1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
//! Useful **type operators** that are not defined in `core::ops`.
//!

use private::{Internal, InternalMarker};
use {Bit, NInt, NonZero, PInt, UInt, UTerm, Unsigned, Z0};

/// A **type operator** that ensures that `Rhs` is the same as `Self`, it is mainly useful
/// for writing macros that can take arbitrary binary or unary operators.
///
/// `Same` is implemented generically for all types; it should never need to be implemented
/// for anything else.
///
/// Note that Rust lazily evaluates types, so this will only fail for two different types if
/// the `Output` is used.
///
/// # Example
/// ```rust
/// use typenum::{Same, U4, U5, Unsigned};
///
/// assert_eq!(<U5 as Same<U5>>::Output::to_u32(), 5);
///
/// // Only an error if we use it:
/// # #[allow(dead_code)]
/// type Undefined = <U5 as Same<U4>>::Output;
/// // Compiler error:
/// // Undefined::to_u32();
/// ```
pub trait Same<Rhs = Self> {
    /// Should always be `Self`
    type Output;
}

impl<T> Same<T> for T {
    type Output = T;
}

/// A **type operator** that returns the absolute value.
///
/// # Example
/// ```rust
/// use typenum::{Abs, N5, Integer};
///
/// assert_eq!(<N5 as Abs>::Output::to_i32(), 5);
/// ```
pub trait Abs {
    /// The absolute value.
    type Output;
}

impl Abs for Z0 {
    type Output = Z0;
}

impl<U: Unsigned + NonZero> Abs for PInt<U> {
    type Output = Self;
}

impl<U: Unsigned + NonZero> Abs for NInt<U> {
    type Output = PInt<U>;
}

/// A **type operator** that provides exponentiation by repeated squaring.
///
/// # Example
/// ```rust
/// use typenum::{Pow, N3, P3, Integer};
///
/// assert_eq!(<N3 as Pow<P3>>::Output::to_i32(), -27);
/// ```
pub trait Pow<Exp> {
    /// The result of the exponentiation.
    type Output;
    /// This function isn't used in this crate, but may be useful for others.
    /// It is implemented for primitives.
    ///
    /// # Example
    /// ```rust
    /// use typenum::{Pow, U3};
    ///
    /// let a = 7u32.powi(U3::new());
    /// let b = 7u32.pow(3);
    /// assert_eq!(a, b);
    ///
    /// let x = 3.0.powi(U3::new());
    /// let y = 27.0;
    /// assert_eq!(x, y);
    /// ```
    fn powi(self, exp: Exp) -> Self::Output;
}

macro_rules! impl_pow_f {
    ($t:ty) => {
        impl Pow<UTerm> for $t {
            type Output = $t;
            #[inline]
            fn powi(self, _: UTerm) -> Self::Output {
                1.0
            }
        }

        impl<U: Unsigned, B: Bit> Pow<UInt<U, B>> for $t {
            type Output = $t;
            // powi is unstable in core, so we have to write this function ourselves.
            // copied from num::pow::pow
            #[inline]
            fn powi(self, _: UInt<U, B>) -> Self::Output {
                let mut exp = <UInt<U, B> as Unsigned>::to_u32();
                let mut base = self;

                if exp == 0 {
                    return 1.0;
                }

                while exp & 1 == 0 {
                    base *= base;
                    exp >>= 1;
                }
                if exp == 1 {
                    return base;
                }

                let mut acc = base.clone();
                while exp > 1 {
                    exp >>= 1;
                    base *= base;
                    if exp & 1 == 1 {
                        acc *= base.clone();
                    }
                }
                acc
            }
        }

        impl Pow<Z0> for $t {
            type Output = $t;
            #[inline]
            fn powi(self, _: Z0) -> Self::Output {
                1.0
            }
        }

        impl<U: Unsigned + NonZero> Pow<PInt<U>> for $t {
            type Output = $t;
            // powi is unstable in core, so we have to write this function ourselves.
            // copied from num::pow::pow
            #[inline]
            fn powi(self, _: PInt<U>) -> Self::Output {
                let mut exp = U::to_u32();
                let mut base = self;

                if exp == 0 {
                    return 1.0;
                }

                while exp & 1 == 0 {
                    base *= base;
                    exp >>= 1;
                }
                if exp == 1 {
                    return base;
                }

                let mut acc = base.clone();
                while exp > 1 {
                    exp >>= 1;
                    base *= base;
                    if exp & 1 == 1 {
                        acc *= base.clone();
                    }
                }
                acc
            }
        }
    };
}

