0.53e#10", Greater);
    test(
        "1/3",
        100,
        Floor,
        "0.32745015023725844332253525998813",
        "0x0.53d3c5e656dd20ec63b484c7e8#100",
        Less,
    );
    test(
        "1/3",
        100,
        Ceiling,
        "0.32745015023725844332253525998852",
        "0x0.53d3c5e656dd20ec63b484c7f0#100",
        Greater,
    );
    test(
        "1/3",
        100,
        Nearest,
        "0.32745015023725844332253525998813",
        "0x0.53d3c5e656dd20ec63b484c7e8#100",
        Less,
    );
    test("22/7", 1, Floor, "1.0", "0x1.0#1", Less);
    test("22/7", 1, Ceiling, "2.0", "0x2.0#1", Greater);
    test("22/7", 1, Nearest, "2.0", "0x2.0#1", Greater);
    test("22/7", 10, Floor, "1.8613", "0x1.dc8#10", Less);
    test("22/7", 10, Ceiling, "1.8633", "0x1.dd0#10", Greater);
    test("22/7", 10, Nearest, "1.8633", "0x1.dd0#10", Greater);
    test(
        "22/7",
        100,
        Floor,
        "1.8626792111346099850190014829486",
        "0x1.dcd88b76c3216f8eaa82640e4#100",
        Less,
    );
    test(
        "22/7",
        100,
        Ceiling,
        "1.8626792111346099850190014829502",
        "0x1.dcd88b76c3216f8eaa82640e6#100",
        Greater,
    );
    test(
        "22/7",
        100,
        Nearest,
        "1.8626792111346099850190014829502",
        "0x1.dcd88b76c3216f8eaa82640e6#100",
        Greater,
    );
    test("-22/7", 1, Floor, "-2.0", "-0x2.0#1", Less);
    test("-22/7", 1, Ceiling, "-1.0", "-0x1.0#1", Greater);
    test("-22/7", 1, Nearest, "-2.0", "-0x2.0#1", Less);
    test("-22/7", 10, Floor, "-1.8633", "-0x1.dd0#10", Less);
    test("-22/7", 10, Ceiling, "-1.8613", "-0x1.dc8#10", Greater);
    test("-22/7", 10, Nearest, "-1.8633", "-0x1.dd0#10", Less);
    test(
        "-22/7",
        100,
        Floor,
        "-1.8626792111346099850190014829502",
        "-0x1.dcd88b76c3216f8eaa82640e6#100",
        Less,
    );
    test(
        "-22/7",
        100,
        Ceiling,
        "-1.8626792111346099850190014829486",
        "-0x1.dcd88b76c3216f8eaa82640e4#100",
        Greater,
    );
    test(
        "-22/7",
        100,
        Nearest,
        "-1.8626792111346099850190014829502",
        "-0x1.dcd88b76c3216f8eaa82640e6#100",
        Less,
    );
    test("100", 1, Floor, "4.0", "0x4.0#1", Less);
    test("100", 1, Ceiling, "8.0", "0x8.0#1", Greater);
    test("100", 1, Nearest, "4.0", "0x4.0#1", Less);
    test("100", 10, Floor, "5.2969", "0x5.4c#10", Less);
    test("100", 10, Ceiling, "5.3047", "0x5.4e#10", Greater);
    test("100", 10, Nearest, "5.2969", "0x5.4c#10", Less);
    test(
        "100",
        100,
        Floor,
        "5.2983423656105887573688256891088",
        "0x5.4c602a4f4f0a7cedac9045f38#100",
        Less,
    );
    test(
        "100",
        100,
        Ceiling,
        "5.2983423656105887573688256891151",
        "0x5.4c602a4f4f0a7cedac9045f40#100",
        Greater,
    );
    test(
        "100",
        100,
        Nearest,
        "5.2983423656105887573688256891151",
        "0x5.4c602a4f4f0a7cedac9045f40#100",
        Greater,
    );
    test("-100", 1, Floor, "-8.0", "-0x8.0#1", Less);
    test("-100", 1, Ceiling, "-4.0", "-0x4.0#1", Greater);
    test("-100", 1, Nearest, "-4.0", "-0x4.0#1", Greater);
    test("-100", 10, Floor, "-5.3047", "-0x5.4e#10", Less);
    test("-100", 10, Ceiling, "-5.2969", "-0x5.4c#10", Greater);
    test("-100", 10, Nearest, "-5.2969", "-0x5.4c#10", Greater);
    test(
        "-100",
        100,
        Floor,
        "-5.2983423656105887573688256891151",
        "-0x5.4c602a4f4f0a7cedac9045f40#100",
        Less,
    );
    test(
        "-100",
        100,
        Ceiling,
        "-5.2983423656105887573688256891088",
        "-0x5.4c602a4f4f0a7cedac9045f38#100",
        Greater,
    );
    test(
        "-100",
        100,
        Nearest,
        "-5.2983423656105887573688256891151",
        "-0x5.4c602a4f4f0a7cedac9045f40#100",
        Less,
    );
    test("1/1000", 1, Floor, "0.00098", "0x0.004#1", Less);
