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