1/* SPDX-License-Identifier: MIT
2 * origin: musl src/math/floor.c */
3
4//! Generic `floor` algorithm.
5//!
6//! Note that this uses the algorithm from musl's `floorf` rather than `floor` or `floorl` 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 floor<F: Float>(x: F) -> F {
14 floor_status(x).val
15}
16
17pub fn floor_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_negative() {
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.
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_positive() {
55 // 0.0 <= x < 1.0; rounding down goes toward +0.0.
56 F::ZERO
57 } else if ix << 1 != zero {
58 // -1.0 < x < 0.0; rounding down goes toward -1.0.
59 F::NEG_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/floor
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 } = floor_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 } = floor_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 and spec cases due to rejected literal lexing at MSRV */
92
93 #[test]
94 #[cfg(f16_enabled)]
95 fn spec_tests_f16() {
96 let cases = [];
97 spec_test::<f16>(&cases);
98 }
99
100 #[test]
101 fn sanity_check_f32() {
102 assert_eq!(floor(0.5f32), 0.0);
103 assert_eq!(floor(1.1f32), 1.0);
104 assert_eq!(floor(2.9f32), 2.0);
105 }
106
107 #[test]
108 fn spec_tests_f32() {
109 let cases = [
110 (0.1, 0.0, Status::INEXACT),
111 (-0.1, -1.0, Status::INEXACT),
112 (0.9, 0.0, Status::INEXACT),
113 (-0.9, -1.0, Status::INEXACT),
114 (1.1, 1.0, Status::INEXACT),
115 (-1.1, -2.0, Status::INEXACT),
116 (1.9, 1.0, Status::INEXACT),
117 (-1.9, -2.0, Status::INEXACT),
118 ];
119 spec_test::<f32>(&cases);
120 }
121
122 #[test]
123 fn sanity_check_f64() {
124 assert_eq!(floor(1.1f64), 1.0);
125 assert_eq!(floor(2.9f64), 2.0);
126 }
127
128 #[test]
129 fn spec_tests_f64() {
130 let cases = [
131 (0.1, 0.0, Status::INEXACT),
132 (-0.1, -1.0, Status::INEXACT),
133 (0.9, 0.0, Status::INEXACT),
134 (-0.9, -1.0, Status::INEXACT),
135 (1.1, 1.0, Status::INEXACT),
136 (-1.1, -2.0, Status::INEXACT),
137 (1.9, 1.0, Status::INEXACT),
138 (-1.9, -2.0, Status::INEXACT),
139 ];
140 spec_test::<f64>(&cases);
141 }
142
143 #[test]
144 #[cfg(f128_enabled)]
145 fn spec_tests_f128() {
146 let cases = [];
147 spec_test::<f128>(&cases);
148 }
149}
150