1// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
2// file at the top-level directory of this distribution and at
3// http://rust-lang.org/COPYRIGHT.
4//
5// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8// option. This file may not be copied, modified, or distributed
9// except according to those terms.
10
11//! Numeric traits for generic mathematics
12//!
13//! ## Compatibility
14//!
15//! The `num-traits` crate is tested for rustc 1.60 and greater.
16
17#![doc(html_root_url = "https://docs.rs/num-traits/0.2")]
18#![deny(unconditional_recursion)]
19#![no_std]
20
21// Need to explicitly bring the crate in for inherent float methods
22#[cfg(feature = "std")]
23extern crate std;
24
25use core::fmt;
26use core::num::Wrapping;
27use core::ops::{Add, Div, Mul, Rem, Sub};
28use core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign};
29
30pub use crate::bounds::Bounded;
31#[cfg(any(feature = "std", feature = "libm"))]
32pub use crate::float::Float;
33pub use crate::float::FloatConst;
34// pub use real::{FloatCore, Real}; // NOTE: Don't do this, it breaks `use num_traits::*;`.
35pub use crate::cast::{cast, AsPrimitive, FromPrimitive, NumCast, ToPrimitive};
36pub use crate::identities::{one, zero, ConstOne, ConstZero, One, Zero};
37pub use crate::int::PrimInt;
38pub use crate::ops::bytes::{FromBytes, ToBytes};
39pub use crate::ops::checked::{
40 CheckedAdd, CheckedDiv, CheckedMul, CheckedNeg, CheckedRem, CheckedShl, CheckedShr, CheckedSub,
41};
42pub use crate::ops::euclid::{CheckedEuclid, Euclid};
43pub use crate::ops::inv::Inv;
44pub use crate::ops::mul_add::{MulAdd, MulAddAssign};
45pub use crate::ops::saturating::{Saturating, SaturatingAdd, SaturatingMul, SaturatingSub};
46pub use crate::ops::wrapping::{
47 WrappingAdd, WrappingMul, WrappingNeg, WrappingShl, WrappingShr, WrappingSub,
48};
49pub use crate::pow::{checked_pow, pow, Pow};
50pub use crate::sign::{abs, abs_sub, signum, Signed, Unsigned};
51
52#[macro_use]
53mod macros;
54
55pub mod bounds;
56pub mod cast;
57pub mod float;
58pub mod identities;
59pub mod int;
60pub mod ops;
61pub mod pow;
62pub mod real;
63pub mod sign;
64
65/// The base trait for numeric types, covering `0` and `1` values,
66/// comparisons, basic numeric operations, and string conversion.
67pub trait Num: PartialEq + Zero + One + NumOps {
68 type FromStrRadixErr;
69
70 /// Convert from a string and radix (typically `2..=36`).
71 ///
72 /// # Examples
73 ///
74 /// ```rust
75 /// use num_traits::Num;
76 ///
77 /// let result = <i32 as Num>::from_str_radix("27", 10);
78 /// assert_eq!(result, Ok(27));
79 ///
80 /// let result = <i32 as Num>::from_str_radix("foo", 10);
81 /// assert!(result.is_err());
82 /// ```
83 ///
84 /// # Supported radices
85 ///
86 /// The exact range of supported radices is at the discretion of each type implementation. For
87 /// primitive integers, this is implemented by the inherent `from_str_radix` methods in the
88 /// standard library, which **panic** if the radix is not in the range from 2 to 36. The
89 /// implementation in this crate for primitive floats is similar.
90 ///
91 /// For third-party types, it is suggested that implementations should follow suit and at least
92 /// accept `2..=36` without panicking, but an `Err` may be returned for any unsupported radix.
93 /// It's possible that a type might not even support the common radix 10, nor any, if string
94 /// parsing doesn't make sense for that type.
95 fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>;
96}
97
98/// Generic trait for types implementing basic numeric operations
99///
100/// This is automatically implemented for types which implement the operators.
101pub trait NumOps<Rhs = Self, Output = Self>:
102 Add<Rhs, Output = Output>
103 + Sub<Rhs, Output = Output>
104 + Mul<Rhs, Output = Output>
105 + Div<Rhs, Output = Output>
106 + Rem<Rhs, Output = Output>
107{
108}
109
110impl<T, Rhs, Output> NumOps<Rhs, Output> for T where
111 T: Add<Rhs, Output = Output>
112 + Sub<Rhs, Output = Output>
113 + Mul<Rhs, Output = Output>
114 + Div<Rhs, Output = Output>
115 + Rem<Rhs, Output = Output>
116{
117}
118
119/// The trait for `Num` types which also implement numeric operations taking
120/// the second operand by reference.
