1 | use core::ops::{Div, Rem}; |
2 | |
3 | pub trait Euclid: Sized + Div<Self, Output = Self> + Rem<Self, Output = Self> { |
4 | /// Calculates Euclidean division, the matching method for `rem_euclid`. |
5 | /// |
6 | /// This computes the integer `n` such that |
7 | /// `self = n * v + self.rem_euclid(v)`. |
8 | /// In other words, the result is `self / v` rounded to the integer `n` |
9 | /// such that `self >= n * v`. |
10 | /// |
11 | /// # Examples |
12 | /// |
13 | /// ``` |
14 | /// use num_traits::Euclid; |
15 | /// |
16 | /// let a: i32 = 7; |
17 | /// let b: i32 = 4; |
18 | /// assert_eq!(Euclid::div_euclid(&a, &b), 1); // 7 > 4 * 1 |
19 | /// assert_eq!(Euclid::div_euclid(&-a, &b), -2); // -7 >= 4 * -2 |
20 | /// assert_eq!(Euclid::div_euclid(&a, &-b), -1); // 7 >= -4 * -1 |
21 | /// assert_eq!(Euclid::div_euclid(&-a, &-b), 2); // -7 >= -4 * 2 |
22 | /// ``` |
23 | fn div_euclid(&self, v: &Self) -> Self; |
24 | |
25 | /// Calculates the least nonnegative remainder of `self (mod v)`. |
26 | /// |
27 | /// In particular, the return value `r` satisfies `0.0 <= r < v.abs()` in |
28 | /// most cases. However, due to a floating point round-off error it can |
29 | /// result in `r == v.abs()`, violating the mathematical definition, if |
30 | /// `self` is much smaller than `v.abs()` in magnitude and `self < 0.0`. |
31 | /// This result is not an element of the function's codomain, but it is the |
32 | /// closest floating point number in the real numbers and thus fulfills the |
33 | /// property `self == self.div_euclid(v) * v + self.rem_euclid(v)` |
34 | /// approximatively. |
35 | /// |
36 | /// # Examples |
37 | /// |
38 | /// ``` |
39 | /// use num_traits::Euclid; |
40 | /// |
41 | /// let a: i32 = 7; |
42 | /// let b: i32 = 4; |
43 | /// assert_eq!(Euclid::rem_euclid(&a, &b), 3); |
44 | /// assert_eq!(Euclid::rem_euclid(&-a, &b), 1); |
45 | /// assert_eq!(Euclid::rem_euclid(&a, &-b), 3); |
46 | /// assert_eq!(Euclid::rem_euclid(&-a, &-b), 1); |
47 | /// ``` |
48 | fn rem_euclid(&self, v: &Self) -> Self; |
49 | } |
50 | |
51 | macro_rules! euclid_forward_impl { |
52 | ($($t:ty)*) => {$( |
53 | #[cfg(has_div_euclid)] |
54 | impl Euclid for $t { |
55 | #[inline] |
56 | fn div_euclid(&self, v: &$t) -> Self { |
57 | <$t>::div_euclid(*self, *v) |
58 | } |
59 | |
60 | #[inline] |
61 | fn rem_euclid(&self, v: &$t) -> Self { |
62 | <$t>::rem_euclid(*self, *v) |
63 | } |
64 | } |
65 | )*} |
66 | } |
67 | |
68 | macro_rules! euclid_int_impl { |
69 | ($($t:ty)*) => {$( |
70 | euclid_forward_impl!($t); |
71 | |
72 | #[cfg(not(has_div_euclid))] |
73 | impl Euclid for $t { |
74 | #[inline] |
75 | fn div_euclid(&self, v: &$t) -> Self { |
76 | let q = self / v; |
77 | if self % v < 0 { |
78 | return if *v > 0 { q - 1 } else { q + 1 } |
79 | } |
80 | q |
81 | } |
82 | |
83 | #[inline] |
84 | fn rem_euclid(&self, v: &$t) -> Self { |
85 | let r = self % v; |
86 | if r < 0 { |
87 | if *v < 0 { |
88 | r - v |
89 | } else { |
90 | r + v |
91 | } |
92 | } else { |
93 | r |
94 | } |
95 | } |
96 | } |
97 | )*} |
98 | } |
99 | |
100 | macro_rules! euclid_uint_impl { |
101 | ($($t:ty)*) => {$( |
102 | euclid_forward_impl!($t); |
103 | |
104 | #[cfg(not(has_div_euclid))] |
105 | impl Euclid for $t { |
106 | #[inline] |
107 | fn div_euclid(&self, v: &$t) -> Self { |
108 | self / v |
109 | } |
110 | |
