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/* SPDX-License-Identifier: MIT */
/* origin: musl src/math/ceilf.c */
//! Generic `ceil` algorithm.
//!
//! Note that this uses the algorithm from musl's `ceilf` rather than `ceil` or `ceill` 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 ceil<F: Float>(x: F) -> F {
ceil_status(x).val
}
#[inline]
pub fn ceil_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 status;
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);
}
// Otherwise, raise an inexact exception.
status = Status::INEXACT;
if x.is_sign_positive() {
ix += m;
}
ix &= !m;
F::from_bits(ix)
} else {
// |x| < 1.0, raise an inexact exception since truncation will happen (unless x == 0).
if ix & F::SIG_MASK == F::Int::ZERO {
status = Status::OK;
} else {
status = Status::INEXACT;
}
if x.is_sign_negative() {
// -1.0 < x <= -0.0; rounding up goes toward -0.0.
F::NEG_ZERO
} else if ix << 1 != zero {
// 0.0 < x < 1.0; rounding up goes toward +1.0.
F::ONE
} else {
// +0.0 remains unchanged
x
}
};
FpResult::new(res, status)
}
#[cfg(test)]
mod tests {
use super::*;
use crate::support::Hexf;
/// Test against https://en.cppreference.com/w/cpp/numeric/math/ceil
fn spec_test<F: Float>(cases: &[(F, F, Status)]) {
let roundtrip = [
F::ZERO,
F::ONE,
F::NEG_ONE,
F::NEG_ZERO,
F::INFINITY,
F::NEG_INFINITY,
];
for x in roundtrip {
let FpResult { val, status } = ceil_status(x);
assert_biteq!(val, x, "{}", Hexf(x));
assert_eq!(status, Status::OK, "{}", Hexf(x));
}
for &(x, res, res_stat) in cases {
let FpResult { val, status } = ceil_status(x);
assert_biteq!(val, res, "{}", Hexf(x));
assert_eq!(status, res_stat, "{}", Hexf(x));
}
}
/* Skipping f16 / f128 "sanity_check"s due to rejected literal lexing at MSRV */
#[test]
#[cfg(f16_enabled)]
fn spec_tests_f16() {
let cases = [
(0.1, 1.0, Status::INEXACT),
(-0.1, -0.0, Status::INEXACT),
(0.9, 1.0, Status::INEXACT),
(-0.9, -0.0, Status::INEXACT),
(1.1, 2.0, Status::INEXACT),
(-1.1, -1.0, Status::INEXACT),
(1.9, 2.0, Status::INEXACT),
(-1.9, -1.0, Status::INEXACT),
];
spec_test::<f16>(&cases);
}
#[test]
fn sanity_check_f32() {
assert_eq!(ceil(1.1f32), 2.0);
assert_eq!(ceil(2.9f32), 3.0);
}
#[test]
fn spec_tests_f32() {
let cases = [
(0.1, 1.0, Status::INEXACT),
(-0.1, -0.0, Status::INEXACT),
(0.9, 1.0, Status::INEXACT),
(-0.9, -0.0, Status::INEXACT),
(1.1, 2.0, Status::INEXACT),
(-1.1, -1.0, Status::INEXACT),
(1.9, 2.0, Status::INEXACT),
(-1.9, -1.0, Status::INEXACT),
];
spec_test::<f32>(&cases);
}
#[test]
fn sanity_check_f64() {
assert_eq!(ceil(1.1f64), 2.0);
assert_eq!(ceil(2.9f64), 3.0);
}
#[test]
fn spec_tests_f64() {
let cases = [
(0.1, 1.0, Status::INEXACT),
(-0.1, -0.0, Status::INEXACT),
(0.9, 1.0, Status::INEXACT),
(-0.9, -0.0, Status::INEXACT),
(1.1, 2.0, Status::INEXACT),
(-1.1, -1.0, Status::INEXACT),
(1.9, 2.0, Status::INEXACT),
(-1.9, -1.0, Status::INEXACT),
];
spec_test::<f64>(&cases);
}
#[test]
#[cfg(f128_enabled)]
fn spec_tests_f128() {
let cases = [
(0.1, 1.0, Status::INEXACT),
(-0.1, -0.0, Status::INEXACT),
(0.9, 1.0, Status::INEXACT),
(-0.9, -0.0, Status::INEXACT),
(1.1, 2.0, Status::INEXACT),
(-1.1, -1.0, Status::INEXACT),
(1.9, 2.0, Status::INEXACT),
(-1.9, -1.0, Status::INEXACT),
];
spec_test::<f128>(&cases);
}
}
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