typenum/
type_operators.rs

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1//! Useful **type operators** that are not defined in `core::ops`.
2
3use crate::{
4    private::{Internal, InternalMarker},
5    Bit, NInt, NonZero, PInt, UInt, UTerm, Unsigned, Z0,
6};
7
8/// A **type operator** that ensures that `Rhs` is the same as `Self`, it is mainly useful
9/// for writing macros that can take arbitrary binary or unary operators.
10///
11/// `Same` is implemented generically for all types; it should never need to be implemented
12/// for anything else.
13///
14/// Note that Rust lazily evaluates types, so this will only fail for two different types if
15/// the `Output` is used.
16///
17/// # Example
18/// ```rust
19/// use typenum::{Same, Unsigned, U4, U5};
20///
21/// assert_eq!(<U5 as Same<U5>>::Output::to_u32(), 5);
22///
23/// // Only an error if we use it:
24/// # #[allow(dead_code)]
25/// type Undefined = <U5 as Same<U4>>::Output;
26/// // Compiler error:
27/// // Undefined::to_u32();
28/// ```
29pub trait Same<Rhs = Self> {
30    /// Should always be `Self`
31    type Output;
32}
33
34impl<T> Same<T> for T {
35    type Output = T;
36}
37
38/// A **type operator** that returns the absolute value.
39///
40/// # Example
41/// ```rust
42/// use typenum::{Abs, Integer, N5};
43///
44/// assert_eq!(<N5 as Abs>::Output::to_i32(), 5);
45/// ```
46pub trait Abs {
47    /// The absolute value.
48    type Output;
49}
50
51impl Abs for Z0 {
52    type Output = Z0;
53}
54
55impl<U: Unsigned + NonZero> Abs for PInt<U> {
56    type Output = Self;
57}
58
59impl<U: Unsigned + NonZero> Abs for NInt<U> {
60    type Output = PInt<U>;
61}
62
63/// A **type operator** that provides exponentiation by repeated squaring.
64///
65/// # Example
66/// ```rust
67/// use typenum::{Integer, Pow, N3, P3};
68///
69/// assert_eq!(<N3 as Pow<P3>>::Output::to_i32(), -27);
70/// ```
71pub trait Pow<Exp> {
72    /// The result of the exponentiation.
73    type Output;
74    /// This function isn't used in this crate, but may be useful for others.
75    /// It is implemented for primitives.
76    ///
77    /// # Example
78    /// ```rust
79    /// use typenum::{Pow, U3};
80    ///
81    /// let a = 7u32.powi(U3::new());
82    /// let b = 7u32.pow(3);
83    /// assert_eq!(a, b);
84    ///
85    /// let x = 3.0.powi(U3::new());
86    /// let y = 27.0;
87    /// assert_eq!(x, y);
88    /// ```
89    fn powi(self, exp: Exp) -> Self::Output;
90}
91
92macro_rules! impl_pow_f {
93    ($t:ty) => {
94        impl Pow<UTerm> for $t {
95            type Output = $t;
96            #[inline]
97            fn powi(self, _: UTerm) -> Self::Output {
98                1.0
99            }
100        }
101
102        impl<U: Unsigned, B: Bit> Pow<UInt<U, B>> for $t {
103            type Output = $t;
104            // powi is unstable in core, so we have to write this function ourselves.
105            // copied from num::pow::pow
106            #[inline]
107            fn powi(self, _: UInt<U, B>) -> Self::Output {
108                let mut exp = <UInt<U, B> as Unsigned>::to_u32();
109                let mut base = self;
110
111                if exp == 0 {
112                    return 1.0;
113                }
114
115                while exp & 1 == 0 {
116                    base *= base;
117                    exp >>= 1;
118                }
119                if exp == 1 {
120                    return base;
121                }
122
123                let mut acc = base.clone();
124                while exp > 1 {
125                    exp >>= 1;
126                    base *= base;
127                    if exp & 1 == 1 {
128                        acc *= base.clone();
129                    }
130                }
131                acc
132            }
133        }
134
135        impl Pow<Z0> for $t {
136            type Output = $t;
137            #[inline]
138            fn powi(self, _: Z0) -> Self::Output {
139                1.0
140            }
141        }
142
143        impl<U: Unsigned + NonZero> Pow<PInt<U>> for $t {
144            type Output = $t;
145            // powi is unstable in core, so we have to write this function ourselves.
