mpmfnum 0.2.0

use rug::Integer;
use std::cmp::Ordering;

use mpmfnum::rfloat::{RFloat, RFloatContext};
use mpmfnum::{Real, RoundingContext, RoundingMode, Split};

/// Testing all the required methods from [`mpmfnum::Number`].
#[test]
fn traits() {
    assert_eq!(RFloat::radix(), 2, "RFloat is a binary format");

    let vals = [
        RFloat::zero(),                           // 0
        RFloat::one(),                            // 1
        RFloat::Real(true, -4, Integer::from(7)), // -7 * 2^-4
        RFloat::PosInfinity,                      // +Inf
        RFloat::NegInfinity,                      // -Inf,
        RFloat::Nan,                              // NaN
    ];

    // RFloat::sign
    let expected = [
        Some(false),
        Some(false),
        Some(true),
        Some(false),
        Some(true),
        None,
    ];
    for (val, &expected) in vals.iter().zip(expected.iter()) {
        let actual = val.sign();
        assert_eq!(
            actual, expected,
            "{:?} has unexpected sign; expected {:?}, actual {:?}",
            val, expected, actual
        );
    }

    // RFloat::exp
    let expected = [None, Some(0), Some(-4), None, None, None];
    for (val, &expected) in vals.iter().zip(expected.iter()) {
        let actual = val.exp();
        assert_eq!(
            actual, expected,
            "{:?} has unexpected exponent (exp); expected {:?}, actual {:?}",
            val, expected, actual
        );
    }

    // RFloat::e
    let expected = [None, Some(0), Some(-2), None, None, None];
    for (val, &expected) in vals.iter().zip(expected.iter()) {
        let actual = val.e();
        assert_eq!(
            actual, expected,
            "{:?} has unexpected exponent (e); expected {:?}, actual {:?}",
            val, expected, actual
        );
    }

    // RFloat::n
    let expected = [None, Some(-1), Some(-5), None, None, None];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        let actual = val.n();
        assert_eq!(
            actual,
            expected.clone(),
            "{:?} has unexpected least significant exponent (n); expected {:?}, actual {:?}",
            val,
            expected,
            actual
        );
    }

    // RFloat::c
    let expected = [
        Some(Integer::from(0)),
        Some(Integer::from(1)),
        Some(Integer::from(7)),
        None,
        None,
        None,
    ];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        let actual = val.c();
        assert_eq!(
            actual,
            expected.clone(),
            "{:?} has unexpected significand (c): expected {:?}, actual {:?}",
            val,
            expected,
            actual
        );
    }

    // RFloat::m
    let expected = [
        Some(Integer::from(0)),
        Some(Integer::from(1)),
        Some(Integer::from(-7)),
        None,
        None,
        None,
    ];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        let actual = val.m();
        assert_eq!(
            actual,
            expected.clone(),
            "{:?} has unexpected significand (m): expected {:?}, actual {:?}",
            val,
            expected,
            actual
        );
    }

    // RFloat::p
    let expected = [Some(0), Some(1), Some(3), None, None, None];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        let actual = val.prec();
        assert_eq!(
            actual,
            expected.clone(),
            "{:?} has unexpected precision (p): expected {:?}, actual {:?}",
            val,
            expected,
            actual
        );
    }

    // RFloat::is_nar
    let expected = [false, false, false, true, true, true];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        let actual = val.is_nar();
        assert_eq!(
            actual,
            expected.clone(),
            "{:?} is unexpectedly not-a-real (NAR): expected {:?}, actual {:?}",
            val,
            expected,
            actual
        );
    }

    // RFloat::is_finite
    let expected = [true, true, true, false, false, false];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        let actual = val.is_finite();
        assert_eq!(
            actual,
            expected.clone(),
            "{:?}  is unexpectedly finite: expected {:?}, actual {:?}",
            val,
            expected,
            actual
        );
    }

    // RFloat::is_infinite
    let expected = [false, false, false, true, true, false];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        let actual = val.is_infinite();
        assert_eq!(
            actual,
            expected.clone(),
            "{:?} is unexpectedly infinite: expected {:?}, actual {:?}",
            val,
            expected,
            actual
        );
    }

