rust/library/coretests/tests/floats/mod.rs

use std::fmt;
use std::ops::{Add, Div, Mul, Rem, Sub};

/// Set the default tolerance for float comparison based on the type.
trait Approx {
    const LIM: Self;
}

impl Approx for f16 {
    const LIM: Self = 1e-3;
}
impl Approx for f32 {
    const LIM: Self = 1e-6;
}
impl Approx for f64 {
    const LIM: Self = 1e-6;
}
impl Approx for f128 {
    const LIM: Self = 1e-9;
}

/// Determine the tolerance for values of the argument type.
const fn lim_for_ty<T: Approx + Copy>(_x: T) -> T {
    T::LIM
}

/// Verify that floats are within a tolerance of each other.
macro_rules! assert_approx_eq_ {
    ($a:expr, $b:expr) => {{ assert_approx_eq!($a, $b, $crate::floats::lim_for_ty($a)) }};
    ($a:expr, $b:expr, $lim:expr) => {{
        let (a, b) = (&$a, &$b);
        let diff = (*a - *b).abs();
        assert!(
            diff <= $lim,
            "{a:?} is not approximately equal to {b:?} (threshold {lim:?}, difference {diff:?})",
            lim = $lim
        );
    }};
}
pub(crate) use assert_approx_eq_ as assert_approx_eq;

/// Verify that floats have the same bitwise representation. Used to avoid the default `0.0 == -0.0`
/// behavior, as well as to ensure exact NaN bitpatterns.
macro_rules! assert_biteq_ {
    (@inner $left:expr, $right:expr, $msg_sep:literal, $($tt:tt)*) => {{
        let l = $left;
        let r = $right;

        // Hack to coerce left and right to the same type
        let mut _eq_ty = l;
        _eq_ty = r;

        // Hack to get the width from a value
        let bits = (l.to_bits() - l.to_bits()).leading_zeros();
        assert!(
            l.to_bits() == r.to_bits(),
            "{msg}{nl}l: {l:?} ({lb:#0width$x})\nr: {r:?} ({rb:#0width$x})",
            msg = format_args!($($tt)*),
            nl = $msg_sep,
            lb = l.to_bits(),
            rb = r.to_bits(),
            width = ((bits / 4) + 2) as usize,
        );

        if !l.is_nan() && !r.is_nan() {
            // Also check that standard equality holds, since most tests use `assert_biteq` rather
            // than `assert_eq`.
            assert_eq!(l, r);
        }
    }};
    ($left:expr, $right:expr , $($tt:tt)*) => {
        assert_biteq_!(@inner $left, $right, "\n", $($tt)*)
    };
    ($left:expr, $right:expr $(,)?) => {
        assert_biteq_!(@inner $left, $right, "", "")
    };
}
pub(crate) use assert_biteq_ as assert_biteq;

mod const_asserts {
    // Shadow some assert implementations that would otherwise not compile in a const-context.
    // Every macro added here also needs to be added in the `float_test!` macro below.

    macro_rules! assert_biteq {
        (@inner $left:expr, $right:expr, $msg_sep:literal, $($tt:tt)*) => {{
            let l = $left;
            let r = $right;

            // Hack to coerce left and right to the same type
            let mut _eq_ty = l;
            _eq_ty = r;

            assert!(l.to_bits() == r.to_bits());

            if !l.is_nan() && !r.is_nan() {
                // Also check that standard equality holds, since most tests use `assert_biteq` rather
                // than `assert_eq`.
                assert!(l == r);
            }
        }};
        ($left:expr, $right:expr , $($tt:tt)*) => {
            assert_biteq!(@inner $left, $right, "\n", $($tt)*)
        };
        ($left:expr, $right:expr $(,)?) => {
            assert_biteq!(@inner $left, $right, "", "")
        };
    }
    pub(crate) use assert_biteq;

    macro_rules! assert_approx_eq {
        ($a:expr, $b:expr) => {{ assert_approx_eq!($a, $b, $crate::floats::lim_for_ty($a)) }};
        ($a:expr, $b:expr, $lim:expr) => {{
            let (a, b) = (&$a, &$b);
            let diff = (*a - *b).abs();
            assert!(diff <= $lim);
        }};
    }
    pub(crate) use assert_approx_eq;
}