    test("1/1000", 1, Ceiling, "0.0020", "0x0.008#1", Greater);
    test("1/1000", 1, Nearest, "0.00098", "0x0.004#1", Less);
    test("1/1000", 10, Floor, "0.00099945", "0x0.00418#10", Less);
    test("1/1000", 10, Ceiling, "0.0010014", "0x0.0041a#10", Greater);
    test("1/1000", 10, Nearest, "0.00099945", "0x0.00418#10", Less);
    test(
        "1/1000",
        100,
        Floor,
        "0.00099999983333340833328869050657113",
        "0x0.0041893694862e5580b27b401a80#100",
        Less,
    );
    test(
        "1/1000",
        100,
        Ceiling,
        "0.00099999983333340833328869050657267",
        "0x0.0041893694862e5580b27b401a88#100",
        Greater,
    );
    test(
        "1/1000",
        100,
        Nearest,
        "0.00099999983333340833328869050657267",
        "0x0.0041893694862e5580b27b401a88#100",
        Greater,
    );
    test("-1/1000000", 1, Floor, "-1.9e-6", "-0x0.00002#1", Less);
    test("-1/1000000", 1, Ceiling, "-9.5e-7", "-0x0.00001#1", Greater);
    test("-1/1000000", 1, Nearest, "-9.5e-7", "-0x0.00001#1", Greater);
    test(
        "-1/1000000",
        10,
        Floor,
        "-1.0002e-6",
        "-0x0.000010c8#10",
        Less,
    );
    test(
        "-1/1000000",
        10,
        Ceiling,
        "-9.9838e-7",
        "-0x0.000010c0#10",
        Greater,
    );
    test(
        "-1/1000000",
        10,
        Nearest,
        "-1.0002e-6",
        "-0x0.000010c8#10",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Floor,
        "-9.9999999999983333333333340833361e-7",
        "-0x0.000010c6f7a0b5ea7a2711cf94320a#100",
        Less,
    );
    test(
        "-1/1000000",
        100,
        Ceiling,
        "-9.9999999999983333333333340833211e-7",
        "-0x0.000010c6f7a0b5ea7a2711cf943208#100",
        Greater,
    );
    test(
        "-1/1000000",
        100,
        Nearest,
        "-9.9999999999983333333333340833361e-7",
        "-0x0.000010c6f7a0b5ea7a2711cf94320a#100",
        Less,
    );
    test(
        "1/100000000000000000000",
        1,
        Floor,
        "6.8e-21",
        "0x2.0E-17#1",
        Less,
    );
    test(
        "1/100000000000000000000",
        1,
        Ceiling,
        "1.4e-20",
        "0x4.0E-17#1",
        Greater,
    );
    test(
        "1/100000000000000000000",
        1,
        Nearest,
        "6.8e-21",
        "0x2.0E-17#1",
        Less,
    );
    test(
        "1/100000000000000000000",
        10,
        Floor,
        "9.9923e-21",
        "0x2.f3E-17#10",
        Less,
    );
    test(
        "1/100000000000000000000",
        10,
        Ceiling,
        "1.0006e-20",
        "0x2.f4E-17#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        10,
        Nearest,
        "1.0006e-20",
        "0x2.f4E-17#10",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Floor,
        "9.9999999999999999999999999999955e-21",
        "0x2.f394219248446baa23d2ec728E-17#100",
        Less,
    );
    test(
        "1/100000000000000000000",
        100,
        Ceiling,
        "1.0000000000000000000000000000006e-20",
        "0x2.f394219248446baa23d2ec72cE-17#100",
        Greater,
    );
    test(
        "1/100000000000000000000",
        100,
        Nearest,
        "9.9999999999999999999999999999955e-21",
        "0x2.f394219248446baa23d2ec728E-17#100",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        1,
        Floor,
        "-3.2e-30",
        "-0x4.0E-25#1",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        1,
        Ceiling,
        "-1.6e-30",
        "-0x2.0E-25#1",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        1,
        Nearest,
        "-3.2e-30",
        "-0x4.0E-25#1",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        10,
        Floor,
        "-2.3697e-30",
        "-0x3.01E-25#10",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        10,
        Ceiling,
        "-2.3666e-30",
        "-0x3.00E-25#10",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        10,