146            // copied from num::pow::pow
147            #[inline]
148            fn powi(self, _: PInt<U>) -> Self::Output {
149                let mut exp = U::to_u32();
150                let mut base = self;
151
152                if exp == 0 {
153                    return 1.0;
154                }
155
156                while exp & 1 == 0 {
157                    base *= base;
158                    exp >>= 1;
159                }
160                if exp == 1 {
161                    return base;
162                }
163
164                let mut acc = base.clone();
165                while exp > 1 {
166                    exp >>= 1;
167                    base *= base;
168                    if exp & 1 == 1 {
169                        acc *= base.clone();
170                    }
171                }
172                acc
173            }
174        }
175
176        impl<U: Unsigned + NonZero> Pow<NInt<U>> for $t {
177            type Output = $t;
178
179            #[inline]
180            fn powi(self, _: NInt<U>) -> Self::Output {
181                <$t as Pow<PInt<U>>>::powi(self, PInt::new()).recip()
182            }
183        }
184    };
185}
186
187impl_pow_f!(f32);
188impl_pow_f!(f64);
189
190macro_rules! impl_pow_i {
191    () => ();
192    ($t: ty $(, $tail:tt)*) => (
193        impl Pow<UTerm> for $t {
194            type Output = $t;
195            #[inline]
196            fn powi(self, _: UTerm) -> Self::Output {
197                1
198            }
199        }
200
201        impl<U: Unsigned, B: Bit> Pow<UInt<U, B>> for $t {
202            type Output = $t;
203            #[inline]
204            fn powi(self, _: UInt<U, B>) -> Self::Output {
205                self.pow(<UInt<U, B> as Unsigned>::to_u32())
206            }
207        }
208
209        impl Pow<Z0> for $t {
210            type Output = $t;
211            #[inline]
212            fn powi(self, _: Z0) -> Self::Output {
213                1
214            }
215        }
216
217        impl<U: Unsigned + NonZero> Pow<PInt<U>> for $t {
218            type Output = $t;
219            #[inline]
220            fn powi(self, _: PInt<U>) -> Self::Output {
221                self.pow(U::to_u32())
222            }
223        }
224
225        impl_pow_i!($($tail),*);
226    );
227}
228
229impl_pow_i!(u8, u16, u32, u64, usize, i8, i16, i32, i64, isize);
230#[cfg(feature = "i128")]
231impl_pow_i!(u128, i128);
232
233#[test]
234fn pow_test() {
235    use crate::consts::*;
236    let z0 = Z0::new();
237    let p3 = P3::new();
238
239    let u0 = U0::new();
240    let u3 = U3::new();
241    let n3 = N3::new();
242
243    macro_rules! check {
244        ($x:ident) => {
245            assert_eq!($x.powi(z0), 1);
246            assert_eq!($x.powi(u0), 1);
247
248            assert_eq!($x.powi(p3), $x * $x * $x);
249            assert_eq!($x.powi(u3), $x * $x * $x);
250        };
251        ($x:ident, $f:ident) => {
252            assert!((<$f as Pow<Z0>>::powi(*$x, z0) - 1.0).abs() < ::core::$f::EPSILON);
253            assert!((<$f as Pow<U0>>::powi(*$x, u0) - 1.0).abs() < ::core::$f::EPSILON);
254
255            assert!((<$f as Pow<P3>>::powi(*$x, p3) - $x * $x * $x).abs() < ::core::$f::EPSILON);
256            assert!((<$f as Pow<U3>>::powi(*$x, u3) - $x * $x * $x).abs() < ::core::$f::EPSILON);
257
258            if *$x == 0.0 {
259                assert!(<$f as Pow<N3>>::powi(*$x, n3).is_infinite());
260            } else {
261                assert!(
262                    (<$f as Pow<N3>>::powi(*$x, n3) - 1. / $x / $x / $x).abs()
263                        < ::core::$f::EPSILON
264                );
265            }
266        };
267    }
268
269    for x in &[0i8, -3, 2] {
270        check!(x);
271    }
272    for x in &[0u8, 1, 5] {
273        check!(x);
274    }
275    for x in &[0usize, 1, 5, 40] {
276        check!(x);
277    }
278    for x in &[0isize, 1, 2, -30, -22, 48] {
279        check!(x);
280    }
281    for x in &[0.0f32, 2.2, -3.5, 378.223] {
282        check!(x, f32);
283    }
284    for x in &[0.0f64, 2.2, -3.5, -2387.2, 234.22] {
285        check!(x, f64);
286    }
287}
288
289/// A **type operator** for comparing `Self` and `Rhs`. It provides a similar functionality to
290/// the function
291/// [`core::cmp::Ord::cmp`](https://doc.rust-lang.org/nightly/core/cmp/trait.Ord.html#tymethod.cmp)
292/// but for types.
