1/* SPDX-License-Identifier: MIT */
2/* origin: musl src/math/ceilf.c */
3
4//! Generic `ceil` algorithm.
5//!
6//! Note that this uses the algorithm from musl's `ceilf` rather than `ceil` or `ceill` because
7//! performance seems to be better (based on icount) and it does not seem to experience rounding
8//! errors on i386.
9
10use super::super::support::{FpResult, Status};
11use super::super::{Float, Int, IntTy, MinInt};
12
13#[inline]
14pub fn ceil<F: Float>(x: F) -> F {
15 ceil_status(x).val
16}
17
18#[inline]
19pub fn ceil_status<F: Float>(x: F) -> FpResult<F> {
20 let zero = IntTy::<F>::ZERO;
21
22 let mut ix = x.to_bits();
23 let e = x.exp_unbiased();
24
25 // If the represented value has no fractional part, no truncation is needed.
26 if e >= F::SIG_BITS as i32 {
27 return FpResult::ok(x);
28 }
29
30 let status;
31 let res = if e >= 0 {
32 // |x| >= 1.0
33 let m = F::SIG_MASK >> e.unsigned();
34 if (ix & m) == zero {
35 // Portion to be masked is already zero; no adjustment needed.
36 return FpResult::ok(x);
37 }
38
39 // Otherwise, raise an inexact exception.
40 status = Status::INEXACT;
41
42 if x.is_sign_positive() {
43 ix += m;
44 }
45
46 ix &= !m;
47 F::from_bits(ix)
48 } else {
49 // |x| < 1.0, raise an inexact exception since truncation will happen (unless x == 0).
50 if ix & F::SIG_MASK == F::Int::ZERO {
51 status = Status::OK;
52 } else {
53 status = Status::INEXACT;
54 }
55
56 if x.is_sign_negative() {
57 // -1.0 < x <= -0.0; rounding up goes toward -0.0.
58 F::NEG_ZERO
59 } else if ix << 1 != zero {
60 // 0.0 < x < 1.0; rounding up goes toward +1.0.
61 F::ONE
62 } else {
63 // +0.0 remains unchanged
64 x
65 }
66 };
67
68 FpResult::new(res, status)
69}
70
71#[cfg(test)]
72mod tests {
73 use super::*;
74 use crate::support::Hexf;
75
76 /// Test against https://en.cppreference.com/w/cpp/numeric/math/ceil
77 fn spec_test<F: Float>(cases: &[(F, F, Status)]) {
78 let roundtrip = [
79 F::ZERO,
80 F::ONE,
81 F::NEG_ONE,
82 F::NEG_ZERO,
83 F::INFINITY,
84 F::NEG_INFINITY,
85 ];
86
87 for x in roundtrip {
88 let FpResult { val, status } = ceil_status(x);
89 assert_biteq!(val, x, "{}", Hexf(x));
90 assert_eq!(status, Status::OK, "{}", Hexf(x));
91 }
92
93 for &(x, res, res_stat) in cases {
94 let FpResult { val, status } = ceil_status(x);
95 assert_biteq!(val, res, "{}", Hexf(x));
96 assert_eq!(status, res_stat, "{}", Hexf(x));
97 }
98 }
99
100 /* Skipping f16 / f128 "sanity_check"s due to rejected literal lexing at MSRV */
101
102 #[test]
103 #[cfg(f16_enabled)]
104 fn spec_tests_f16() {
105 let cases = [
106 (0.1, 1.0, Status::INEXACT),
107 (-0.1, -0.0, Status::INEXACT),
108 (0.9, 1.0, Status::INEXACT),
109 (-0.9, -0.0, Status::INEXACT),
110 (1.1, 2.0, Status::INEXACT),
111 (-1.1, -1.0, Status::INEXACT),
112 (1.9, 2.0, Status::INEXACT),
113 (-1.9, -1.0, Status::INEXACT),
114 ];
115 spec_test::<f16>(&cases);
116 }
117
118 #[test]
119 fn sanity_check_f32() {
120 assert_eq!(ceil(1.1f32), 2.0);
121 assert_eq!(ceil(2.9f32), 3.0);
122 }
123
124 #[test]
125 fn spec_tests_f32() {
126 let cases = [
127 (0.1, 1.0, Status::INEXACT),
128 (-0.1, -0.0, Status::INEXACT),
129 (0.9, 1.0, Status::INEXACT),
130 (-0.9, -0.0, Status::INEXACT),
131 (1.1, 2.0, Status::INEXACT),
132 (-1.1, -1.0, Status::INEXACT),
133 (1.9, 2.0, Status::INEXACT),
134 (-1.9, -1.0, Status::INEXACT),
135 ];
136 spec_test::<f32>(&cases);
137 }
138
139 #[test]
140 fn sanity_check_f64() {
141 assert_eq!(ceil(1.1f64), 2.0);
142 assert_eq!(ceil(2.9f64), 3.0);
143 }
144
145 #[test]
146 fn spec_tests_f64() {
147 let cases = [
148 (0.1, 1.0, Status::INEXACT),
149 (-0.1, -0.0, Status::INEXACT),
150 (0.9, 1.0, Status::INEXACT),
151 (-0.9, -0.0, Status::INEXACT),
152 (1.1, 2.0, Status::INEXACT),
153 (-1.1, -1.0, Status::INEXACT),
154 (1.9, 2.0, Status::INEXACT),
155 (-1.9, -1.0, Status::INEXACT),
156 ];
157 spec_test::<f64>(&cases);
158 }
159
160 #[test]
161 #[cfg(f128_enabled)]
162 fn spec_tests_f128() {
163 let cases = [
164 (0.1, 1.0, Status::INEXACT),
165 (-0.1, -0.0, Status::INEXACT),
166 (0.9, 1.0, Status::INEXACT),
167 (-0.9, -0.0, Status::INEXACT),
168 (1.1, 2.0, Status::INEXACT),
169 (-1.1, -1.0, Status::INEXACT),
170 (1.9, 2.0, Status::INEXACT),
171 (-1.9, -1.0, Status::INEXACT),
172 ];
173 spec_test::<f128>(&cases);
174 }
175}
176