        Nearest,
        "-2.3666e-30",
        "-0x3.00E-25#10",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Floor,
        "-2.3665827156630354162351856958508e-30",
        "-0x3.0000000000000000000000004E-25#100",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Ceiling,
        "-2.3665827156630354162351856958484e-30",
        "-0x3.0000000000000000000000000E-25#100",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Nearest,
        "-2.3665827156630354162351856958484e-30",
        "-0x3.0000000000000000000000000E-25#100",
        Greater,
    );
    test("1488522235/2", 1, Floor, "16.0", "0x1.0E+1#1", Less);
    test("1488522235/2", 1, Ceiling, "32.0", "0x2.0E+1#1", Greater);
    test("1488522235/2", 1, Nearest, "16.0", "0x1.0E+1#1", Less);
    test("1488522235/2", 10, Floor, "21.094", "0x15.18#10", Less);
    test("1488522235/2", 10, Ceiling, "21.125", "0x15.20#10", Greater);
    test("1488522235/2", 10, Nearest, "21.125", "0x15.20#10", Greater);
    test(
        "1488522235/2",
        100,
        Floor,
        "21.121049676165439428678979107033",
        "0x15.1efd1c90526b838dc390cdf8#100",
        Less,
    );
    test(
        "1488522235/2",
        100,
        Ceiling,
        "21.121049676165439428678979107058",
        "0x15.1efd1c90526b838dc390cdfa#100",
        Greater,
    );
    test(
        "1488522235/2",
        100,
        Nearest,
        "21.121049676165439428678979107033",
        "0x15.1efd1c90526b838dc390cdf8#100",
        Less,
    );
    test("7442611177/10", 1, Floor, "16.0", "0x1.0E+1#1", Less);
    test("7442611177/10", 1, Ceiling, "32.0", "0x2.0E+1#1", Greater);
    test("7442611177/10", 1, Nearest, "16.0", "0x1.0E+1#1", Less);
    test("7442611177/10", 10, Floor, "21.094", "0x15.18#10", Less);
    test(
        "7442611177/10",
        10,
        Ceiling,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "7442611177/10",
        10,
        Nearest,
        "21.125",
        "0x15.20#10",
        Greater,
    );
    test(
        "7442611177/10",
        100,
        Floor,
        "21.121049676434162320780255257063",
        "0x15.1efd1c9179e2489f1a6da274#100",
        Less,
    );
    test(
        "7442611177/10",
        100,
        Ceiling,
        "21.121049676434162320780255257088",
        "0x15.1efd1c9179e2489f1a6da276#100",
        Greater,
    );
    test(
        "7442611177/10",
        100,
        Nearest,
        "21.121049676434162320780255257088",
        "0x15.1efd1c9179e2489f1a6da276#100",
        Greater,
    );
    test("-7442611177/10", 1, Floor, "-32.0", "-0x2.0E+1#1", Less);
    test(
        "-7442611177/10",
        1,
        Ceiling,
        "-16.0",
        "-0x1.0E+1#1",
        Greater,
    );
    test(
        "-7442611177/10",
        1,
        Nearest,
        "-16.0",
        "-0x1.0E+1#1",
        Greater,
    );
    test("-7442611177/10", 10, Floor, "-21.125", "-0x15.20#10", Less);
    test(
        "-7442611177/10",
        10,
        Ceiling,
        "-21.094",
        "-0x15.18#10",
        Greater,
    );
    test(
        "-7442611177/10",
        10,
        Nearest,
        "-21.125",
        "-0x15.20#10",
        Less,
    );
    test(
        "-7442611177/10",
        100,
        Floor,
        "-21.121049676434162320780255257088",
        "-0x15.1efd1c9179e2489f1a6da276#100",
        Less,
    );
    test(
        "-7442611177/10",
        100,
        Ceiling,
        "-21.121049676434162320780255257063",
        "-0x15.1efd1c9179e2489f1a6da274#100",
        Greater,
    );
    test(
        "-7442611177/10",
        100,
        Nearest,
        "-21.121049676434162320780255257088",
        "-0x15.1efd1c9179e2489f1a6da276#100",
        Less,
    );
    test("744261118", 1, Floor, "16.0", "0x1.0E+1#1", Less);
    test("744261118", 1, Ceiling, "32.0", "0x2.0E+1#1", Greater);
    test("744261118", 1, Nearest, "16.0", "0x1.0E+1#1", Less);
    test("744261118", 10, Floor, "21.094", "0x15.18#10", Less);