    // RFloat::is_zero
    let expected = [true, false, false, false, false, false];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        let actual = val.is_zero();
        assert_eq!(
            actual,
            expected.clone(),
            "{:?} is unexpectedly zero: expected {:?}, actual {:?}",
            val,
            expected,
            actual
        );
    }

    // RFloat::is_negative
    let expected = [None, Some(false), Some(true), Some(false), Some(true), None];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        let actual = val.is_negative();
        assert_eq!(
            actual,
            expected.clone(),
            "{:?} is unexpectedly zero: expected {:?}, actual {:?}",
            val,
            expected,
            actual
        );
    }
}

/// Testing rounding for easy cases
#[test]
fn round_trivial() {
    // rounding context
    let ctx = RFloatContext::new().with_max_p(1);

    // round(zero) = round
    let zero = RFloat::zero();
    let (p, n) = ctx.round_params(&zero);
    let split = Split::new(&zero, p, n);
    let err = split.lost();
    let rounded = ctx.round(&zero);
    assert!(rounded.is_zero(), "round(0) = 0");
    assert!(err.is_zero(), "rounding 0 should have a zero lost bits");

    // round(+Inf) = +Inf
    let rounded = ctx.round(&RFloat::PosInfinity);
    assert!(rounded.is_infinite(), "round(+Inf) = +Inf");

    // round(-Inf) = -Inf
    let rounded = ctx.round(&RFloat::NegInfinity);
    assert!(rounded.is_infinite(), "round(-Inf) = -Inf");

    // round(Nan) = Nan
    let rounded = ctx.round(&RFloat::Nan);
    assert!(rounded.is_nar(), "round(-Nan) = Nan");
}

fn round1(ctx: &RFloatContext, num: &RFloat) -> (RFloat, RFloat) {
    let (p, n) = ctx.round_params(num);
    let split = Split::new(num, p, n);
    let err = split.lost().clone();
    let rounded = ctx.round(num);
    (rounded, err)
}

/// Testing rounding using fixed-point rounding
#[test]
fn round_fixed() {
    let one_3_4 = RFloat::Real(false, -2, Integer::from(7));
    let one_1_2 = RFloat::Real(false, -1, Integer::from(3));
    let one = RFloat::one();
    let three_4 = RFloat::Real(false, -2, Integer::from(3));
    let one_4 = RFloat::Real(false, -2, Integer::from(1));
    let zero = RFloat::zero();

    let neg_one = RFloat::Real(true, 0, Integer::from(1));

    // 1 (min_n == -1) => 1
    let ctx = RFloatContext::new()
        .with_min_n(-1)
        .with_rounding_mode(RoundingMode::ToZero);
    let (rounded, err) = round1(&ctx, &one);
    assert_eq!(rounded, RFloat::one(), "rounding should not have lost bits");
    assert!(err.is_zero(), "lost bits should be 0");

    // 1 (min_n == 0) => 0
    let ctx = RFloatContext::new()
        .with_min_n(0)
        .with_rounding_mode(RoundingMode::ToZero);
    let (rounded, err) = round1(&ctx, &one);
    assert_eq!(rounded, RFloat::zero(), "rounding should be truncated to 0");
    assert_eq!(err, RFloat::one(), "lost bits should be 1");

    // -1 (min_n == 0) => 0
    let ctx = RFloatContext::new()
        .with_min_n(0)
        .with_rounding_mode(RoundingMode::ToZero);
    let (rounded, err) = round1(&ctx, &neg_one);
    assert_eq!(rounded, zero, "rounding should truncated to 0");
    assert_eq!(err, neg_one, "lost bits should be -1");

    // 1.75 (min_n == -1) => 1
    let ctx = RFloatContext::new()
        .with_min_n(-1)
        .with_rounding_mode(RoundingMode::ToZero);
    let (rounded, err) = round1(&ctx, &one_3_4);
    assert_eq!(rounded, one, "rounding should truncated to 0");
    assert_eq!(err, three_4, "lost bits should be 3/4");

