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 i128); |

120 | euclid_uint_impl!(usize u8 u16 u32 u64 u128); |

121 | |

122 | #[cfg(all(has_div_euclid, feature = "std"))] |

123 | euclid_forward_impl!(f32 f64); |

124 | |

125 | #[cfg(not(all(has_div_euclid, feature = "std")))] |

126 | impl Euclid for f32 { |

127 | #[inline] |

128 | fn div_euclid(&self, v: &f32) -> f32 { |

129 | let q = <f32 as crate::float::FloatCore>::trunc(self / v); |

130 | if self % v < 0.0 { |

131 | return if *v > 0.0 { q - 1.0 } else { q + 1.0 }; |

132 | } |

133 | q |

134 | } |

135 | |

136 | #[inline] |

137 | fn rem_euclid(&self, v: &f32) -> f32 { |

138 | let r = self % v; |

139 | if r < 0.0 { |

140 | r + <f32 as crate::float::FloatCore>::abs(*v) |

141 | } else { |

142 | r |

143 | } |

144 | } |

145 | } |

146 | |

147 | #[cfg(not(all(has_div_euclid, feature = "std")))] |

148 | impl Euclid for f64 { |

149 | #[inline] |

150 | fn div_euclid(&self, v: &f64) -> f64 { |

151 | let q = <f64 as crate::float::FloatCore>::trunc(self / v); |

152 | if self % v < 0.0 { |

153 | return if *v > 0.0 { q - 1.0 } else { q + 1.0 }; |

154 | } |

155 | q |

156 | } |

157 | |

158 | #[inline] |

159 | fn rem_euclid(&self, v: &f64) -> f64 { |

160 | let r = self % v; |

161 | if r < 0.0 { |

162 | r + <f64 as crate::float::FloatCore>::abs(*v) |

163 | } else { |

164 | r |

165 | } |

166 | } |

167 | } |

168 | |

169 | pub trait CheckedEuclid: Euclid { |

170 | /// Performs euclid division that returns `None` instead of panicking on division by zero |

171 | /// and instead of wrapping around on underflow and overflow. |

172 | fn checked_div_euclid(&self, v: &Self) -> Option<Self>; |

173 | |

174 | /// Finds the euclid remainder of dividing two numbers, checking for underflow, overflow and |