    test("744261118", 10, Ceiling, "21.125", "0x15.20#10", Greater);
    test("744261118", 10, Nearest, "21.125", "0x15.20#10", Greater);
    test(
        "744261118",
        100,
        Floor,
        "21.121049676837246658796771995816",
        "0x15.1efd1c93351470369d535cce#100",
        Less,
    );
    test(
        "744261118",
        100,
        Ceiling,
        "21.121049676837246658796771995841",
        "0x15.1efd1c93351470369d535cd0#100",
        Greater,
    );
    test(
        "744261118",
        100,
        Nearest,
        "21.121049676837246658796771995816",
        "0x15.1efd1c93351470369d535cce#100",
        Less,
    );
    test("-744261118", 1, Floor, "-32.0", "-0x2.0E+1#1", Less);
    test("-744261118", 1, Ceiling, "-16.0", "-0x1.0E+1#1", Greater);
    test("-744261118", 1, Nearest, "-16.0", "-0x1.0E+1#1", Greater);
    test("-744261118", 10, Floor, "-21.125", "-0x15.20#10", Less);
    test("-744261118", 10, Ceiling, "-21.094", "-0x15.18#10", Greater);
    test("-744261118", 10, Nearest, "-21.125", "-0x15.20#10", Less);
    test(
        "-744261118",
        100,
        Floor,
        "-21.121049676837246658796771995841",
        "-0x15.1efd1c93351470369d535cd0#100",
        Less,
    );
    test(
        "-744261118",
        100,
        Ceiling,
        "-21.121049676837246658796771995816",
        "-0x15.1efd1c93351470369d535cce#100",
        Greater,
    );
    test(
        "-744261118",
        100,
        Nearest,
        "-21.121049676837246658796771995816",
        "-0x15.1efd1c93351470369d535cce#100",
        Greater,
    );
    test("10000000000", 1, Floor, "16.0", "0x1.0E+1#1", Less);
    test("10000000000", 1, Ceiling, "32.0", "0x2.0E+1#1", Greater);
    test("10000000000", 1, Nearest, "16.0", "0x1.0E+1#1", Less);
    test("10000000000", 10, Floor, "23.719", "0x17.b8#10", Less);
    test("10000000000", 10, Ceiling, "23.750", "0x17.c0#10", Greater);
    test("10000000000", 10, Nearest, "23.719", "0x17.b8#10", Less);
    test(
        "10000000000",
        100,
        Floor,
        "23.718998110500402149599646668292",
        "0x17.b810429a7c2a5d4073437aea#100",
        Less,
    );
    test(
        "10000000000",
        100,
        Ceiling,
        "23.718998110500402149599646668318",
        "0x17.b810429a7c2a5d4073437aec#100",
        Greater,
    );
    test(
        "10000000000",
        100,
        Nearest,
        "23.718998110500402149599646668292",
        "0x17.b810429a7c2a5d4073437aea#100",
        Less,
    );
    test(
        "1/1000",
        100,
        Down,
        "0.00099999983333340833328869050657113",
        "0x0.0041893694862e5580b27b401a80#100",
        Less,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Down,
        "-2.3665827156630354162351856958484e-30",
        "-0x3.0000000000000000000000000E-25#100",
        Greater,
    );
    test(
        "1/1000",
        100,
        Up,
        "0.00099999983333340833328869050657267",
        "0x0.0041893694862e5580b27b401a88#100",
        Greater,
    );
    test(
        "-108086391056891904/45671926166590716193865151022383844364247891967",
        100,
        Up,
        "-2.3665827156630354162351856958508e-30",
        "-0x3.0000000000000000000000004E-25#100",
        Less,
    );
    test("1/65537", 2, Floor, "0.000011", "0x0.0000c#2", Less);
    test("1/65537", 2, Ceiling, "0.000015", "0x0.00010#2", Greater);
    test("1/65537", 2, Nearest, "0.000015", "0x0.00010#2", Greater);
    test("8/4194311", 2, Up, "1.9e-6", "0x0.00002#2", Greater);
    test("-8/4194311", 2, Up, "-1.9e-6", "-0x0.00002#2", Less);
    test("-1/3", 1, Floor, "-0.50", "-0x0.8#1", Less);
    test("-1/3", 1, Ceiling, "-0.25", "-0x0.4#1", Greater);
    test("-1/3", 1, Nearest, "-0.25", "-0x0.4#1", Greater);
    test("-1/3", 10, Floor, "-0.32764", "-0x0.53e#10", Less);
    test("-1/3", 10, Ceiling, "-0.32715", "-0x0.53c#10", Greater);
    test("-1/3", 10, Nearest, "-0.32764", "-0x0.53e#10", Less);
    test(
        "-1/3",