111 | #[inline] |
112 | fn rem_euclid(&self, v: &$t) -> Self { |
113 | self % v |
114 | } |
115 | } |
116 | )*} |
117 | } |
118 | |
119 | euclid_int_impl!(isize i8 i16 i32 i64); |
120 | euclid_uint_impl!(usize u8 u16 u32 u64); |
121 | #[cfg (has_i128)] |
122 | euclid_int_impl!(i128); |
123 | #[cfg (has_i128)] |
124 | euclid_uint_impl!(u128); |
125 | |
126 | #[cfg (all(has_div_euclid, feature = "std" ))] |
127 | euclid_forward_impl!(f32 f64); |
128 | |
129 | #[cfg (not(all(has_div_euclid, feature = "std" )))] |
130 | impl Euclid for f32 { |
131 | #[inline ] |
132 | fn div_euclid(&self, v: &f32) -> f32 { |
133 | let q = <f32 as ::float::FloatCore>::trunc(self / v); |
134 | if self % v < 0.0 { |
135 | return if *v > 0.0 { q - 1.0 } else { q + 1.0 }; |
136 | } |
137 | q |
138 | } |
139 | |
140 | #[inline ] |
141 | fn rem_euclid(&self, v: &f32) -> f32 { |
142 | let r = self % v; |
143 | if r < 0.0 { |
144 | r + <f32 as ::float::FloatCore>::abs(*v) |
145 | } else { |
146 | r |
147 | } |
148 | } |
149 | } |
150 | |
151 | #[cfg (not(all(has_div_euclid, feature = "std" )))] |
152 | impl Euclid for f64 { |
153 | #[inline ] |
154 | fn div_euclid(&self, v: &f64) -> f64 { |
155 | let q = <f64 as ::float::FloatCore>::trunc(self / v); |
156 | if self % v < 0.0 { |
157 | return if *v > 0.0 { q - 1.0 } else { q + 1.0 }; |
158 | } |
159 | q |
160 | } |
161 | |
162 | #[inline ] |
163 | fn rem_euclid(&self, v: &f64) -> f64 { |
164 | let r = self % v; |
165 | if r < 0.0 { |
166 | r + <f64 as ::float::FloatCore>::abs(*v) |
167 | } else { |
168 | r |
169 | } |
170 | } |
171 | } |
172 | |
173 | pub trait CheckedEuclid: Euclid { |
174 | /// Performs euclid division that returns `None` instead of panicking on division by zero |
175 | /// and instead of wrapping around on underflow and overflow. |
176 | fn checked_div_euclid(&self, v: &Self) -> Option<Self>; |
177 | |
178 | /// Finds the euclid remainder of dividing two numbers, checking for underflow, overflow and |
179 | /// division by zero. If any of that happens, `None` is returned. |
180 | fn checked_rem_euclid(&self, v: &Self) -> Option<Self>; |
181 | } |
182 | |
183 | macro_rules! checked_euclid_forward_impl { |
184 | ($($t:ty)*) => {$( |
185 | #[cfg(has_div_euclid)] |
186 | impl CheckedEuclid for $t { |
187 | #[inline] |
188 | fn checked_div_euclid(&self, v: &$t) -> Option<Self> { |
189 | <$t>::checked_div_euclid(*self, *v) |
190 | } |
191 | |
192 | #[inline] |
193 | fn checked_rem_euclid(&self, v: &$t) -> Option<Self> { |
194 | <$t>::checked_rem_euclid(*self, *v) |
195 | } |
196 | } |
197 | )*} |
198 | } |
199 | |
200 | macro_rules! checked_euclid_int_impl { |
201 | ($($t:ty)*) => {$( |
202 | checked_euclid_forward_impl!($t); |
203 | |
204 | #[cfg(not(has_div_euclid))] |
205 | impl CheckedEuclid for $t { |
206 | #[inline] |
207 | fn checked_div_euclid(&self, v: &$t) -> Option<$t> { |
208 | if *v == 0 || (*self == Self::min_value() && *v == -1) { |
209 | None |
210 | } else { |
211 | Some(Euclid::div_euclid(self, v)) |
212 | } |
213 | } |
214 | |
215 | #[inline] |
216 | fn checked_rem_euclid(&self, v: &$t) -> Option<$t> { |
217 | if *v == 0 || (*self == Self::min_value() && *v == -1) { |
218 | None |
219 | } else { |
220 | Some(Euclid::rem_euclid(self, v)) |
221 | } |
222 | } |
223 | } |
224 | )*} |
225 | } |
226 | |
227 | macro_rules! checked_euclid_uint_impl { |