293///
294/// # Example
295/// ```rust
296/// use typenum::{Cmp, Ord, N3, P2, P5};
297/// use std::cmp::Ordering;
298///
299/// assert_eq!(<P2 as Cmp<N3>>::Output::to_ordering(), Ordering::Greater);
300/// assert_eq!(<P2 as Cmp<P2>>::Output::to_ordering(), Ordering::Equal);
301/// assert_eq!(<P2 as Cmp<P5>>::Output::to_ordering(), Ordering::Less);
302pub trait Cmp<Rhs = Self> {
303    /// The result of the comparison. It should only ever be one of `Greater`, `Less`, or `Equal`.
304    type Output;
305
306    #[doc(hidden)]
307    fn compare<IM: InternalMarker>(&self, _: &Rhs) -> Self::Output;
308}
309
310/// A **type operator** that gives the length of an `Array` or the number of bits in a `UInt`.
311pub trait Len {
312    /// The length as a type-level unsigned integer.
313    type Output: crate::Unsigned;
314    /// This function isn't used in this crate, but may be useful for others.
315    fn len(&self) -> Self::Output;
316}
317
318/// Division as a partial function. This **type operator** performs division just as `Div`, but is
319/// only defined when the result is an integer (i.e. there is no remainder).
320pub trait PartialDiv<Rhs = Self> {
321    /// The type of the result of the division
322    type Output;
323    /// Method for performing the division
324    fn partial_div(self, _: Rhs) -> Self::Output;
325}
326
327/// A **type operator** that returns the minimum of `Self` and `Rhs`.
328pub trait Min<Rhs = Self> {
329    /// The type of the minimum of `Self` and `Rhs`
330    type Output;
331    /// Method returning the minimum
332    fn min(self, rhs: Rhs) -> Self::Output;
333}
334
335/// A **type operator** that returns the maximum of `Self` and `Rhs`.
336pub trait Max<Rhs = Self> {
337    /// The type of the maximum of `Self` and `Rhs`
338    type Output;
339    /// Method returning the maximum
340    fn max(self, rhs: Rhs) -> Self::Output;
341}
342
343use crate::Compare;
344
345/// A **type operator** that returns `True` if `Self < Rhs`, otherwise returns `False`.
346pub trait IsLess<Rhs = Self> {
347    /// The type representing either `True` or `False`
348    type Output: Bit;
349    /// Method returning `True` or `False`.
350    fn is_less(self, rhs: Rhs) -> Self::Output;
351}
352
353use crate::private::IsLessPrivate;
354impl<A, B> IsLess<B> for A
355where
356    A: Cmp<B> + IsLessPrivate<B, Compare<A, B>>,
357{
358    type Output = <A as IsLessPrivate<B, Compare<A, B>>>::Output;
359
360    #[inline]
361    fn is_less(self, rhs: B) -> Self::Output {
362        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
363        self.is_less_private(rhs, lhs_cmp_rhs)
364    }
365}
366
367/// A **type operator** that returns `True` if `Self == Rhs`, otherwise returns `False`.
368pub trait IsEqual<Rhs = Self> {
369    /// The type representing either `True` or `False`
370    type Output: Bit;
371    /// Method returning `True` or `False`.