/// Generate float tests for all our float types, for compile-time and run-time behavior.
///
/// By default all tests run for all float types. Configuration can be applied via `attrs`.
///
/// ```ignore (this is only a sketch)
/// float_test! {
///     name: fn_name, /* function under test */
///     attrs: {
///         // Apply a configuration to the test for a single type
///         f16: #[cfg(target_has_reliable_f16_math)],
///         // Types can be excluded with `cfg(false)`
///         f64: #[cfg(false)],
///     },
///     test<Float> {
///         /* write tests here, using `Float` as the type */
///     }
/// }
macro_rules! float_test {
    (
        name: $name:ident,
        attrs: {
            $(const: #[ $($const_meta:meta),+ ] ,)?
            $(f16: #[ $($f16_meta:meta),+ ] ,)?
            $(const f16: #[ $($f16_const_meta:meta),+ ] ,)?
            $(f32: #[ $($f32_meta:meta),+ ] ,)?
            $(const f32: #[ $($f32_const_meta:meta),+ ] ,)?
            $(f64: #[ $($f64_meta:meta),+ ] ,)?
            $(const f64: #[ $($f64_const_meta:meta),+ ] ,)?
            $(f128: #[ $($f128_meta:meta),+ ] ,)?
            $(const f128: #[ $($f128_const_meta:meta),+ ] ,)?
        },
        test<$fty:ident> $test:block
    ) => {
        mod $name {
            use super::*;

            #[test]
            $( $( #[$f16_meta] )+ )?
            fn test_f16() {
                type $fty = f16;
                $test
            }

            #[test]
            $( $( #[$f32_meta] )+ )?
            fn test_f32() {
                type $fty = f32;
                $test
            }

            #[test]
            $( $( #[$f64_meta] )+ )?
            fn test_f64() {
                type $fty = f64;
                $test
            }

            #[test]
            $( $( #[$f128_meta] )+ )?
            fn test_f128() {
                type $fty = f128;
                $test
            }

            $( $( #[$const_meta] )+ )?
            mod const_ {
                #[allow(unused)]
                use super::Approx;
                #[allow(unused)]
                use $crate::floats::const_asserts::{assert_biteq, assert_approx_eq};

                #[test]
                $( $( #[$f16_const_meta] )+ )?
                fn test_f16() {
                    type $fty = f16;
                    const { $test }
                }

                #[test]
                $( $( #[$f32_const_meta] )+ )?
                fn test_f32() {
                    type $fty = f32;
                    const { $test }
                }

                #[test]
                $( $( #[$f64_const_meta] )+ )?
                fn test_f64() {
                    type $fty = f64;
                    const { $test }
                }

                #[test]
                $( $( #[$f128_const_meta] )+ )?
                fn test_f128() {
                    type $fty = f128;
                    const { $test }
                }
            }
        }
    };
}

/// Helper function for testing numeric operations
pub fn test_num<T>(ten: T, two: T)
where
    T: PartialEq
        + Add<Output = T>
        + Sub<Output = T>
        + Mul<Output = T>
        + Div<Output = T>
        + Rem<Output = T>
        + fmt::Debug
        + Copy,
{
    assert_eq!(ten.add(two), ten + two);
    assert_eq!(ten.sub(two), ten - two);
    assert_eq!(ten.mul(two), ten * two);
    assert_eq!(ten.div(two), ten / two);
    assert_eq!(ten.rem(two), ten % two);
}

mod f128;
mod f16;
mod f32;
mod f64;

float_test! {
    name: min,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((0.0 as Float).min(0.0), 0.0);
        assert_biteq!((-0.0 as Float).min(-0.0), -0.0);
        assert_biteq!((9.0 as Float).min(9.0), 9.0);
        assert_biteq!((-9.0 as Float).min(0.0), -9.0);
        assert_biteq!((0.0 as Float).min(9.0), 0.0);
        assert_biteq!((-0.0 as Float).min(9.0), -0.0);
        assert_biteq!((-0.0 as Float).min(-9.0), -9.0);
        assert_biteq!(Float::INFINITY.min(9.0), 9.0);
        assert_biteq!((9.0 as Float).min(Float::INFINITY), 9.0);
        assert_biteq!(Float::INFINITY.min(-9.0), -9.0);
        assert_biteq!((-9.0 as Float).min(Float::INFINITY), -9.0);
        assert_biteq!(Float::NEG_INFINITY.min(9.0), Float::NEG_INFINITY);
        assert_biteq!((9.0 as Float).min(Float::NEG_INFINITY), Float::NEG_INFINITY);
        assert_biteq!(Float::NEG_INFINITY.min(-9.0), Float::NEG_INFINITY);
        assert_biteq!((-9.0 as Float).min(Float::NEG_INFINITY), Float::NEG_INFINITY);
        assert_biteq!(Float::NAN.min(9.0), 9.0);
        assert_biteq!(Float::NAN.min(-9.0), -9.0);
        assert_biteq!((9.0 as Float).min(Float::NAN), 9.0);
        assert_biteq!((-9.0 as Float).min(Float::NAN), -9.0);
        assert!(Float::NAN.min(Float::NAN).is_nan());
    }
}