228 | ($($t:ty)*) => {$( |
229 | checked_euclid_forward_impl!($t); |
230 | |
231 | #[cfg(not(has_div_euclid))] |
232 | impl CheckedEuclid for $t { |
233 | #[inline] |
234 | fn checked_div_euclid(&self, v: &$t) -> Option<$t> { |
235 | if *v == 0 { |
236 | None |
237 | } else { |
238 | Some(Euclid::div_euclid(self, v)) |
239 | } |
240 | } |
241 | |
242 | #[inline] |
243 | fn checked_rem_euclid(&self, v: &$t) -> Option<$t> { |
244 | if *v == 0 { |
245 | None |
246 | } else { |
247 | Some(Euclid::rem_euclid(self, v)) |
248 | } |
249 | } |
250 | } |
251 | )*} |
252 | } |
253 | |
254 | checked_euclid_int_impl!(isize i8 i16 i32 i64); |
255 | checked_euclid_uint_impl!(usize u8 u16 u32 u64); |
256 | #[cfg (has_i128)] |
257 | checked_euclid_int_impl!(i128); |
258 | #[cfg (has_i128)] |
259 | checked_euclid_uint_impl!(u128); |
260 | |
261 | #[cfg (test)] |
262 | mod tests { |
263 | use super::*; |
264 | |
265 | #[test ] |
266 | fn euclid_unsigned() { |
267 | macro_rules! test_euclid { |
268 | ($($t:ident)+) => { |
269 | $( |
270 | { |
271 | let x: $t = 10; |
272 | let y: $t = 3; |
273 | assert_eq!(Euclid::div_euclid(&x, &y), 3); |
274 | assert_eq!(Euclid::rem_euclid(&x, &y), 1); |
275 | } |
276 | )+ |
277 | }; |
278 | } |
279 | |
280 | test_euclid!(usize u8 u16 u32 u64); |
281 | } |
282 | |
283 | #[test ] |
284 | fn euclid_signed() { |
285 | macro_rules! test_euclid { |
286 | ($($t:ident)+) => { |
287 | $( |
288 | { |
289 | let x: $t = 10; |
290 | let y: $t = -3; |
291 | assert_eq!(Euclid::div_euclid(&x, &y), -3); |
292 | assert_eq!(Euclid::div_euclid(&-x, &y), 4); |
293 | assert_eq!(Euclid::rem_euclid(&x, &y), 1); |
294 | assert_eq!(Euclid::rem_euclid(&-x, &y), 2); |
295 | let x: $t = $t::min_value() + 1; |
296 | let y: $t = -1; |
297 | assert_eq!(Euclid::div_euclid(&x, &y), $t::max_value()); |
298 | } |
299 | )+ |
300 | }; |
301 | } |
302 | |
303 | test_euclid!(isize i8 i16 i32 i64); |
304 | } |
305 | |
306 | #[test ] |
307 | fn euclid_float() { |
308 | macro_rules! test_euclid { |
309 | ($($t:ident)+) => { |
310 | $( |
311 | { |
312 | let x: $t = 12.1; |
313 | let y: $t = 3.2; |
314 | assert!(Euclid::div_euclid(&x, &y) * y + Euclid::rem_euclid(&x, &y) - x |
315 | <= 46.4 * <$t as ::float::FloatCore>::epsilon()); |
316 | assert!(Euclid::div_euclid(&x, &-y) * -y + Euclid::rem_euclid(&x, &-y) - x |
317 | <= 46.4 * <$t as ::float::FloatCore>::epsilon()); |
318 | assert!(Euclid::div_euclid(&-x, &y) * y + Euclid::rem_euclid(&-x, &y) + x |
319 | <= 46.4 * <$t as ::float::FloatCore>::epsilon()); |
320 | assert!(Euclid::div_euclid(&-x, &-y) * -y + Euclid::rem_euclid(&-x, &-y) + x |
321 | <= 46.4 * <$t as ::float::FloatCore>::epsilon()); |
322 | } |
323 | )+ |
324 | }; |
325 | } |
326 | |
327 | test_euclid!(f32 f64); |
328 | } |
329 | |
330 | #[test ] |
331 | fn euclid_checked() { |
332 | macro_rules! test_euclid_checked { |
333 | ($($t:ident)+) => { |
334 | $( |
335 | { |
336 | assert_eq!(CheckedEuclid::checked_div_euclid(&$t::min_value(), &-1), None); |
337 | assert_eq!(CheckedEuclid::checked_rem_euclid(&$t::min_value(), &-1), None); |
338 | assert_eq!(CheckedEuclid::checked_div_euclid(&1, &0), None); |
339 | assert_eq!(CheckedEuclid::checked_rem_euclid(&1, &0), None); |
340 | } |
341 | )+ |
342 | }; |
343 | } |
344 | |
345 | test_euclid_checked!(isize i8 i16 i32 i64); |
346 | } |
347 | } |
348 | |