    // 1.75 (min_n == -2) => 1.5
    let ctx = RFloatContext::new()
        .with_min_n(-2)
        .with_rounding_mode(RoundingMode::ToZero);
    let (rounded, err) = round1(&ctx, &one_3_4);
    assert_eq!(rounded, one_1_2, "rounding should truncated to 0");
    assert_eq!(err, one_4, "lost bits should be 1/4");

    // 1 (min_n == 10) => 0
    let ctx = RFloatContext::new()
        .with_min_n(10)
        .with_rounding_mode(RoundingMode::ToZero);
    let (rounded, err) = round1(&ctx, &one);
    assert_eq!(rounded, zero, "rounding should truncated to 0");
    assert_eq!(err, one, "lost bits should be 1");
}

/// Testing rounding using floating-point rounding
#[test]
fn round_float() {
    let one_1_2 = RFloat::Real(false, -1, Integer::from(3));
    let one_1_4 = RFloat::Real(false, -2, Integer::from(5));
    let one_1_8 = RFloat::Real(false, -3, Integer::from(9));
    let one = RFloat::one();
    let one_4 = RFloat::Real(false, -2, Integer::from(1));
    let one_8 = RFloat::Real(false, -3, Integer::from(1));
    let zero = RFloat::zero();

    // 1.25, 3 bits

    // rounding 1.25 with 3 bits, exact
    let ctx = RFloatContext::new().with_max_p(3);
    let (rounded, err) = round1(&ctx, &one_1_4);
    assert_eq!(rounded, one_1_4, "rounding should be exact");
    assert_eq!(err, zero, "lost bits is zero");

    // 1.25, 2 bits

    // rounding 1.25 with 2 bits, round-to-nearest
    let ctx = ctx.with_max_p(2);
    let (rounded, err) = round1(&ctx, &one_1_4);
    assert_eq!(rounded, one, "rounding goes to 1");
    assert_eq!(err, one_4, "lost bits is 1/4");

    // rounding 1.25 with 2 bits, round-to-positive
    let ctx = ctx.with_rounding_mode(RoundingMode::ToPositive);
    let (rounded, err) = round1(&ctx, &one_1_4);
    assert_eq!(rounded, one_1_2, "rounding goes to 3/2");
    assert_eq!(err, one_4, "lost bits is -1/4");

    // rounding 1.25 with 2 bits, round-to-negative
    let ctx = ctx.with_rounding_mode(RoundingMode::ToNegative);
    let (rounded, err) = round1(&ctx, &one_1_4);
    assert_eq!(rounded, one, "rounding goes to 1");
    assert_eq!(err, one_4, "lost bits is 1/4");

    // rounding 1.25 with 2 bits, round-to-even
    let ctx = ctx.with_rounding_mode(RoundingMode::ToEven);
    let (rounded, err) = round1(&ctx, &one_1_4);
    assert_eq!(rounded, one, "rounding goes to 1");
    assert_eq!(err, one_4, "lost bits is 1/4");

    // rounding 1.25 with 2 bits, round-to-odd
    let ctx = ctx.with_rounding_mode(RoundingMode::ToOdd);
    let (rounded, err) = round1(&ctx, &one_1_4);
    assert_eq!(rounded, one_1_2, "rounding goes to 3/2");
    assert_eq!(err, one_4, "lost bits is -1/4");

    // 1.125, 2 bit

    // rounding 1.125 with 2 bits, round-to-nearest
    let ctx = ctx.with_rounding_mode(RoundingMode::NearestTiesToEven);
    let (rounded, err) = round1(&ctx, &one_1_8);
    assert_eq!(rounded, one, "rounding goes to 1");
    assert_eq!(err, one_8, "lost bits is 1/8");

    // rounding 1.125 with 2 bits, round-to-positive
    let ctx = ctx.with_rounding_mode(RoundingMode::ToPositive);
    let (rounded, err) = round1(&ctx, &one_1_8);
    assert_eq!(rounded, one_1_2, "rounding goes to 3/2");
    assert_eq!(err, one_8, "lost bits is 1/8");

    // rounding 1.125 with 2 bits, round-to-negative
    let ctx = ctx.with_rounding_mode(RoundingMode::ToNegative);
    let (rounded, err) = round1(&ctx, &one_1_8);
    assert_eq!(rounded, one, "rounding goes to 1");
    assert_eq!(err, one_8, "lost bits is 1/8");