121///
122/// This is automatically implemented for types which implement the operators.
123pub trait NumRef: Num + for<'r> dynNumOps<&'r Self> {}
124impl<T> NumRef for T where T: Num + for<'r> dynNumOps<&'r T> {}
125
126/// The trait for `Num` references which implement numeric operations, taking the
127/// second operand either by value or by reference.
128///
129/// This is automatically implemented for all types which implement the operators. It covers
130/// every type implementing the operations though, regardless of it being a reference or
131/// related to `Num`.
132pub trait RefNum<Base>: NumOps<Base, Base> + for<'r> dynNumOps<&'r Base, Base> {}
133impl<T, Base> RefNum<Base> for T where T: NumOps<Base, Base> + for<'r> dynNumOps<&'r Base, Base> {}
134
135/// Generic trait for types implementing numeric assignment operators (like `+=`).
136///
137/// This is automatically implemented for types which implement the operators.
138pub trait NumAssignOps<Rhs = Self>:
139 AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
140{
141}
142
143impl<T, Rhs> NumAssignOps<Rhs> for T where
144 T: AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
145{
146}
147
148/// The trait for `Num` types which also implement assignment operators.
149///
150/// This is automatically implemented for types which implement the operators.
151pub trait NumAssign: Num + NumAssignOps {}
152impl<T> NumAssign for T where T: Num + NumAssignOps {}
153
154/// The trait for `NumAssign` types which also implement assignment operations
155/// taking the second operand by reference.
156///
157/// This is automatically implemented for types which implement the operators.
158pub trait NumAssignRef: NumAssign + for<'r> dynNumAssignOps<&'r Self> {}
159impl<T> NumAssignRef for T where T: NumAssign + for<'r> dynNumAssignOps<&'r T> {}
160
161macro_rules! int_trait_impl {
162 ($name:ident for $($t:ty)*) => ($(
163 impl $name for $t {
164 type FromStrRadixErr = ::core::num::ParseIntError;
165 #[inline]
166 fn from_str_radix(s: &str, radix: u32)
167 -> Result<Self, ::core::num::ParseIntError>
168 {
169 <$t>::from_str_radix(s, radix)
170 }
171 }
172 )*)
173}
174int_trait_impl!(Num for usize u8 u16 u32 u64 u128);
175int_trait_impl!(Num for isize i8 i16 i32 i64 i128);
176
177impl<T: Num> Num for Wrapping<T>
178where
179 Wrapping<T>: NumOps,
180{
181 type FromStrRadixErr = T::FromStrRadixErr;
182 fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
183 T::from_str_radix(str, radix).map(op:Wrapping)
184 }
185}
186
187#[derive(Debug)]
188pub enum FloatErrorKind {
189 Empty,
190 Invalid,
191}
192// FIXME: core::num::ParseFloatError is stable in 1.0, but opaque to us,
193// so there's not really any way for us to reuse it.
194#[derive(Debug)]
195pub struct ParseFloatError {
196 pub kind: FloatErrorKind,
197}
198
199impl fmt::Display for ParseFloatError {
200 fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
201 let description: &'static str = match self.kind {
202 FloatErrorKind::Empty => "cannot parse float from empty string",
203 FloatErrorKind::Invalid => "invalid float literal",
204 };
205
206 description.fmt(f)
207 }
208}
209
210fn str_to_ascii_lower_eq_str(a: &str, b: &str) -> bool {
211 a.len() == b.len()
212 && a.bytes().zip(b.bytes()).all(|(a: u8, b: u8)| {
213 let a_to_ascii_lower: u8 = a | (((b'A' <= a && a <= b'Z') as u8) << 5);
214 a_to_ascii_lower == b
215 })
216}
217
218// FIXME: The standard library from_str_radix on floats was deprecated, so we're stuck
219// with this implementation ourselves until we want to make a breaking change.