372    fn is_equal(self, rhs: Rhs) -> Self::Output;
373}
374
375use crate::private::IsEqualPrivate;
376impl<A, B> IsEqual<B> for A
377where
378    A: Cmp<B> + IsEqualPrivate<B, Compare<A, B>>,
379{
380    type Output = <A as IsEqualPrivate<B, Compare<A, B>>>::Output;
381
382    #[inline]
383    fn is_equal(self, rhs: B) -> Self::Output {
384        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
385        self.is_equal_private(rhs, lhs_cmp_rhs)
386    }
387}
388
389/// A **type operator** that returns `True` if `Self > Rhs`, otherwise returns `False`.
390pub trait IsGreater<Rhs = Self> {
391    /// The type representing either `True` or `False`
392    type Output: Bit;
393    /// Method returning `True` or `False`.
394    fn is_greater(self, rhs: Rhs) -> Self::Output;
395}
396
397use crate::private::IsGreaterPrivate;
398impl<A, B> IsGreater<B> for A
399where
400    A: Cmp<B> + IsGreaterPrivate<B, Compare<A, B>>,
401{
402    type Output = <A as IsGreaterPrivate<B, Compare<A, B>>>::Output;
403
404    #[inline]
405    fn is_greater(self, rhs: B) -> Self::Output {
406        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
407        self.is_greater_private(rhs, lhs_cmp_rhs)
408    }
409}
410
411/// A **type operator** that returns `True` if `Self <= Rhs`, otherwise returns `False`.
412pub trait IsLessOrEqual<Rhs = Self> {
413    /// The type representing either `True` or `False`
414    type Output: Bit;
415    /// Method returning `True` or `False`.
416    fn is_less_or_equal(self, rhs: Rhs) -> Self::Output;
417}
418
419use crate::private::IsLessOrEqualPrivate;
420impl<A, B> IsLessOrEqual<B> for A
421where
422    A: Cmp<B> + IsLessOrEqualPrivate<B, Compare<A, B>>,
423{
424    type Output = <A as IsLessOrEqualPrivate<B, Compare<A, B>>>::Output;
425
426    #[inline]
427    fn is_less_or_equal(self, rhs: B) -> Self::Output {
428        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
429        self.is_less_or_equal_private(rhs, lhs_cmp_rhs)
430    }
431}
432
433/// A **type operator** that returns `True` if `Self != Rhs`, otherwise returns `False`.
434pub trait IsNotEqual<Rhs = Self> {
435    /// The type representing either `True` or `False`
436    type Output: Bit;
437    /// Method returning `True` or `False`.
438    fn is_not_equal(self, rhs: Rhs) -> Self::Output;
439}
440
441use crate::private::IsNotEqualPrivate;
442impl<A, B> IsNotEqual<B> for A
443where
444    A: Cmp<B> + IsNotEqualPrivate<B, Compare<A, B>>,
445{
446    type Output = <A as IsNotEqualPrivate<B, Compare<A, B>>>::Output;
447
448    #[inline]
449    fn is_not_equal(self, rhs: B) -> Self::Output {
450        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
451        self.is_not_equal_private(rhs, lhs_cmp_rhs)
452    }
453}
454
455/// A **type operator** that returns `True` if `Self >= Rhs`, otherwise returns `False`.
456pub trait IsGreaterOrEqual<Rhs = Self> {
457    /// The type representing either `True` or `False`
458    type Output: Bit;
459    /// Method returning `True` or `False`.
460    fn is_greater_or_equal(self, rhs: Rhs) -> Self::Output;
461}
462
463use crate::private::IsGreaterOrEqualPrivate;
464impl<A, B> IsGreaterOrEqual<B> for A
465where
466    A: Cmp<B> + IsGreaterOrEqualPrivate<B, Compare<A, B>>,
467{
468    type Output = <A as IsGreaterOrEqualPrivate<B, Compare<A, B>>>::Output;
469
470    #[inline]
471    fn is_greater_or_equal(self, rhs: B) -> Self::Output {
472        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
473        self.is_greater_or_equal_private(rhs, lhs_cmp_rhs)
474    }
475}
476
477/**
478A convenience macro for comparing type numbers. Use `op!` instead.