    // rounding 1.125 with 2 bits, round-to-even
    let ctx = ctx.with_rounding_mode(RoundingMode::ToEven);
    let (rounded, err) = round1(&ctx, &one_1_8);
    assert_eq!(rounded, one, "rounding goes to 1");
    assert_eq!(err, one_8, "lost bits is 1/8");

    // rounding 1.125 with 2 bits, round-to-odd
    let ctx = ctx.with_rounding_mode(RoundingMode::ToOdd);
    let (rounded, err) = round1(&ctx, &one_1_8);
    assert_eq!(rounded, one_1_2, "rounding goes to 3/2");
    assert_eq!(err, one_8, "lost bits is -3/8");
}

/// Testing rounding using floating-point rounding using subnormals
#[test]
fn round_float_subnorm() {
    let one = RFloat::one();
    let half_way = RFloat::Real(false, -3, Integer::from(7));
    let tiny_val = RFloat::Real(false, -2, Integer::from(3));
    let one_2 = RFloat::Real(false, -1, Integer::from(1));
    let one_4 = RFloat::Real(false, -2, Integer::from(1));
    let one_8 = RFloat::Real(false, -3, Integer::from(1));

    // No subnormals, round-to-nearest
    let ctx = RFloatContext::new().with_max_p(2);
    let (rounded, err) = round1(&ctx, &half_way);
    assert_eq!(one, rounded, "rounding to 1");
    assert_eq!(err, one_8, "lost bits is 1/8");

    // No subnormals, round-away-zero
    let ctx = ctx.with_rounding_mode(RoundingMode::AwayZero);
    let (rounded, err) = round1(&ctx, &half_way);
    assert_eq!(one, rounded, "rounding to 1");
    assert_eq!(err, one_8, "lost bits is 1/8");

    // No subnormals, round-to-zero
    let ctx = ctx.with_rounding_mode(RoundingMode::ToZero);
    let (rounded, err) = round1(&ctx, &half_way);
    assert_eq!(tiny_val, rounded, "rounding to 3/4");
    assert_eq!(err, one_8, "lost bits is 1/8");

    // RFloat<2, 4>, round-to-nearest
    let ctx = RFloatContext::new().with_max_p(2).with_min_n(-2);
    let (rounded, err) = round1(&ctx, &tiny_val);
    assert_eq!(one, rounded, "rounding to 1");
    assert_eq!(err, one_4, "lost bits is 1/4");

    // RFloat<2, 4>, round-away-zero
    let ctx = ctx.with_rounding_mode(RoundingMode::AwayZero);
    let (rounded, err) = round1(&ctx, &tiny_val);
    assert_eq!(one, rounded, "rounding to 1");
    assert_eq!(err, one_4, "lost bits is 1/4");

    // RFloat<2, 4>, round-to-zero
    let ctx = ctx.with_rounding_mode(RoundingMode::ToZero);
    let (rounded, err) = round1(&ctx, &tiny_val);
    assert_eq!(one_2, rounded, "rounding to 1/2");
    assert_eq!(err, one_4, "lost bits is 1/4");

    // RFloat<2, 4>, round-to-even
    let ctx = ctx.with_rounding_mode(RoundingMode::ToEven);
    let (rounded, err) = round1(&ctx, &tiny_val);
    assert_eq!(one, rounded, "rounding to 1");
    assert_eq!(err, one_4, "lost bits is 1/4");

    // RFloat<2, 4>, round-to-odd
    let ctx = ctx.with_rounding_mode(RoundingMode::ToOdd);
    let (rounded, err) = round1(&ctx, &tiny_val);
    assert_eq!(one_2, rounded, "rounding to 1/2");
    assert_eq!(err, one_4, "lost bits is 1/4");
}

fn assert_expected_cmp(x: &RFloat, y: &RFloat, expected: &Option<Ordering>) {
    let actual = x.partial_cmp(y);
    assert_eq!(
        actual,
        expected.clone(),
        "unexpected comparison result between {:?} and {:?}: expected {:?}, actual {:?}",
        x,
        y,
        expected,
        actual
    );
}