float_test! {
    name: max,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((0.0 as Float).max(0.0), 0.0);
        assert_biteq!((-0.0 as Float).max(-0.0), -0.0);
        assert_biteq!((9.0 as Float).max(9.0), 9.0);
        assert_biteq!((-9.0 as Float).max(0.0), 0.0);
        assert_biteq!((-9.0 as Float).max(-0.0), -0.0);
        assert_biteq!((0.0 as Float).max(9.0), 9.0);
        assert_biteq!((0.0 as Float).max(-9.0), 0.0);
        assert_biteq!((-0.0 as Float).max(-9.0), -0.0);
        assert_biteq!(Float::INFINITY.max(9.0), Float::INFINITY);
        assert_biteq!((9.0 as Float).max(Float::INFINITY), Float::INFINITY);
        assert_biteq!(Float::INFINITY.max(-9.0), Float::INFINITY);
        assert_biteq!((-9.0 as Float).max(Float::INFINITY), Float::INFINITY);
        assert_biteq!(Float::NEG_INFINITY.max(9.0), 9.0);
        assert_biteq!((9.0 as Float).max(Float::NEG_INFINITY), 9.0);
        assert_biteq!(Float::NEG_INFINITY.max(-9.0), -9.0);
        assert_biteq!((-9.0 as Float).max(Float::NEG_INFINITY), -9.0);
        assert_biteq!(Float::NAN.max(9.0), 9.0);
        assert_biteq!(Float::NAN.max(-9.0), -9.0);
        assert_biteq!((9.0 as Float).max(Float::NAN), 9.0);
        assert_biteq!((-9.0 as Float).max(Float::NAN), -9.0);
        assert!(Float::NAN.max(Float::NAN).is_nan());
    }
}

float_test! {
    name: minimum,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((0.0 as Float).minimum(0.0), 0.0);
        assert_biteq!((-0.0 as Float).minimum(0.0), -0.0);
        assert_biteq!((-0.0 as Float).minimum(-0.0), -0.0);
        assert_biteq!((9.0 as Float).minimum(9.0), 9.0);
        assert_biteq!((-9.0 as Float).minimum(0.0), -9.0);
        assert_biteq!((0.0 as Float).minimum(9.0), 0.0);
        assert_biteq!((-0.0 as Float).minimum(9.0), -0.0);
        assert_biteq!((-0.0 as Float).minimum(-9.0), -9.0);
        assert_biteq!(Float::INFINITY.minimum(9.0), 9.0);
        assert_biteq!((9.0 as Float).minimum(Float::INFINITY), 9.0);
        assert_biteq!(Float::INFINITY.minimum(-9.0), -9.0);
        assert_biteq!((-9.0 as Float).minimum(Float::INFINITY), -9.0);
        assert_biteq!(Float::NEG_INFINITY.minimum(9.0), Float::NEG_INFINITY);
        assert_biteq!((9.0 as Float).minimum(Float::NEG_INFINITY), Float::NEG_INFINITY);
        assert_biteq!(Float::NEG_INFINITY.minimum(-9.0), Float::NEG_INFINITY);
        assert_biteq!((-9.0 as Float).minimum(Float::NEG_INFINITY), Float::NEG_INFINITY);
        assert!(Float::NAN.minimum(9.0).is_nan());
        assert!(Float::NAN.minimum(-9.0).is_nan());
        assert!((9.0 as Float).minimum(Float::NAN).is_nan());
        assert!((-9.0 as Float).minimum(Float::NAN).is_nan());
        assert!(Float::NAN.minimum(Float::NAN).is_nan());
    }
}