impl_pow_f!(f32);
impl_pow_f!(f64);

macro_rules! impl_pow_i {
    () => ();
    ($t: ty $(, $tail:tt)*) => (
        impl Pow<UTerm> for $t {
            type Output = $t;
            #[inline]
            fn powi(self, _: UTerm) -> Self::Output {
                1
            }
        }

        impl<U: Unsigned, B: Bit> Pow<UInt<U, B>> for $t {
            type Output = $t;
            #[inline]
            fn powi(self, _: UInt<U, B>) -> Self::Output {
                self.pow(<UInt<U, B> as Unsigned>::to_u32())
            }
        }

        impl Pow<Z0> for $t {
            type Output = $t;
            #[inline]
            fn powi(self, _: Z0) -> Self::Output {
                1
            }
        }

        impl<U: Unsigned + NonZero> Pow<PInt<U>> for $t {
            type Output = $t;
            #[inline]
            fn powi(self, _: PInt<U>) -> Self::Output {
                self.pow(U::to_u32())
            }
        }

        impl_pow_i!($($tail),*);
    );
}

impl_pow_i!(u8, u16, u32, u64, usize, i8, i16, i32, i64, isize);
#[cfg(feature = "i128")]
impl_pow_i!(u128, i128);

#[test]
fn pow_test() {
    use consts::*;
    let z0 = Z0::new();
    let p3 = P3::new();

    let u0 = U0::new();
    let u3 = U3::new();

    macro_rules! check {
        ($x:ident) => {
            assert_eq!($x.powi(z0), 1);
            assert_eq!($x.powi(u0), 1);

            assert_eq!($x.powi(p3), $x * $x * $x);
            assert_eq!($x.powi(u3), $x * $x * $x);
        };
        ($x:ident, $f:ident) => {
            assert!((<$f as Pow<Z0>>::powi(*$x, z0) - 1.0).abs() < ::core::$f::EPSILON);
            assert!((<$f as Pow<U0>>::powi(*$x, u0) - 1.0).abs() < ::core::$f::EPSILON);

            assert!((<$f as Pow<P3>>::powi(*$x, p3) - $x * $x * $x).abs() < ::core::$f::EPSILON);
            assert!((<$f as Pow<U3>>::powi(*$x, u3) - $x * $x * $x).abs() < ::core::$f::EPSILON);
        };
    }

    for x in &[0i8, -3, 2] {
        check!(x);
    }
    for x in &[0u8, 1, 5] {
        check!(x);
    }
    for x in &[0usize, 1, 5, 40] {
        check!(x);
    }
    for x in &[0isize, 1, 2, -30, -22, 48] {
        check!(x);
    }
    for x in &[0.0f32, 2.2, -3.5, 378.223] {
        check!(x, f32);
    }
    for x in &[0.0f64, 2.2, -3.5, -2387.2, 234.22] {
        check!(x, f64);
    }
}

/// A **type operator** for comparing `Self` and `Rhs`. It provides a similar functionality to
/// the function
/// [`core::cmp::Ord::cmp`](https://doc.rust-lang.org/nightly/core/cmp/trait.Ord.html#tymethod.cmp)
/// but for types.
///
/// # Example
/// ```rust
/// use typenum::{Cmp, Ord, N3, P2, P5};
/// use std::cmp::Ordering;
///
/// assert_eq!(<P2 as Cmp<N3>>::Output::to_ordering(), Ordering::Greater);
/// assert_eq!(<P2 as Cmp<P2>>::Output::to_ordering(), Ordering::Equal);
/// assert_eq!(<P2 as Cmp<P5>>::Output::to_ordering(), Ordering::Less);
pub trait Cmp<Rhs = Self> {
    /// The result of the comparison. It should only ever be one of `Greater`, `Less`, or `Equal`.
    type Output;

    #[doc(hidden)]
    fn compare<IM: InternalMarker>(&self, &Rhs) -> Self::Output;
}

/// A **type operator** that gives the length of an `Array` or the number of bits in a `UInt`.
pub trait Len {
    /// The length as a type-level unsigned integer.
    type Output: ::Unsigned;
    /// This function isn't used in this crate, but may be useful for others.
    fn len(&self) -> Self::Output;
}

/// Division as a partial function. This **type operator** performs division just as `Div`, but is
/// only defined when the result is an integer (i.e. there is no remainder).
pub trait PartialDiv<Rhs = Self> {
    /// The type of the result of the division
    type Output;
    /// Method for performing the division
    fn partial_div(self, _: Rhs) -> Self::Output;
}