479
480Due to the intricacies of the macro system, if the left-hand operand is more complex than a simple
481`ident`, you must place a comma between it and the comparison sign.
482
483For example, you can do `cmp!(P5 > P3)` or `cmp!(typenum::P5, > typenum::P3)` but not
484`cmp!(typenum::P5 > typenum::P3)`.
485
486The result of this comparison will always be one of `True` (aka `B1`) or `False` (aka `B0`).
487
488# Example
489```rust
490#[macro_use] extern crate typenum;
491use typenum::consts::*;
492use typenum::Bit;
493
494fn main() {
495type Result = cmp!(P9 == op!(P1 + P2 * (P2 - N2)));
496assert_eq!(Result::to_bool(), true);
497}
498```
499 */
500#[deprecated(since = "1.9.0", note = "use the `op!` macro instead")]
501#[macro_export]
502macro_rules! cmp {
503    ($a:ident < $b:ty) => {
504        <$a as $crate::IsLess<$b>>::Output
505    };
506    ($a:ty, < $b:ty) => {
507        <$a as $crate::IsLess<$b>>::Output
508    };
509
510    ($a:ident == $b:ty) => {
511        <$a as $crate::IsEqual<$b>>::Output
512    };
513    ($a:ty, == $b:ty) => {
514        <$a as $crate::IsEqual<$b>>::Output
515    };
516
517    ($a:ident > $b:ty) => {
518        <$a as $crate::IsGreater<$b>>::Output
519    };
520    ($a:ty, > $b:ty) => {
521        <$a as $crate::IsGreater<$b>>::Output
522    };
523
524    ($a:ident <= $b:ty) => {
525        <$a as $crate::IsLessOrEqual<$b>>::Output
526    };
527    ($a:ty, <= $b:ty) => {
528        <$a as $crate::IsLessOrEqual<$b>>::Output
529    };
530
531    ($a:ident != $b:ty) => {
532        <$a as $crate::IsNotEqual<$b>>::Output
533    };
534    ($a:ty, != $b:ty) => {
535        <$a as $crate::IsNotEqual<$b>>::Output
536    };
537
538    ($a:ident >= $b:ty) => {
539        <$a as $crate::IsGreaterOrEqual<$b>>::Output
540    };
541    ($a:ty, >= $b:ty) => {
542        <$a as $crate::IsGreaterOrEqual<$b>>::Output
543    };
544}
545
546/// A **type operator** for taking the integer square root of `Self`.
547///
548/// The integer square root of `n` is the largest integer `m` such
549/// that `n >= m*m`. This definition is equivalent to truncating the
550/// real-valued square root: `floor(real_sqrt(n))`.
551pub trait SquareRoot {
552    /// The result of the integer square root.
553    type Output;
554}
555
556/// A **type operator** for taking the integer binary logarithm of `Self`.
557///
558/// The integer binary logarighm of `n` is the largest integer `m` such
559/// that `n >= 2^m`. This definition is equivalent to truncating the
560/// real-valued binary logarithm: `floor(log2(n))`.
561pub trait Logarithm2 {
562    /// The result of the integer binary logarithm.
563    type Output;
564}
565
566/// A **type operator** that computes the [greatest common divisor][gcd] of `Self` and `Rhs`.
567///
568/// [gcd]: https://en.wikipedia.org/wiki/Greatest_common_divisor
569///
570/// # Example
571///
572/// ```rust
573/// use typenum::{Gcd, Unsigned, U12, U8};
574///
575/// assert_eq!(<U12 as Gcd<U8>>::Output::to_i32(), 4);
576/// ```
577pub trait Gcd<Rhs> {
578    /// The greatest common divisor.
579    type Output;
580}
581
582/// A **type operator** for taking a concrete integer value from a type.
583///
584/// It returns arbitrary integer value without explicitly specifying the
585/// type. It is useful when you pass the values to methods that accept
586/// distinct types without runtime casting.
587pub trait ToInt<T> {
588    /// Method returning the concrete value for the type.
589    fn to_int() -> T;
590}
typenum/type_operators.rs

typenum/
type_operators.rs