float_test! {
    name: maximum,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((0.0 as Float).maximum(0.0), 0.0);
        assert_biteq!((-0.0 as Float).maximum(0.0), 0.0);
        assert_biteq!((-0.0 as Float).maximum(-0.0), -0.0);
        assert_biteq!((9.0 as Float).maximum(9.0), 9.0);
        assert_biteq!((-9.0 as Float).maximum(0.0), 0.0);
        assert_biteq!((-9.0 as Float).maximum(-0.0), -0.0);
        assert_biteq!((0.0 as Float).maximum(9.0), 9.0);
        assert_biteq!((0.0 as Float).maximum(-9.0), 0.0);
        assert_biteq!((-0.0 as Float).maximum(-9.0), -0.0);
        assert_biteq!(Float::INFINITY.maximum(9.0), Float::INFINITY);
        assert_biteq!((9.0 as Float).maximum(Float::INFINITY), Float::INFINITY);
        assert_biteq!(Float::INFINITY.maximum(-9.0), Float::INFINITY);
        assert_biteq!((-9.0 as Float).maximum(Float::INFINITY), Float::INFINITY);
        assert_biteq!(Float::NEG_INFINITY.maximum(9.0), 9.0);
        assert_biteq!((9.0 as Float).maximum(Float::NEG_INFINITY), 9.0);
        assert_biteq!(Float::NEG_INFINITY.maximum(-9.0), -9.0);
        assert_biteq!((-9.0 as Float).maximum(Float::NEG_INFINITY), -9.0);
        assert!(Float::NAN.maximum(9.0).is_nan());
        assert!(Float::NAN.maximum(-9.0).is_nan());
        assert!((9.0 as Float).maximum(Float::NAN).is_nan());
        assert!((-9.0 as Float).maximum(Float::NAN).is_nan());
        assert!(Float::NAN.maximum(Float::NAN).is_nan());
    }
}

float_test! {
    name: midpoint,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((0.5 as Float).midpoint(0.5), 0.5);
        assert_biteq!((0.5 as Float).midpoint(2.5), 1.5);
        assert_biteq!((3.0 as Float).midpoint(4.0), 3.5);
        assert_biteq!((-3.0 as Float).midpoint(4.0), 0.5);
        assert_biteq!((3.0 as Float).midpoint(-4.0), -0.5);
        assert_biteq!((-3.0 as Float).midpoint(-4.0), -3.5);
        assert_biteq!((0.0 as Float).midpoint(0.0), 0.0);
        assert_biteq!((-0.0 as Float).midpoint(-0.0), -0.0);
        assert_biteq!((-5.0 as Float).midpoint(5.0), 0.0);
        assert_biteq!(Float::MAX.midpoint(Float::MIN), 0.0);
        assert_biteq!(Float::MIN.midpoint(Float::MAX), 0.0);
        assert_biteq!(Float::MAX.midpoint(Float::MIN_POSITIVE), Float::MAX / 2.);
        assert_biteq!((-Float::MAX).midpoint(Float::MIN_POSITIVE), -Float::MAX / 2.);
        assert_biteq!(Float::MAX.midpoint(-Float::MIN_POSITIVE), Float::MAX / 2.);
        assert_biteq!((-Float::MAX).midpoint(-Float::MIN_POSITIVE), -Float::MAX / 2.);
        assert_biteq!((Float::MIN_POSITIVE).midpoint(Float::MAX), Float::MAX / 2.);
        assert_biteq!((Float::MIN_POSITIVE).midpoint(-Float::MAX), -Float::MAX / 2.);
        assert_biteq!((-Float::MIN_POSITIVE).midpoint(Float::MAX), Float::MAX / 2.);
        assert_biteq!((-Float::MIN_POSITIVE).midpoint(-Float::MAX), -Float::MAX / 2.);
        assert_biteq!(Float::MAX.midpoint(Float::MAX), Float::MAX);
        assert_biteq!(
            (Float::MIN_POSITIVE).midpoint(Float::MIN_POSITIVE),
            Float::MIN_POSITIVE
        );
        assert_biteq!(
            (-Float::MIN_POSITIVE).midpoint(-Float::MIN_POSITIVE),
            -Float::MIN_POSITIVE
        );
        assert_biteq!(Float::MAX.midpoint(5.0), Float::MAX / 2.0 + 2.5);
        assert_biteq!(Float::MAX.midpoint(-5.0), Float::MAX / 2.0 - 2.5);
        assert_biteq!(Float::INFINITY.midpoint(Float::INFINITY), Float::INFINITY);
        assert_biteq!(
            Float::NEG_INFINITY.midpoint(Float::NEG_INFINITY),
            Float::NEG_INFINITY
        );
        assert!(Float::NEG_INFINITY.midpoint(Float::INFINITY).is_nan());
        assert!(Float::INFINITY.midpoint(Float::NEG_INFINITY).is_nan());
        assert!(Float::NAN.midpoint(1.0).is_nan());
        assert!((1.0 as Float).midpoint(Float::NAN).is_nan());
        assert!(Float::NAN.midpoint(Float::NAN).is_nan());
    }
}