        100,
        Floor,
        "-0.32745015023725844332253525998852",
        "-0x0.53d3c5e656dd20ec63b484c7f0#100",
        Less,
    );
    test(
        "-1/3",
        100,
        Ceiling,
        "-0.32745015023725844332253525998813",
        "-0x0.53d3c5e656dd20ec63b484c7e8#100",
        Greater,
    );
    test(
        "-1/3",
        100,
        Nearest,
        "-0.32745015023725844332253525998813",
        "-0x0.53d3c5e656dd20ec63b484c7e8#100",
        Greater,
    );
    test("1/1000000", 1, Floor, "9.5e-7", "0x0.00001#1", Less);
    test("1/1000000", 1, Ceiling, "1.9e-6", "0x0.00002#1", Greater);
    test("1/1000000", 1, Nearest, "9.5e-7", "0x0.00001#1", Less);
    test("1/1000000", 10, Floor, "9.9838e-7", "0x0.000010c0#10", Less);
    test(
        "1/1000000",
        10,
        Ceiling,
        "1.0002e-6",
        "0x0.000010c8#10",
        Greater,
    );
    test(
        "1/1000000",
        10,
        Nearest,
        "1.0002e-6",
        "0x0.000010c8#10",
        Greater,
    );
    test(
        "1/1000000",
        100,
        Floor,
        "9.9999999999983333333333340833211e-7",
        "0x0.000010c6f7a0b5ea7a2711cf943208#100",
        Less,
    );
    test(
        "1/1000000",
        100,
        Ceiling,
        "9.9999999999983333333333340833361e-7",
        "0x0.000010c6f7a0b5ea7a2711cf94320a#100",
        Greater,
    );
    test(
        "1/1000000",
        100,
        Nearest,
        "9.9999999999983333333333340833361e-7",
        "0x0.000010c6f7a0b5ea7a2711cf94320a#100",
        Greater,
    );
    test("1000000", 1, Floor, "8.0", "0x8.0#1", Less);
    test("1000000", 1, Ceiling, "16.0", "0x1.0E+1#1", Greater);
    test("1000000", 1, Nearest, "16.0", "0x1.0E+1#1", Greater);
    test("1000000", 10, Floor, "14.500", "0xe.80#10", Less);
    test("1000000", 10, Ceiling, "14.516", "0xe.84#10", Greater);
    test("1000000", 10, Nearest, "14.516", "0xe.84#10", Greater);
    test(
        "1000000",
        100,
        Floor,
        "14.508657738524469413525180755814",
        "0xe.823764bfd1e5fa37c6bf52ed#100",
        Less,
    );
    test(
        "1000000",
        100,
        Ceiling,
        "14.508657738524469413525180755826",
        "0xe.823764bfd1e5fa37c6bf52ee#100",
        Greater,
    );
    test(
        "1000000",
        100,
        Nearest,
        "14.508657738524469413525180755814",
        "0xe.823764bfd1e5fa37c6bf52ed#100",
        Less,
    );
    test(
        "10000000000000000000000000000000000000000",
        1,
        Floor,
        "64.0",
        "0x4.0E+1#1",
        Less,
    );
    test(
        "10000000000000000000000000000000000000000",
        1,
        Ceiling,
        "1.3e2",
        "0x8.0E+1#1",
        Greater,
    );
    test(
        "10000000000000000000000000000000000000000",
        1,
        Nearest,
        "64.0",
        "0x4.0E+1#1",
        Less,
    );
    test(
        "10000000000000000000000000000000000000000",
        10,
        Floor,
        "92.750",
        "0x5c.c#10",
        Less,
    );
    test(
        "10000000000000000000000000000000000000000",
        10,
        Ceiling,
        "92.875",
        "0x5c.e#10",
        Greater,
    );
    test(
        "10000000000000000000000000000000000000000",
        10,
        Nearest,
        "92.750",
        "0x5c.c#10",
        Less,
    );
    test(
        "10000000000000000000000000000000000000000",
        100,
        Floor,
        "92.796550900321772670136890308810",
        "0x5c.cbeac2827b3b07fe40298ec8#100",
        Less,
    );
    test(
        "10000000000000000000000000000000000000000",
        100,
        Ceiling,
        "92.796550900321772670136890308911",
        "0x5c.cbeac2827b3b07fe40298ed0#100",
        Greater,
    );
    test(
        "10000000000000000000000000000000000000000",
        100,
        Nearest,
        "92.796550900321772670136890308810",
        "0x5c.cbeac2827b3b07fe40298ec8#100",
        Less,
    );
    test(
        "1/10000000000000000000000000000000000000000",