220// (would have to drop it from `Num` though)
221macro_rules! float_trait_impl {
222 ($name:ident for $($t:ident)*) => ($(
223 impl $name for $t {
224 type FromStrRadixErr = ParseFloatError;
225
226 fn from_str_radix(src: &str, radix: u32)
227 -> Result<Self, Self::FromStrRadixErr>
228 {
229 use self::FloatErrorKind::*;
230 use self::ParseFloatError as PFE;
231
232 // Special case radix 10 to use more accurate standard library implementation
233 if radix == 10 {
234 return src.parse().map_err(|_| PFE {
235 kind: if src.is_empty() { Empty } else { Invalid },
236 });
237 }
238
239 // Special values
240 if str_to_ascii_lower_eq_str(src, "inf")
241 || str_to_ascii_lower_eq_str(src, "infinity")
242 {
243 return Ok(core::$t::INFINITY);
244 } else if str_to_ascii_lower_eq_str(src, "-inf")
245 || str_to_ascii_lower_eq_str(src, "-infinity")
246 {
247 return Ok(core::$t::NEG_INFINITY);
248 } else if str_to_ascii_lower_eq_str(src, "nan") {
249 return Ok(core::$t::NAN);
250 } else if str_to_ascii_lower_eq_str(src, "-nan") {
251 return Ok(-core::$t::NAN);
252 }
253
254 fn slice_shift_char(src: &str) -> Option<(char, &str)> {
255 let mut chars = src.chars();
256 Some((chars.next()?, chars.as_str()))
257 }
258
259 let (is_positive, src) = match slice_shift_char(src) {
260 None => return Err(PFE { kind: Empty }),
261 Some(('-', "")) => return Err(PFE { kind: Empty }),
262 Some(('-', src)) => (false, src),
263 Some((_, _)) => (true, src),
264 };
265
266 // The significand to accumulate
267 let mut sig = if is_positive { 0.0 } else { -0.0 };
268 // Necessary to detect overflow
269 let mut prev_sig = sig;
270 let mut cs = src.chars().enumerate();
271 // Exponent prefix and exponent index offset
272 let mut exp_info = None::<(char, usize)>;
273
274 // Parse the integer part of the significand
275 for (i, c) in cs.by_ref() {
276 match c.to_digit(radix) {
277 Some(digit) => {
278 // shift significand one digit left
279 sig *= radix as $t;
280
281 // add/subtract current digit depending on sign
282 if is_positive {
283 sig += (digit as isize) as $t;
284 } else {
285 sig -= (digit as isize) as $t;
286 }
287
288 // Detect overflow by comparing to last value, except
289 // if we've not seen any non-zero digits.
290 if prev_sig != 0.0 {
291 if is_positive && sig <= prev_sig
292 { return Ok(core::$t::INFINITY); }
293 if !is_positive && sig >= prev_sig
294 { return Ok(core::$t::NEG_INFINITY); }
295
296 // Detect overflow by reversing the shift-and-add process
297 if is_positive && (prev_sig != (sig - digit as $t) / radix as $t)
298 { return Ok(core::$t::INFINITY); }
299 if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
300 { return Ok(core::$t::NEG_INFINITY); }
301 }
302 prev_sig = sig;
303 },
304 None => match c {
305 'e' | 'E' | 'p' | 'P' => {
306 exp_info = Some((c, i + 1));
307 break; // start of exponent
308 },
309 '.' => {
310 break; // start of fractional part
311 },
312 _ => {
313 return Err(PFE { kind: Invalid });
314 },
315 },
316 }
317 }
318
319 // If we are not yet at the exponent parse the fractional
320 // part of the significand
321 if exp_info.is_none() {
322 let mut power = 1.0;
323 for (i, c) in cs.by_ref() {
324 match c.to_digit(radix) {
325 Some(digit) => {
326 // Decrease power one order of magnitude
327 power /= radix as $t;
328 // add/subtract current digit depending on sign
329 sig = if is_positive {
330 sig + (digit as $t) * power
331 } else {
332 sig - (digit as $t) * power
333 };
334 // Detect overflow by comparing to last value
335 if is_positive && sig < prev_sig
336 { return Ok(core::$t::INFINITY); }
337 if !is_positive && sig > prev_sig
338 { return Ok(core::$t::NEG_INFINITY); }
339 prev_sig = sig;
340 },
341 None => match c {
342 'e' | 'E' | 'p' | 'P' => {
343 exp_info = Some((c, i + 1));
344 break; // start of exponent
345 },
346 _ => {
347 return Err(PFE { kind: Invalid });
348 },
349 },
350 }
351 }
352 }
353
354 // Parse and calculate the exponent
355 let exp = match exp_info {
356 Some((c, offset)) => {
357 let base = match c {
358 'E' | 'e' if radix == 10 => 10.0,
359 'P' | 'p' if radix == 16 => 2.0,
360 _ => return Err(PFE { kind: Invalid }),
361 };
362
363 // Parse the exponent as decimal integer
364 let src = &src[offset..];
365 let (is_positive, exp) = match slice_shift_char(src) {
366 Some(('-', src)) => (false, src.parse::<usize>()),
367 Some(('+', src)) => (true, src.parse::<usize>()),
368 Some((_, _)) => (true, src.parse::<usize>()),
369 None => return Err(PFE { kind: Invalid }),
370 };
371
372 #[cfg(feature = "std")]
373 fn pow(base: $t, exp: usize) -> $t {
374 Float::powi(base, exp as i32)
375 }
376 // otherwise uses the generic `pow` from the root
377
378 match (is_positive, exp) {
379 (true, Ok(exp)) => pow(base, exp),
380 (false, Ok(exp)) => 1.0 / pow(base, exp),
381 (_, Err(_)) => return Err(PFE { kind: Invalid }),
382 }
383 },
384 None => 1.0, // no exponent
385 };
386
387 Ok(sig * exp)
388 }
389 }
390 )*)
391}
392float_trait_impl!(Num for f32 f64);
393
394/// A value bounded by a minimum and a maximum
395///
396/// If input is less than min then this returns min.