/// A **type operator** that returns the minimum of `Self` and `Rhs`.
pub trait Min<Rhs = Self> {
    /// The type of the minimum of `Self` and `Rhs`
    type Output;
    /// Method returning the minimum
    fn min(self, rhs: Rhs) -> Self::Output;
}

/// A **type operator** that returns the maximum of `Self` and `Rhs`.
pub trait Max<Rhs = Self> {
    /// The type of the maximum of `Self` and `Rhs`
    type Output;
    /// Method returning the maximum
    fn max(self, rhs: Rhs) -> Self::Output;
}

use Compare;

/// A **type operator** that returns `True` if `Self < Rhs`, otherwise returns `False`.
pub trait IsLess<Rhs = Self> {
    /// The type representing either `True` or `False`
    type Output: Bit;
    /// Method returning `True` or `False`.
    fn is_less(self, rhs: Rhs) -> Self::Output;
}

use private::IsLessPrivate;
impl<A, B> IsLess<B> for A
where
    A: Cmp<B> + IsLessPrivate<B, Compare<A, B>>,
{
    type Output = <A as IsLessPrivate<B, Compare<A, B>>>::Output;

    #[inline]
    fn is_less(self, rhs: B) -> Self::Output {
        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
        self.is_less_private(rhs, lhs_cmp_rhs)
    }
}

/// A **type operator** that returns `True` if `Self == Rhs`, otherwise returns `False`.
pub trait IsEqual<Rhs = Self> {
    /// The type representing either `True` or `False`
    type Output: Bit;
    /// Method returning `True` or `False`.
    fn is_equal(self, rhs: Rhs) -> Self::Output;
}

use private::IsEqualPrivate;
impl<A, B> IsEqual<B> for A
where
    A: Cmp<B> + IsEqualPrivate<B, Compare<A, B>>,
{
    type Output = <A as IsEqualPrivate<B, Compare<A, B>>>::Output;

    #[inline]
    fn is_equal(self, rhs: B) -> Self::Output {
        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
        self.is_equal_private(rhs, lhs_cmp_rhs)
    }
}

/// A **type operator** that returns `True` if `Self > Rhs`, otherwise returns `False`.
pub trait IsGreater<Rhs = Self> {
    /// The type representing either `True` or `False`
    type Output: Bit;
    /// Method returning `True` or `False`.
    fn is_greater(self, rhs: Rhs) -> Self::Output;
}

use private::IsGreaterPrivate;
impl<A, B> IsGreater<B> for A
where
    A: Cmp<B> + IsGreaterPrivate<B, Compare<A, B>>,
{
    type Output = <A as IsGreaterPrivate<B, Compare<A, B>>>::Output;

    #[inline]
    fn is_greater(self, rhs: B) -> Self::Output {
        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
        self.is_greater_private(rhs, lhs_cmp_rhs)
    }
}

/// A **type operator** that returns `True` if `Self <= Rhs`, otherwise returns `False`.
pub trait IsLessOrEqual<Rhs = Self> {
    /// The type representing either `True` or `False`
    type Output: Bit;
    /// Method returning `True` or `False`.
    fn is_less_or_equal(self, rhs: Rhs) -> Self::Output;
}

use private::IsLessOrEqualPrivate;
impl<A, B> IsLessOrEqual<B> for A
where
    A: Cmp<B> + IsLessOrEqualPrivate<B, Compare<A, B>>,
{
    type Output = <A as IsLessOrEqualPrivate<B, Compare<A, B>>>::Output;

    #[inline]
    fn is_less_or_equal(self, rhs: B) -> Self::Output {
        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
        self.is_less_or_equal_private(rhs, lhs_cmp_rhs)
    }
}

/// A **type operator** that returns `True` if `Self != Rhs`, otherwise returns `False`.
pub trait IsNotEqual<Rhs = Self> {
    /// The type representing either `True` or `False`
    type Output: Bit;
    /// Method returning `True` or `False`.
    fn is_not_equal(self, rhs: Rhs) -> Self::Output;
}

use private::IsNotEqualPrivate;
impl<A, B> IsNotEqual<B> for A
where
    A: Cmp<B> + IsNotEqualPrivate<B, Compare<A, B>>,
{
    type Output = <A as IsNotEqualPrivate<B, Compare<A, B>>>::Output;