// Separate test since the `for` loops cannot be run in `const`.
float_test! {
    name: midpoint_large_magnitude,
    attrs: {
        const: #[cfg(false)],
        // FIXME(f16_f128): `powi` does not work in Miri for these types
        f16: #[cfg(all(not(miri), target_has_reliable_f16_math))],
        f128: #[cfg(all(not(miri), target_has_reliable_f128_math))],
    },
    test<Float> {
        // test if large differences in magnitude are still correctly computed.
        // NOTE: that because of how small x and y are, x + y can never overflow
        // so (x + y) / 2.0 is always correct
        // in particular, `2.pow(i)` will  never be at the max exponent, so it could
        // be safely doubled, while j is significantly smaller.
        for i in Float::MAX_EXP.saturating_sub(64)..Float::MAX_EXP {
            for j in 0..64u8 {
                let large = (2.0 as Float).powi(i);
                // a much smaller number, such that there is no chance of overflow to test
                // potential double rounding in midpoint's implementation.
                let small = (2.0 as Float).powi(Float::MAX_EXP - 1)
                    * Float::EPSILON
                    * Float::from(j);

                let naive = (large + small) / 2.0;
                let midpoint = large.midpoint(small);

                assert_biteq!(naive, midpoint);
            }
        }
    }
}

float_test! {
    name: abs,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((-1.0 as Float).abs(), 1.0);
        assert_biteq!((1.0 as Float).abs(), 1.0);
        assert_biteq!(Float::NEG_INFINITY.abs(), Float::INFINITY);
        assert_biteq!(Float::INFINITY.abs(), Float::INFINITY);
    }
}

float_test! {
    name: copysign,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((1.0 as Float).copysign(-2.0), -1.0);
        assert_biteq!((-1.0 as Float).copysign(2.0), 1.0);
        assert_biteq!(Float::INFINITY.copysign(-0.0), Float::NEG_INFINITY);
        assert_biteq!(Float::NEG_INFINITY.copysign(0.0), Float::INFINITY);
    }
}

float_test! {
    name: rem_euclid,
    attrs: {
        const: #[cfg(false)],
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert!(Float::INFINITY.rem_euclid(42.0 as Float).is_nan());
        assert_biteq!((42.0 as Float).rem_euclid(Float::INFINITY), 42.0 as Float);
        assert!((42.0 as Float).rem_euclid(Float::NAN).is_nan());
        assert!(Float::INFINITY.rem_euclid(Float::INFINITY).is_nan());
        assert!(Float::INFINITY.rem_euclid(Float::NAN).is_nan());
        assert!(Float::NAN.rem_euclid(Float::INFINITY).is_nan());
    }
}

float_test! {
    name: div_euclid,
    attrs: {
        const: #[cfg(false)],
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((42.0 as Float).div_euclid(Float::INFINITY), 0.0);
        assert!((42.0 as Float).div_euclid(Float::NAN).is_nan());
        assert!(Float::INFINITY.div_euclid(Float::INFINITY).is_nan());
        assert!(Float::INFINITY.div_euclid(Float::NAN).is_nan());
        assert!(Float::NAN.div_euclid(Float::INFINITY).is_nan());
    }
}