397/// If input is greater than max then this returns max.
398/// Otherwise this returns input.
399///
400/// **Panics** in debug mode if `!(min <= max)`.
401#[inline]
402pub fn clamp<T: PartialOrd>(input: T, min: T, max: T) -> T {
403 debug_assert!(min <= max, "min must be less than or equal to max");
404 if input < min {
405 min
406 } else if input > max {
407 max
408 } else {
409 input
410 }
411}
412
413/// A value bounded by a minimum value
414///
415/// If input is less than min then this returns min.
416/// Otherwise this returns input.
417/// `clamp_min(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::min(std::f32::NAN, 1.0)`.
418///
419/// **Panics** in debug mode if `!(min == min)`. (This occurs if `min` is `NAN`.)
420#[inline]
421#[allow(clippy::eq_op)]
422pub fn clamp_min<T: PartialOrd>(input: T, min: T) -> T {
423 debug_assert!(min == min, "min must not be NAN");
424 if input < min {
425 min
426 } else {
427 input
428 }
429}
430
431/// A value bounded by a maximum value
432///
433/// If input is greater than max then this returns max.
434/// Otherwise this returns input.
435/// `clamp_max(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::max(std::f32::NAN, 1.0)`.
436///
437/// **Panics** in debug mode if `!(max == max)`. (This occurs if `max` is `NAN`.)
438#[inline]
439#[allow(clippy::eq_op)]
440pub fn clamp_max<T: PartialOrd>(input: T, max: T) -> T {
441 debug_assert!(max == max, "max must not be NAN");
442 if input > max {
443 max
444 } else {
445 input
446 }
447}
448
449#[test]
450fn clamp_test() {
451 // Int test
452 assert_eq!(1, clamp(1, -1, 2));
453 assert_eq!(-1, clamp(-2, -1, 2));
454 assert_eq!(2, clamp(3, -1, 2));
455 assert_eq!(1, clamp_min(1, -1));
456 assert_eq!(-1, clamp_min(-2, -1));
457 assert_eq!(-1, clamp_max(1, -1));
458 assert_eq!(-2, clamp_max(-2, -1));
459
460 // Float test
461 assert_eq!(1.0, clamp(1.0, -1.0, 2.0));
462 assert_eq!(-1.0, clamp(-2.0, -1.0, 2.0));
463 assert_eq!(2.0, clamp(3.0, -1.0, 2.0));
464 assert_eq!(1.0, clamp_min(1.0, -1.0));
465 assert_eq!(-1.0, clamp_min(-2.0, -1.0));
466 assert_eq!(-1.0, clamp_max(1.0, -1.0));
467 assert_eq!(-2.0, clamp_max(-2.0, -1.0));
468 assert!(clamp(::core::f32::NAN, -1.0, 1.0).is_nan());
469 assert!(clamp_min(::core::f32::NAN, 1.0).is_nan());
470 assert!(clamp_max(::core::f32::NAN, 1.0).is_nan());
471}
472
473#[test]
474#[should_panic]
475#[cfg(debug_assertions)]
476fn clamp_nan_min() {
477 clamp(0., ::core::f32::NAN, 1.);
478}
479
480#[test]
481#[should_panic]
482#[cfg(debug_assertions)]
483fn clamp_nan_max() {
484 clamp(0., -1., ::core::f32::NAN);
485}
486
487#[test]
488#[should_panic]
489#[cfg(debug_assertions)]
490fn clamp_nan_min_max() {
491 clamp(0., ::core::f32::NAN, ::core::f32::NAN);
492}
493
494#[test]
495#[should_panic]
496#[cfg(debug_assertions)]
497fn clamp_min_nan_min() {
498 clamp_min(0., ::core::f32::NAN);
499}
500
501#[test]
502#[should_panic]
503#[cfg(debug_assertions)]
504fn clamp_max_nan_max() {