        1,
        Floor,
        "9.2e-41",
        "0x8.0E-34#1",
        Less,
    );
    test(
        "1/10000000000000000000000000000000000000000",
        1,
        Ceiling,
        "1.8e-40",
        "0x1.0E-33#1",
        Greater,
    );
    test(
        "1/10000000000000000000000000000000000000000",
        1,
        Nearest,
        "9.2e-41",
        "0x8.0E-34#1",
        Less,
    );
    test(
        "1/10000000000000000000000000000000000000000",
        10,
        Floor,
        "9.9907e-41",
        "0x8.b4E-34#10",
        Less,
    );
    test(
        "1/10000000000000000000000000000000000000000",
        10,
        Ceiling,
        "1.0009e-40",
        "0x8.b8E-34#10",
        Greater,
    );
    test(
        "1/10000000000000000000000000000000000000000",
        10,
        Nearest,
        "1.0009e-40",
        "0x8.b8E-34#10",
        Greater,
    );
    test(
        "1/10000000000000000000000000000000000000000",
        100,
        Floor,
        "9.9999999999999999999999999999898e-41",
        "0x8.b61313bbabce2c62323ac4b3E-34#100",
        Less,
    );
    test(
        "1/10000000000000000000000000000000000000000",
        100,
        Ceiling,
        "1.0000000000000000000000000000004e-40",
        "0x8.b61313bbabce2c62323ac4b4E-34#100",
        Greater,
    );
    test(
        "1/10000000000000000000000000000000000000000",
        100,
        Nearest,
        "1.0000000000000000000000000000004e-40",
        "0x8.b61313bbabce2c62323ac4b4E-34#100",
        Greater,
    );
    test(
        "-1/10000000000000000000000000000000000000000",
        1,
        Floor,
        "-1.8e-40",
        "-0x1.0E-33#1",
        Less,
    );
    test(
        "-1/10000000000000000000000000000000000000000",
        1,
        Ceiling,
        "-9.2e-41",
        "-0x8.0E-34#1",
        Greater,
    );
    test(
        "-1/10000000000000000000000000000000000000000",
        1,
        Nearest,
        "-9.2e-41",
        "-0x8.0E-34#1",
        Greater,
    );
    test(
        "-1/10000000000000000000000000000000000000000",
        10,
        Floor,
        "-1.0009e-40",
        "-0x8.b8E-34#10",
        Less,
    );
    test(
        "-1/10000000000000000000000000000000000000000",
        10,
        Ceiling,
        "-9.9907e-41",
        "-0x8.b4E-34#10",
        Greater,
    );
    test(
        "-1/10000000000000000000000000000000000000000",
        10,
        Nearest,
        "-1.0009e-40",
        "-0x8.b8E-34#10",
        Less,
    );
    test(
        "-1/10000000000000000000000000000000000000000",
        100,
        Floor,
        "-1.0000000000000000000000000000004e-40",
        "-0x8.b61313bbabce2c62323ac4b4E-34#100",
        Less,
    );
    test(
        "-1/10000000000000000000000000000000000000000",
        100,
        Ceiling,
        "-9.9999999999999999999999999999898e-41",
        "-0x8.b61313bbabce2c62323ac4b3E-34#100",
        Greater,
    );
    test(
        "-1/10000000000000000000000000000000000000000",
        100,
        Nearest,
        "-1.0000000000000000000000000000004e-40",
        "-0x8.b61313bbabce2c62323ac4b4E-34#100",
        Less,
    );
    // - the series needs a second term to decide the rounding
    test(
        "-1/2048",
        24,
        Nearest,
        "-0.000488281221",
        "-0x0.001fffffe#24",
        Greater,
    );
    // - the series needs a third term
    test(
        "-62914563/68719476736",
        32,
        Nearest,
        "-0.00091552725962",
        "-0x0.003bffffa38#32",
        Less,
    );
    test(
        "17592185552895/72198331524186112",
        42,
        Nearest,
        "0.00024366470813691",
        "0x0.000ff803f3e00c#42",
        Less,
    );
    test(
        "21/787061080478274202283",
        219,
        Nearest,
        "2.668153783851046068064085870059240647975574549532107864539271612541e-20",
        "0x7.dffffffffffffffff03fffffffffffffaeba40000000000001e821E-17#219",
        Greater,
    );
}