#[test]
fn ordering() {
    // values to compare against
    let vals = [
        RFloat::zero(),
        RFloat::one(),
        RFloat::PosInfinity.clone(),
        RFloat::NegInfinity.clone(),
        RFloat::Nan.clone(),
    ];

    // compare with 0
    let zero = RFloat::zero();
    let expected = [
        Some(Ordering::Equal),
        Some(Ordering::Less),
        Some(Ordering::Less),
        Some(Ordering::Greater),
        None,
    ];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        assert_expected_cmp(&zero, val, expected);
    }

    // compare with 1
    let one = RFloat::one();
    let expected = [
        Some(Ordering::Greater),
        Some(Ordering::Equal),
        Some(Ordering::Less),
        Some(Ordering::Greater),
        None,
    ];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        assert_expected_cmp(&one, val, expected);
    }

    // compare with +Inf
    let expected = [
        Some(Ordering::Greater),
        Some(Ordering::Greater),
        Some(Ordering::Equal),
        Some(Ordering::Greater),
        None,
    ];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        assert_expected_cmp(&RFloat::PosInfinity, val, expected);
    }

    // compare with -Inf
    let expected = [
        Some(Ordering::Less),
        Some(Ordering::Less),
        Some(Ordering::Less),
        Some(Ordering::Equal),
        None,
    ];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        assert_expected_cmp(&RFloat::NegInfinity, val, expected);
    }

    // compare with Nan
    let expected = [None, None, None, None, None];
    for (val, expected) in vals.iter().zip(expected.iter()) {
        assert_expected_cmp(&RFloat::Nan, val, expected);
    }

    // test normalization
    let one = RFloat::one();
    let also_one = RFloat::Real(false, -1, Integer::from(2));
    assert_eq!(
        one.partial_cmp(&also_one),
        Some(Ordering::Equal),
        "should be the same"
    );

    let still_one = RFloat::Real(false, -2, Integer::from(4));
    assert_eq!(
        one.partial_cmp(&still_one),
        Some(Ordering::Equal),
        "should be the same"
    );
}

fn is_equal(x: &RFloat, y: &RFloat) -> bool {
    match (x, y) {
        (RFloat::Nan, RFloat::Nan) => true,
        (_, _) => *x == *y,
    }
}

fn assert_expected_mul(x: &RFloat, y: &RFloat, expected: &RFloat) {
    let left = x.clone() * y.clone();
    let right = y.clone() * x.clone();
    assert!(
        is_equal(&left, expected),
        "for {:?} * {:?}: expected {:?}, actual {:?}",
        x,
        y,
        expected,
        left
    );
    assert!(
        is_equal(&left, expected),
        "multiplication is commutative: {:?} != {:?}",
        left,
        right
    );
}

#[test]
fn multiplication() {
    // test values
    let zero = RFloat::zero(); // 0
    let one = RFloat::one(); // 1
    let frac = RFloat::Real(true, -4, Integer::from(7)); // -7 * 2^-4
    let pos_inf = RFloat::PosInfinity; // +Inf
    let neg_inf = RFloat::NegInfinity; // -Inf,
    let nan = RFloat::Nan; // NaN

    let vals = [&zero, &one, &frac, &pos_inf, &neg_inf, &nan];

    // Multiply by 0
    let expected = [&zero, &zero, &zero, &nan, &nan, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_mul(&zero, val, expected);
    }

    // Multiply by 1
    let expected = [&zero, &one, &frac, &pos_inf, &neg_inf, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_mul(&one, val, expected);
    }

    // Multiply by -7 * 2^-4
    let frac_sqr = RFloat::Real(false, -8, Integer::from(49));
    let expected = [&zero, &frac, &frac_sqr, &neg_inf, &pos_inf, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_mul(&frac, val, expected);
    }

    // Multiply by +Inf
    let expected = [&nan, &pos_inf, &neg_inf, &pos_inf, &neg_inf, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_mul(&pos_inf, val, expected);
    }

    // Multiply by -Inf
    let expected = [&nan, &neg_inf, &pos_inf, &neg_inf, &pos_inf, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_mul(&neg_inf, val, expected);
    }