float_test! {
    name: floor,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((1.0 as Float).floor(), 1.0);
        assert_biteq!((1.3 as Float).floor(), 1.0);
        assert_biteq!((1.5 as Float).floor(), 1.0);
        assert_biteq!((1.7 as Float).floor(), 1.0);
        assert_biteq!((0.5 as Float).floor(), 0.0);
        assert_biteq!((0.0 as Float).floor(), 0.0);
        assert_biteq!((-0.0 as Float).floor(), -0.0);
        assert_biteq!((-0.5 as Float).floor(), -1.0);
        assert_biteq!((-1.0 as Float).floor(), -1.0);
        assert_biteq!((-1.3 as Float).floor(), -2.0);
        assert_biteq!((-1.5 as Float).floor(), -2.0);
        assert_biteq!((-1.7 as Float).floor(), -2.0);
        assert_biteq!(Float::MAX.floor(), Float::MAX);
        assert_biteq!(Float::MIN.floor(), Float::MIN);
        assert_biteq!(Float::MIN_POSITIVE.floor(), 0.0);
        assert_biteq!((-Float::MIN_POSITIVE).floor(), -1.0);
        assert!(Float::NAN.floor().is_nan());
        assert_biteq!(Float::INFINITY.floor(), Float::INFINITY);
        assert_biteq!(Float::NEG_INFINITY.floor(), Float::NEG_INFINITY);
    }
}

float_test! {
    name: ceil,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((1.0 as Float).ceil(), 1.0);
        assert_biteq!((1.3 as Float).ceil(), 2.0);
        assert_biteq!((1.5 as Float).ceil(), 2.0);
        assert_biteq!((1.7 as Float).ceil(), 2.0);
        assert_biteq!((0.5 as Float).ceil(), 1.0);
        assert_biteq!((0.0 as Float).ceil(), 0.0);
        assert_biteq!((-0.0 as Float).ceil(), -0.0);
        assert_biteq!((-0.5 as Float).ceil(), -0.0);
        assert_biteq!((-1.0 as Float).ceil(), -1.0);
        assert_biteq!((-1.3 as Float).ceil(), -1.0);
        assert_biteq!((-1.5 as Float).ceil(), -1.0);
        assert_biteq!((-1.7 as Float).ceil(), -1.0);
        assert_biteq!(Float::MAX.ceil(), Float::MAX);
        assert_biteq!(Float::MIN.ceil(), Float::MIN);
        assert_biteq!(Float::MIN_POSITIVE.ceil(), 1.0);
        assert_biteq!((-Float::MIN_POSITIVE).ceil(), -0.0);
        assert!(Float::NAN.ceil().is_nan());
        assert_biteq!(Float::INFINITY.ceil(), Float::INFINITY);
        assert_biteq!(Float::NEG_INFINITY.ceil(), Float::NEG_INFINITY);
    }
}

float_test! {
    name: round,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((2.5 as Float).round(), 3.0);
        assert_biteq!((1.0 as Float).round(), 1.0);
        assert_biteq!((1.3 as Float).round(), 1.0);
        assert_biteq!((1.5 as Float).round(), 2.0);
        assert_biteq!((1.7 as Float).round(), 2.0);
        assert_biteq!((0.5 as Float).round(), 1.0);
        assert_biteq!((0.0 as Float).round(), 0.0);
        assert_biteq!((-0.0 as Float).round(), -0.0);
        assert_biteq!((-0.5 as Float).round(), -1.0);
        assert_biteq!((-1.0 as Float).round(), -1.0);
        assert_biteq!((-1.3 as Float).round(), -1.0);
        assert_biteq!((-1.5 as Float).round(), -2.0);
        assert_biteq!((-1.7 as Float).round(), -2.0);
        assert_biteq!(Float::MAX.round(), Float::MAX);
        assert_biteq!(Float::MIN.round(), Float::MIN);
        assert_biteq!(Float::MIN_POSITIVE.round(), 0.0);
        assert_biteq!((-Float::MIN_POSITIVE).round(), -0.0);
        assert!(Float::NAN.round().is_nan());
        assert_biteq!(Float::INFINITY.round(), Float::INFINITY);
        assert_biteq!(Float::NEG_INFINITY.round(), Float::NEG_INFINITY);
    }
}