#[test]
fn test_asinh_rational_extreme() {
    // |x| = 2^(-2^30 - 10) is too small to be a `Float`, and asinh(x) underflows
    let x = Rational::power_of_2(-(1i64 << 30) - 10);
    for (rm, out, o_out) in [
        (Floor, Float::ZERO, Less),
        (Down, Float::ZERO, Less),
        (Nearest, Float::ZERO, Less),
        (Ceiling, Float::min_positive_value_prec(10), Greater),
        (Up, Float::min_positive_value_prec(10), Greater),
    ] {
        let (c, o) = Float::asinh_rational_prec_round_ref(&x, 10, rm);
        assert_eq!(ComparableFloat(c.clone()), ComparableFloat(out));
        assert_eq!(o, o_out);
        let (c_neg, o_neg) = Float::asinh_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`; asinh(x) = ln(2|x|) + c with 0 < c < 2^(-2^31),
    // far below an ulp of the result, so the result is the rounding of ln(2^(2^30 + 1))
    let x = Rational::power_of_2(1i64 << 30);
    let two_x = Rational::power_of_2((1i64 << 30) + 1);
    for rm in [Floor, Ceiling, Down, Up, Nearest] {
        let (c, o) = Float::asinh_rational_prec_round_ref(&x, 100, rm);
        let (l, o_l) = Float::ln_rational_prec_round_ref(&two_x, 100, rm);
        assert_eq!(ComparableFloat(c.clone()), ComparableFloat(l));
        assert_eq!(o, o_l);
        let (c_neg, o_neg) = Float::asinh_rational_prec_round(-&x, 100, -rm);
        assert_eq!(ComparableFloat(c_neg), ComparableFloat(-c));
        assert_eq!(o_neg, o.reverse());
    }
}

