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 crate::support::{Float, FpResult, Int, IntTy, MinInt, Status};
11
12#[inline]
13pub fn ceil<F: Float>(x: F) -> F {
14 ceil_status(x).val
15}
16
17#[inline]
18pub fn ceil_status<F: Float>(x: F) -> FpResult<F> {
19 let zero = IntTy::<F>::ZERO;
20
21 let mut ix = x.to_bits();
22 let e = x.exp_unbiased();
23
24 // If the represented value has no fractional part, no truncation is needed.
25 if e >= F::SIG_BITS as i32 {
26 return FpResult::ok(x);
27 }
28
29 let status;
30 let res = if e >= 0 {
31 // |x| >= 1.0
32 let m = F::SIG_MASK >> e.unsigned();
33 if (ix & m) == zero {
34 // Portion to be masked is already zero; no adjustment needed.
35 return FpResult::ok(x);
36 }
37
38 // Otherwise, raise an inexact exception.
39 status = Status::INEXACT;
40
41 if x.is_sign_positive() {
42 ix += m;
43 }
44
45 ix &= !m;
46 F::from_bits(ix)
47 } else {
48 // |x| < 1.0, raise an inexact exception since truncation will happen (unless x == 0).
49 if ix & F::SIG_MASK == F::Int::ZERO {
50 status = Status::OK;
51 } else {
52 status = Status::INEXACT;
53 }
54
55 if x.is_sign_negative() {
56 // -1.0 < x <= -0.0; rounding up goes toward -0.0.
57 F::NEG_ZERO
58 } else if ix << 1 != zero {
59 // 0.0 < x < 1.0; rounding up goes toward +1.0.
60 F::ONE
61 } else {
62 // +0.0 remains unchanged
63 x
64 }
65 };
66
67 FpResult::new(res, status)
68}
69
70#[cfg(test)]
71mod tests {
72 use super::*;
73 use crate::support::Hexf;
74
75 /// Test against https://en.cppreference.com/w/cpp/numeric/math/ceil
76 fn spec_test<F: Float>(cases: &[(F, F, Status)]) {
77 let roundtrip = [
78 F::ZERO,
79 F::ONE,
80 F::NEG_ONE,
81 F::NEG_ZERO,
82 F::INFINITY,
83 F::NEG_INFINITY,
84 ];
85
86 for x in roundtrip {
87 let FpResult { val, status } = ceil_status(x);
88 assert_biteq!(val, x, "{}", Hexf(x));
89 assert_eq!(status, Status::OK, "{}", Hexf(x));
90 }
91
92 for &(x, res, res_stat) in cases {
93 let FpResult { val, status } = ceil_status(x);
94 assert_biteq!(val, res, "{}", Hexf(x));
95 assert_eq!(status, res_stat, "{}", Hexf(x));
96 }
97 }
98
99 /* Skipping f16 / f128 "sanity_check"s due to rejected literal lexing at MSRV */
100
101 #[test]
102 #[cfg(f16_enabled)]
103 fn spec_tests_f16() {
104 let cases = [
105 (0.1, 1.0, Status::INEXACT),
106 (-0.1, -0.0, Status::INEXACT),
107 (0.9, 1.0, Status::INEXACT),
108 (-0.9, -0.0, Status::INEXACT),
109 (1.1, 2.0, Status::INEXACT),
110 (-1.1, -1.0, Status::INEXACT),
111 (1.9, 2.0, Status::INEXACT),
112 (-1.9, -1.0, Status::INEXACT),
113 ];
114 spec_test::<f16>(&cases);
115 }
116
117 #[test]
118 fn sanity_check_f32() {
119 assert_eq!(ceil(1.1f32), 2.0);
120 assert_eq!(ceil(2.9f32), 3.0);
121 }
122
123 #[test]
124 fn spec_tests_f32() {
125 let cases = [
126 (0.1, 1.0, Status::INEXACT),
127 (-0.1, -0.0, Status::INEXACT),
128 (0.9, 1.0, Status::INEXACT),
129 (-0.9, -0.0, Status::INEXACT),
130 (1.1, 2.0, Status::INEXACT),
131 (-1.1, -1.0, Status::INEXACT),
132 (1.9, 2.0, Status::INEXACT),
133 (-1.9, -1.0, Status::INEXACT),
134 ];
135 spec_test::<f32>(&cases);
136 }
137
138 #[test]
139 fn sanity_check_f64() {
140 assert_eq!(ceil(1.1f64), 2.0);
141 assert_eq!(ceil(2.9f64), 3.0);
142 }
143
144 #[test]
145 fn spec_tests_f64() {
146 let cases = [
147 (0.1, 1.0, Status::INEXACT),
148 (-0.1, -0.0, Status::INEXACT),
149 (0.9, 1.0, Status::INEXACT),
150 (-0.9, -0.0, Status::INEXACT),
151 (1.1, 2.0, Status::INEXACT),
152 (-1.1, -1.0, Status::INEXACT),
153 (1.9, 2.0, Status::INEXACT),
154 (-1.9, -1.0, Status::INEXACT),
155 ];
156 spec_test::<f64>(&cases);
157 }
158
159 #[test]
160 #[cfg(f128_enabled)]
161 fn spec_tests_f128() {
162 let cases = [
163 (0.1, 1.0, Status::INEXACT),
164 (-0.1, -0.0, Status::INEXACT),
165 (0.9, 1.0, Status::INEXACT),
166 (-0.9, -0.0, Status::INEXACT),
167 (1.1, 2.0, Status::INEXACT),
168 (-1.1, -1.0, Status::INEXACT),
169 (1.9, 2.0, Status::INEXACT),
170 (-1.9, -1.0, Status::INEXACT),
171 ];
172 spec_test::<f128>(&cases);
173 }
174}
175