floor.rs

/* SPDX-License-Identifier: MIT
 * origin: musl src/math/floor.c */

//! Generic `floor` algorithm.
//!
//! Note that this uses the algorithm from musl's `floorf` rather than `floor` or `floorl` because
//! performance seems to be better (based on icount) and it does not seem to experience rounding
//! errors on i386.

use crate::support::{Float, FpResult, Int, IntTy, MinInt, Status};

#[inline]
pub fn floor<F: Float>(x: F) -> F {
    floor_status(x).val
}

#[inline]
pub fn floor_status<F: Float>(x: F) -> FpResult<F> {
    let zero = IntTy::<F>::ZERO;

    let mut ix = x.to_bits();
    let e = x.exp_unbiased();

    // If the represented value has no fractional part, no truncation is needed.
    if e >= F::SIG_BITS as i32 {
        return FpResult::ok(x);
    }

    let res = if e >= 0 {
        // |x| >= 1.0
        let m = F::SIG_MASK >> e.unsigned();
        if ix & m == zero {
            // Portion to be masked is already zero; no adjustment needed.
            return FpResult::ok(x);
        }

        if x.is_sign_negative() {
            ix += m;
        }

        ix &= !m;
        F::from_bits(ix)
    } else {
        // |x| < 1.0, zero or inexact with truncation

        if (ix & !F::SIGN_MASK) == F::Int::ZERO {
            return FpResult::ok(x);
        }

        if x.is_sign_positive() {
            // 0.0 <= x < 1.0; rounding down goes toward +0.0.
            F::ZERO
        } else {
            // -1.0 < x < 0.0; rounding down goes toward -1.0.
            F::NEG_ONE
        }
    };

    FpResult::new(res, Status::INEXACT)
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::support::Hexf;

    macro_rules! cases {
        ($f:ty) => {
            [
                // roundtrip
                (0.0, 0.0, Status::OK),
                (-0.0, -0.0, Status::OK),
                (1.0, 1.0, Status::OK),
                (-1.0, -1.0, Status::OK),
                (<$f>::INFINITY, <$f>::INFINITY, Status::OK),
                (<$f>::NEG_INFINITY, <$f>::NEG_INFINITY, Status::OK),
                // with rounding
                (0.1, 0.0, Status::INEXACT),
                (-0.1, -1.0, Status::INEXACT),
                (0.5, 0.0, Status::INEXACT),
                (-0.5, -1.0, Status::INEXACT),
                (0.9, 0.0, Status::INEXACT),
                (-0.9, -1.0, Status::INEXACT),
                (1.1, 1.0, Status::INEXACT),
                (-1.1, -2.0, Status::INEXACT),
                (1.5, 1.0, Status::INEXACT),
                (-1.5, -2.0, Status::INEXACT),
                (1.9, 1.0, Status::INEXACT),
                (-1.9, -2.0, Status::INEXACT),
            ]
        };
    }

    #[track_caller]
    fn check<F: Float>(cases: &[(F, F, Status)]) {
        for &(x, exp_res, exp_stat) in cases {
            let FpResult { val, status } = floor_status(x);
            assert_biteq!(val, exp_res, "{x:?} {}", Hexf(x));
            assert_eq!(
                status,
                exp_stat,
                "{x:?} {} -> {exp_res:?} {}",
                Hexf(x),
                Hexf(exp_res)
            );
        }
    }

    #[test]
    #[cfg(f16_enabled)]
    fn check_f16() {
        check::<f16>(&cases!(f16));
        check::<f16>(&[
            (hf16!("0x1p10"), hf16!("0x1p10"), Status::OK),
            (hf16!("-0x1p10"), hf16!("-0x1p10"), Status::OK),
        ]);
    }

    #[test]
    fn check_f32() {
        check::<f32>(&cases!(f32));
        check::<f32>(&[
            (hf32!("0x1p23"), hf32!("0x1p23"), Status::OK),
            (hf32!("-0x1p23"), hf32!("-0x1p23"), Status::OK),
        ]);
    }

    #[test]
    fn check_f64() {
        check::<f64>(&cases!(f64));
        check::<f64>(&[
            (hf64!("0x1p52"), hf64!("0x1p52"), Status::OK),
            (hf64!("-0x1p52"), hf64!("-0x1p52"), Status::OK),
        ]);
    }

    #[test]
    #[cfg(f128_enabled)]
    fn spec_tests_f128() {
        check::<f128>(&cases!(f128));
        check::<f128>(&[
            (hf128!("0x1p112"), hf128!("0x1p112"), Status::OK),
            (hf128!("-0x1p112"), hf128!("-0x1p112"), Status::OK),
        ]);
    }
}