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

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

#[test]
#[should_panic]
fn asinh_rational_prec_round_fail_1() {
    Float::asinh_rational_prec_round(Rational::ONE, 0, Floor);
}

#[test]
#[should_panic]
fn asinh_rational_prec_round_fail_2() {
    Float::asinh_rational_prec_round(Rational::ONE, 10, Exact);
}

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

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

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

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

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

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

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

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

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

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

#[test]
#[allow(clippy::type_repetition_in_bounds)]
fn test_primitive_float_asinh_rational() {
    fn test<T: PrimitiveFloat>(x: &Rational, out: T)
    where
        Float: From<T> + PartialOrd<T>,
        for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float>,
    {
        assert_eq!(
            NiceFloat(primitive_float_asinh_rational::<T>(x)),
            NiceFloat(out)
        );
    }
    let test_s = |s: &str| Rational::from_str(s).unwrap();
    test::<f32>(&test_s("0"), 0.0);
    test::<f32>(&test_s("1"), 0.8813736);
    test::<f32>(&test_s("-1"), -0.8813736);
    test::<f32>(&test_s("1/3"), 0.32745016);
    test::<f32>(&test_s("-1/3"), -0.32745016);
    test::<f32>(&test_s("22/7"), 1.8626792);
    test::<f32>(&test_s("89"), 5.181815);
    test::<f32>(&test_s("90"), 5.192988);
    test::<f32>(&test_s("-90"), -5.192988);
    test::<f32>(&test_s("710"), 7.258413);
    test::<f32>(&test_s("7101/10"), 7.2585535);
    test::<f32>(&test_s("711"), 7.25982);
    test::<f32>(&test_s("-711"), -7.25982);
    test::<f32>(&test_s("10000"), 9.903487);
    test::<f32>(&test_s("1/100000000000000000000"), 1.0e-20);
    test::<f32>(&test_s("-1/100000000000000000000"), -1.0e-20);
    test::<f32>(
        &test_s("1/10000000000000000000000000000000000000000"),
        1.0e-40,
    );
    test::<f32>(
        &test_s("-1/10000000000000000000000000000000000000000"),
        -1.0e-40,
    );
    test::<f32>(
        &test_s("1/100000000000000000000000000000000000000000000000000"),
        0.0,
    );
    test::<f32>(
        &test_s("-1/100000000000000000000000000000000000000000000000000"),
        -0.0,
    );

    test::<f64>(&test_s("0"), 0.0);
    test::<f64>(&test_s("1"), 0.881373587019543);
    test::<f64>(&test_s("-1"), -0.881373587019543);
    test::<f64>(&test_s("1/3"), 0.32745015023725843);
    test::<f64>(&test_s("-1/3"), -0.32745015023725843);
    test::<f64>(&test_s("22/7"), 1.86267921113461);
    test::<f64>(&test_s("89"), 5.181815110469487);
    test::<f64>(&test_s("90"), 5.192987713658941);
    test::<f64>(&test_s("-90"), -5.192987713658941);
    test::<f64>(&test_s("710"), 7.258412646528284);
    test::<f64>(&test_s("7101/10"), 7.258553481541301);
    test::<f64>(&test_s("711"), 7.259820104902117);
    test::<f64>(&test_s("-711"), -7.259820104902117);
    test::<f64>(&test_s("10000"), 9.903487555036127);
    test::<f64>(&test_s("1/100000000000000000000"), 1.0e-20);
    test::<f64>(&test_s("-1/100000000000000000000"), -1.0e-20);
    test::<f64>(
        &test_s("1/10000000000000000000000000000000000000000"),
        1.0e-40,
    );
    test::<f64>(
        &test_s("-1/10000000000000000000000000000000000000000"),
        -1.0e-40,
    );
    test::<f64>(
        &test_s("1/100000000000000000000000000000000000000000000000000"),
        1.0e-50,
    );
    test::<f64>(
        &test_s("-1/100000000000000000000000000000000000000000000000000"),
        -1.0e-50,
    );

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

#[allow(clippy::type_repetition_in_bounds)]
fn primitive_float_asinh_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_asinh_rational::<T>(&x);
        // the hyperbolic sine of a rational is never NaN
        assert!(!c.is_nan());
        // asinh is odd (a `Rational` has no negative zero, so x = 0 is excluded)
        if x != 0u32 {
            assert_eq!(
                NiceFloat(primitive_float_asinh_rational::<T>(&-&x)),
                NiceFloat(-c)
            );
        }
        // the result is the correctly rounded hyperbolic sine as given by the oracle and rounded
        // once to the primitive type
        let rug_c: T = round_once_to_primitive(|p| {
            <Float as From<&rug::Float>>::from(&rug_asinh_rational_prec(&x, p).0)
        });
        assert_eq!(NiceFloat(rug_c), NiceFloat(c));
    });

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

#[test]
fn primitive_float_asinh_rational_properties() {
    apply_fn_to_primitive_floats!(primitive_float_asinh_rational_properties_helper);
}