float_test! {
    name: round_ties_even,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((2.5 as Float).round_ties_even(), 2.0);
        assert_biteq!((1.0 as Float).round_ties_even(), 1.0);
        assert_biteq!((1.3 as Float).round_ties_even(), 1.0);
        assert_biteq!((1.5 as Float).round_ties_even(), 2.0);
        assert_biteq!((1.7 as Float).round_ties_even(), 2.0);
        assert_biteq!((0.5 as Float).round_ties_even(), 0.0);
        assert_biteq!((0.0 as Float).round_ties_even(), 0.0);
        assert_biteq!((-0.0 as Float).round_ties_even(), -0.0);
        assert_biteq!((-0.5 as Float).round_ties_even(), -0.0);
        assert_biteq!((-1.0 as Float).round_ties_even(), -1.0);
        assert_biteq!((-1.3 as Float).round_ties_even(), -1.0);
        assert_biteq!((-1.5 as Float).round_ties_even(), -2.0);
        assert_biteq!((-1.7 as Float).round_ties_even(), -2.0);
        assert_biteq!(Float::MAX.round_ties_even(), Float::MAX);
        assert_biteq!(Float::MIN.round_ties_even(), Float::MIN);
        assert_biteq!(Float::MIN_POSITIVE.round_ties_even(), 0.0);
        assert_biteq!((-Float::MIN_POSITIVE).round_ties_even(), -0.0);
        assert!(Float::NAN.round_ties_even().is_nan());
        assert_biteq!(Float::INFINITY.round_ties_even(), Float::INFINITY);
        assert_biteq!(Float::NEG_INFINITY.round_ties_even(), Float::NEG_INFINITY);
    }
}

float_test! {
    name: trunc,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((1.0 as Float).trunc(), 1.0);
        assert_biteq!((1.3 as Float).trunc(), 1.0);
        assert_biteq!((1.5 as Float).trunc(), 1.0);
        assert_biteq!((1.7 as Float).trunc(), 1.0);
        assert_biteq!((0.5 as Float).trunc(), 0.0);
        assert_biteq!((0.0 as Float).trunc(), 0.0);
        assert_biteq!((-0.0 as Float).trunc(), -0.0);
        assert_biteq!((-0.5 as Float).trunc(), -0.0);
        assert_biteq!((-1.0 as Float).trunc(), -1.0);
        assert_biteq!((-1.3 as Float).trunc(), -1.0);
        assert_biteq!((-1.5 as Float).trunc(), -1.0);
        assert_biteq!((-1.7 as Float).trunc(), -1.0);
        assert_biteq!(Float::MAX.trunc(), Float::MAX);
        assert_biteq!(Float::MIN.trunc(), Float::MIN);
        assert_biteq!(Float::MIN_POSITIVE.trunc(), 0.0);
        assert_biteq!((-Float::MIN_POSITIVE).trunc(), -0.0);
        assert!(Float::NAN.trunc().is_nan());
        assert_biteq!(Float::INFINITY.trunc(), Float::INFINITY);
        assert_biteq!(Float::NEG_INFINITY.trunc(), Float::NEG_INFINITY);
    }
}

float_test! {
    name: fract,
    attrs: {
        f16: #[cfg(any(miri, target_has_reliable_f16_math))],
        f128: #[cfg(any(miri, target_has_reliable_f128_math))],
    },
    test<Float> {
        assert_biteq!((1.0 as Float).fract(), 0.0);
        assert_approx_eq!((1.3 as Float).fract(), 0.3); // rounding differs between float types
        assert_biteq!((1.5 as Float).fract(), 0.5);
        assert_approx_eq!((1.7 as Float).fract(), 0.7);
        assert_biteq!((0.5 as Float).fract(), 0.5);
        assert_biteq!((0.0 as Float).fract(), 0.0);
        assert_biteq!((-0.0 as Float).fract(), 0.0);
        assert_biteq!((-0.5 as Float).fract(), -0.5);
        assert_biteq!((-1.0 as Float).fract(), 0.0);
        assert_approx_eq!((-1.3 as Float).fract(), -0.3); // rounding differs between float types
        assert_biteq!((-1.5 as Float).fract(), -0.5);
        assert_approx_eq!((-1.7 as Float).fract(), -0.7);
        assert_biteq!(Float::MAX.fract(), 0.0);
        assert_biteq!(Float::MIN.fract(), 0.0);
        assert_biteq!(Float::MIN_POSITIVE.fract(), Float::MIN_POSITIVE);
        assert!(Float::MIN_POSITIVE.fract().is_sign_positive());
        assert_biteq!((-Float::MIN_POSITIVE).fract(), -Float::MIN_POSITIVE);
        assert!((-Float::MIN_POSITIVE).fract().is_sign_negative());
        assert!(Float::NAN.fract().is_nan());
        assert!(Float::INFINITY.fract().is_nan());
        assert!(Float::NEG_INFINITY.fract().is_nan());
    }
}