    // Multiply by Nan
    let expected = [&nan; 6];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_mul(&nan, val, expected);
    }
}

fn assert_expected_add(x: &RFloat, y: &RFloat, expected: &RFloat) {
    let left = x.clone() + y.clone();
    let right = y.clone() + x.clone();
    assert!(
        is_equal(&left, expected),
        "for {:?} + {:?}: expected {:?}, actual {:?}",
        x,
        y,
        expected,
        left
    );
    assert!(
        is_equal(&left, expected),
        "addition is commutative: {:?} != {:?}",
        left,
        right
    );
}

#[test]
fn addition() {
    // test values
    let zero = RFloat::zero(); // 0
    let one = RFloat::one(); // 1
    let frac = RFloat::Real(true, -4, Integer::from(7)); // -7 * 2^-4
    let pos_inf = RFloat::PosInfinity; // +Inf
    let neg_inf = RFloat::NegInfinity; // -Inf,
    let nan = RFloat::Nan; // NaN

    let two = RFloat::Real(false, 0, Integer::from(2)); // 2
    let two_frac = RFloat::Real(true, -4, Integer::from(14)); // 14 * 2^-4
    let one_m_frac = RFloat::Real(false, -4, Integer::from(9)); // 9 * 2^-4

    let vals = [&zero, &one, &frac, &pos_inf, &neg_inf, &nan];

    // Add by 0
    let expected = [&zero, &one, &frac, &pos_inf, &neg_inf, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_add(&zero, val, expected);
    }

    // Add by 1
    let expected = [&one, &two, &one_m_frac, &pos_inf, &neg_inf, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_add(&one, val, expected);
    }

    // Add by -7 * 2^-4
    let expected = [&frac, &one_m_frac, &two_frac, &pos_inf, &neg_inf, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_add(&frac, val, expected);
    }

    // Add by +Inf
    let expected = [&pos_inf, &pos_inf, &pos_inf, &pos_inf, &nan, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_add(&pos_inf, val, expected);
    }

    // Add by -Inf
    let expected = [&neg_inf, &neg_inf, &neg_inf, &nan, &neg_inf, &nan];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_add(&neg_inf, val, expected);
    }

    // Add by Nan
    let expected = [&nan; 6];
    for (&val, &expected) in vals.iter().zip(expected.iter()) {
        assert_expected_add(&nan, val, expected);
    }
}

#[test]
fn neg() {
    // test values
    let zero = RFloat::zero(); // 0
    let one = RFloat::one(); // 1
    let frac = RFloat::Real(true, -4, Integer::from(7)); // -7 * 2^-4
    let pos_inf = RFloat::PosInfinity; // +Inf
    let neg_inf = RFloat::NegInfinity; // -Inf,

    let neg_zero = -zero;
    let neg_one = -one;
    let neg_frac = -frac;
    let neg_pos_inf = -pos_inf;
    let neg_neg_inf = -neg_inf;

    assert!(!neg_zero.sign().unwrap(), "-0 should not have a sign");
    assert!(neg_one.sign().unwrap(), "-1 is signed");
    assert!(!neg_frac.sign().unwrap(), "-(-7 * 2^-4) is not signed");
    assert!(neg_pos_inf.sign().unwrap(), "-(+Inf) is signed");
    assert!(!neg_neg_inf.sign().unwrap(), "-(-Inf) is not signed");
}

#[test]
fn mpfr_integration() {
    // test values
    let zero = RFloat::zero(); // 0
    let one = RFloat::one(); // 1
    let frac = RFloat::Real(true, -4, Integer::from(7)); // -7 * 2^-4
    let pos_inf = RFloat::PosInfinity;
    let neg_inf = RFloat::NegInfinity;
    let nan = RFloat::Nan;

    let vals = [zero, one, frac, pos_inf, neg_inf, nan];

    for val in &vals {
        let f: RFloat = val.clone().into();
        let val2 = RFloat::from(f);
        assert!(
            is_equal(val, &val2),
            "conversion should have been exact: {:?} != {:?}",
            val,
            val2
        );
    }
}