    #[inline]
    fn is_not_equal(self, rhs: B) -> Self::Output {
        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
        self.is_not_equal_private(rhs, lhs_cmp_rhs)
    }
}

/// A **type operator** that returns `True` if `Self >= Rhs`, otherwise returns `False`.
pub trait IsGreaterOrEqual<Rhs = Self> {
    /// The type representing either `True` or `False`
    type Output: Bit;
    /// Method returning `True` or `False`.
    fn is_greater_or_equal(self, rhs: Rhs) -> Self::Output;
}

use private::IsGreaterOrEqualPrivate;
impl<A, B> IsGreaterOrEqual<B> for A
where
    A: Cmp<B> + IsGreaterOrEqualPrivate<B, Compare<A, B>>,
{
    type Output = <A as IsGreaterOrEqualPrivate<B, Compare<A, B>>>::Output;

    #[inline]
    fn is_greater_or_equal(self, rhs: B) -> Self::Output {
        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
        self.is_greater_or_equal_private(rhs, lhs_cmp_rhs)
    }
}

/**
A convenience macro for comparing type numbers. Use `op!` instead.

Due to the intricacies of the macro system, if the left-hand operand is more complex than a simple
`ident`, you must place a comma between it and the comparison sign.

For example, you can do `cmp!(P5 > P3)` or `cmp!(typenum::P5, > typenum::P3)` but not
`cmp!(typenum::P5 > typenum::P3)`.

The result of this comparison will always be one of `True` (aka `B1`) or `False` (aka `B0`).

# Example
```rust
#[macro_use] extern crate typenum;
use typenum::consts::*;
use typenum::Bit;

fn main() {
type Result = cmp!(P9 == op!(P1 + P2 * (P2 - N2)));
assert_eq!(Result::to_bool(), true);
}
```
 */
#[deprecated(since = "1.9.0", note = "use the `op!` macro instead")]
#[macro_export]
macro_rules! cmp {
    ($a:ident < $b:ty) => {
        <$a as $crate::IsLess<$b>>::Output
    };
    ($a:ty, < $b:ty) => {
        <$a as $crate::IsLess<$b>>::Output
    };

    ($a:ident == $b:ty) => {
        <$a as $crate::IsEqual<$b>>::Output
    };
    ($a:ty, == $b:ty) => {
        <$a as $crate::IsEqual<$b>>::Output
    };

    ($a:ident > $b:ty) => {
        <$a as $crate::IsGreater<$b>>::Output
    };
    ($a:ty, > $b:ty) => {
        <$a as $crate::IsGreater<$b>>::Output
    };

    ($a:ident <= $b:ty) => {
        <$a as $crate::IsLessOrEqual<$b>>::Output
    };
    ($a:ty, <= $b:ty) => {
        <$a as $crate::IsLessOrEqual<$b>>::Output
    };

    ($a:ident != $b:ty) => {
        <$a as $crate::IsNotEqual<$b>>::Output
    };
    ($a:ty, != $b:ty) => {
        <$a as $crate::IsNotEqual<$b>>::Output
    };

    ($a:ident >= $b:ty) => {
        <$a as $crate::IsGreaterOrEqual<$b>>::Output
    };
    ($a:ty, >= $b:ty) => {
        <$a as $crate::IsGreaterOrEqual<$b>>::Output
    };
}

/// A **type operator** for taking the integer square root of `Self`.
///
/// The integer square root of `n` is the largest integer `m` such
/// that `n >= m*m`. This definition is equivalent to truncating the
/// real-valued square root: `floor(real_sqrt(n))`.
pub trait SquareRoot {
    /// The result of the integer square root.
    type Output;
}

/// A **type operator** for taking the integer binary logarithm of `Self`.
///
/// The integer binary logarighm of `n` is the largest integer `m` such
/// that `n >= 2^m`. This definition is equivalent to truncating the
/// real-valued binary logarithm: `floor(log2(n))`.
pub trait Logarithm2 {
    /// The result of the integer binary logarithm.
    type Output;
}

/// A **type operator** that computes the [greatest common divisor][gcd] of `Self` and `Rhs`.
///
/// [gcd]: https://en.wikipedia.org/wiki/Greatest_common_divisor
///
/// # Example
///
/// ```rust
/// use typenum::{Gcd, U12, U8, Unsigned};
///
/// assert_eq!(<U12 as Gcd<U8>>::Output::to_i32(), 4);
/// ```
pub trait Gcd<Rhs> {
    /// The greatest common divisor.
    type Output;
}