175 | /// division by zero. If any of that happens, `None` is returned. |

176 | fn checked_rem_euclid(&self, v: &Self) -> Option<Self>; |

177 | } |

178 | |

179 | macro_rules! checked_euclid_forward_impl { |

180 | ($($t:ty)*) => {$( |

181 | #[cfg(has_div_euclid)] |

182 | impl CheckedEuclid for $t { |

183 | #[inline] |

184 | fn checked_div_euclid(&self, v: &$t) -> Option<Self> { |

185 | <$t>::checked_div_euclid(*self, *v) |

186 | } |

187 | |

188 | #[inline] |

189 | fn checked_rem_euclid(&self, v: &$t) -> Option<Self> { |

190 | <$t>::checked_rem_euclid(*self, *v) |

191 | } |

192 | } |

193 | )*} |

194 | } |

195 | |

196 | macro_rules! checked_euclid_int_impl { |

197 | ($($t:ty)*) => {$( |

198 | checked_euclid_forward_impl!($t); |

199 | |

200 | #[cfg(not(has_div_euclid))] |

201 | impl CheckedEuclid for $t { |

202 | #[inline] |

203 | fn checked_div_euclid(&self, v: &$t) -> Option<$t> { |

204 | if *v == 0 || (*self == Self::min_value() && *v == -1) { |

205 | None |

206 | } else { |

207 | Some(Euclid::div_euclid(self, v)) |

208 | } |

209 | } |

210 | |

211 | #[inline] |

212 | fn checked_rem_euclid(&self, v: &$t) -> Option<$t> { |

213 | if *v == 0 || (*self == Self::min_value() && *v == -1) { |

214 | None |

215 | } else { |

216 | Some(Euclid::rem_euclid(self, v)) |

217 | } |

218 | } |

219 | } |

220 | )*} |

221 | } |

222 | |

223 | macro_rules! checked_euclid_uint_impl { |

224 | ($($t:ty)*) => {$( |

225 | checked_euclid_forward_impl!($t); |

226 | |

227 | #[cfg(not(has_div_euclid))] |

228 | impl CheckedEuclid for $t { |

229 | #[inline] |

230 | fn checked_div_euclid(&self, v: &$t) -> Option<$t> { |

231 | if *v == 0 { |

232 | None |

233 | } else { |

234 | Some(Euclid::div_euclid(self, v)) |

235 | } |

236 | } |

237 | |

238 | #[inline] |

239 | fn checked_rem_euclid(&self, v: &$t) -> Option<$t> { |

240 | if *v == 0 { |

241 | None |

242 | } else { |

243 | Some(Euclid::rem_euclid(self, v)) |

244 | } |

245 | } |

246 | } |

247 | )*} |

248 | } |

249 | |

250 | checked_euclid_int_impl!(isize i8 i16 i32 i64 i128); |

251 | checked_euclid_uint_impl!(usize u8 u16 u32 u64 u128); |

252 | |

253 | #[cfg(test)] |

254 | mod tests { |

255 | use super::*; |

256 | |

257 | #[test] |

258 | fn euclid_unsigned() { |

259 | macro_rules! test_euclid { |

260 | ($($t:ident)+) => { |

261 | $( |

262 | { |

263 | let x: $t = 10; |

264 | let y: $t = 3; |

265 | assert_eq!(Euclid::div_euclid(&x, &y), 3); |

266 | assert_eq!(Euclid::rem_euclid(&x, &y), 1); |

267 | } |

268 | )+ |

269 | }; |

270 | } |

271 | |

272 | test_euclid!(usize u8 u16 u32 u64); |

273 | } |

274 | |

275 | #[test] |

276 | fn euclid_signed() { |

277 | macro_rules! test_euclid { |

278 | ($($t:ident)+) => { |

279 | $( |

280 | { |

281 | let x: $t = 10; |

282 | let y: $t = -3; |

283 | assert_eq!(Euclid::div_euclid(&x, &y), -3); |

284 | assert_eq!(Euclid::div_euclid(&-x, &y), 4); |

285 | assert_eq!(Euclid::rem_euclid(&x, &y), 1); |

286 | assert_eq!(Euclid::rem_euclid(&-x, &y), 2); |

287 | let x: $t = $t::min_value() + 1; |

288 | let y: $t = -1; |

289 | assert_eq!(Euclid::div_euclid(&x, &y), $t::max_value()); |

290 | } |

291 | )+ |

292 | }; |

293 | } |

294 | |

295 | test_euclid!(isize i8 i16 i32 i64 i128); |

296 | } |

297 | |

298 | #[test] |

299 | fn euclid_float() { |

300 | macro_rules! test_euclid { |

301 | ($($t:ident)+) => { |

302 | $( |

303 | { |

304 | let x: $t = 12.1; |

305 | let y: $t = 3.2; |

306 | assert!(Euclid::div_euclid(&x, &y) * y + Euclid::rem_euclid(&x, &y) - x |

307 | <= 46.4 * <$t as crate::float::FloatCore>::epsilon()); |

308 | assert!(Euclid::div_euclid(&x, &-y) * -y + Euclid::rem_euclid(&x, &-y) - x |

309 | <= 46.4 * <$t as crate::float::FloatCore>::epsilon()); |

310 | assert!(Euclid::div_euclid(&-x, &y) * y + Euclid::rem_euclid(&-x, &y) + x |

311 | <= 46.4 * <$t as crate::float::FloatCore>::epsilon()); |

312 | assert!(Euclid::div_euclid(&-x, &-y) * -y + Euclid::rem_euclid(&-x, &-y) + x |

313 | <= 46.4 * <$t as crate::float::FloatCore>::epsilon()); |

314 | } |

315 | )+ |

316 | }; |

317 | } |

318 | |

319 | test_euclid!(f32 f64); |

320 | } |

321 | |

322 | #[test] |

323 | fn euclid_checked() { |

324 | macro_rules! test_euclid_checked { |

325 | ($($t:ident)+) => { |

326 | $( |

327 | { |

328 | assert_eq!(CheckedEuclid::checked_div_euclid(&$t::min_value(), &-1), None); |

329 | assert_eq!(CheckedEuclid::checked_rem_euclid(&$t::min_value(), &-1), None); |

330 | assert_eq!(CheckedEuclid::checked_div_euclid(&1, &0), None); |

331 | assert_eq!(CheckedEuclid::checked_rem_euclid(&1, &0), None); |

332 | } |

333 | )+ |

334 | }; |

335 | } |

336 | |

337 | test_euclid_checked!(isize i8 i16 i32 i64 i128); |

338 | } |

339 | } |

340 |