505 clamp_max(0., ::core::f32::NAN);
506}
507
508#[test]
509fn from_str_radix_unwrap() {
510 // The Result error must impl Debug to allow unwrap()
511
512 let i: i32 = Num::from_str_radix("0", 10).unwrap();
513 assert_eq!(i, 0);
514
515 let f: f32 = Num::from_str_radix("0.0", 10).unwrap();
516 assert_eq!(f, 0.0);
517}
518
519#[test]
520fn from_str_radix_multi_byte_fail() {
521 // Ensure parsing doesn't panic, even on invalid sign characters
522 assert!(f32::from_str_radix("™0.2", 10).is_err());
523
524 // Even when parsing the exponent sign
525 assert!(f32::from_str_radix("0.2E™1", 10).is_err());
526}
527
528#[test]
529fn from_str_radix_ignore_case() {
530 assert_eq!(
531 f32::from_str_radix("InF", 16).unwrap(),
532 ::core::f32::INFINITY
533 );
534 assert_eq!(
535 f32::from_str_radix("InfinitY", 16).unwrap(),
536 ::core::f32::INFINITY
537 );
538 assert_eq!(
539 f32::from_str_radix("-InF", 8).unwrap(),
540 ::core::f32::NEG_INFINITY
541 );
542 assert_eq!(
543 f32::from_str_radix("-InfinitY", 8).unwrap(),
544 ::core::f32::NEG_INFINITY
545 );
546 assert!(f32::from_str_radix("nAn", 4).unwrap().is_nan());
547 assert!(f32::from_str_radix("-nAn", 4).unwrap().is_nan());
548}
549
550#[test]
551fn wrapping_is_num() {
552 fn require_num<T: Num>(_: &T) {}
553 require_num(&Wrapping(42_u32));
554 require_num(&Wrapping(-42));
555}
556
557#[test]
558fn wrapping_from_str_radix() {
559 macro_rules! test_wrapping_from_str_radix {
560 ($($t:ty)+) => {
561 $(
562 for &(s, r) in &[("42", 10), ("42", 2), ("-13.0", 10), ("foo", 10)] {
563 let w = Wrapping::<$t>::from_str_radix(s, r).map(|w| w.0);
564 assert_eq!(w, <$t as Num>::from_str_radix(s, r));
565 }
566 )+
567 };
568 }
569
570 test_wrapping_from_str_radix!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
571}
572
573#[test]
574fn check_num_ops() {
575 fn compute<T: Num + Copy>(x: T, y: T) -> T {
576 x * y / y % y + y - y
577 }
578 assert_eq!(compute(1, 2), 1)
579}
580
581#[test]
582fn check_numref_ops() {
583 fn compute<T: NumRef>(x: T, y: &T) -> T {
584 x * y / y % y + y - y
585 }
586 assert_eq!(compute(1, &2), 1)
587}
588
589#[test]
590fn check_refnum_ops() {
591 fn compute<T: Copy>(x: &T, y: T) -> T
592 where
593 for<'a> &'a T: RefNum<T>,
594 {
595 &(&(&(&(x * y) / y) % y) + y) - y
596 }
597 assert_eq!(compute(&1, 2), 1)
598}
599
600#[test]
601fn check_refref_ops() {
602 fn compute<T>(x: &T, y: &T) -> T
603 where
604 for<'a> &'a T: RefNum<T>,
605 {
606 &(&(&(&(x * y) / y) % y) + y) - y
607 }
608 assert_eq!(compute(&1, &2), 1)
609}
610
611#[test]
612fn check_numassign_ops() {
613 fn compute<T: NumAssign + Copy>(mut x: T, y: T) -> T {
614 x *= y;
615 x /= y;
616 x %= y;
617 x += y;
618 x -= y;
619 x
620 }
621 assert_eq!(compute(1, 2), 1)
622}
623
624#[test]
625fn check_numassignref_ops() {
626 fn compute<T: NumAssignRef + Copy>(mut x: T, y: &T) -> T {
627 x *= y;
628 x /= y;
629 x %= y;
630 x += y;
631 x -= y;
632 x
633 }
634 assert_eq!(compute(1, &2), 1)
635}
636