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
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
use crate::intrinsics;
use crate::iter::{from_fn, TrustedLen, TrustedRandomAccess};
use crate::num::NonZero;
use crate::ops::{Range, Try};

/// An iterator for stepping iterators by a custom amount.
///
/// This `struct` is created by the [`step_by`] method on [`Iterator`]. See
/// its documentation for more.
///
/// [`step_by`]: Iterator::step_by
/// [`Iterator`]: trait.Iterator.html
#[must_use = "iterators are lazy and do nothing unless consumed"]
#[stable(feature = "iterator_step_by", since = "1.28.0")]
#[derive(Clone, Debug)]
pub struct StepBy<I> {
    /// This field is guaranteed to be preprocessed by the specialized `SpecRangeSetup::setup`
    /// in the constructor.
    /// For most iterators that processing is a no-op, but for Range<{integer}> types it is lossy
    /// which means the inner iterator cannot be returned to user code.
    /// Additionally this type-dependent preprocessing means specialized implementations
    /// cannot be used interchangeably.
    iter: I,
    /// This field is `step - 1`, aka the correct amount to pass to `nth` when iterating.
    /// It MUST NOT be `usize::MAX`, as `unsafe` code depends on being able to add one
    /// without the risk of overflow.  (This is important so that length calculations
    /// don't need to check for division-by-zero, for example.)
    step_minus_one: usize,
    first_take: bool,
}

impl<I> StepBy<I> {
    #[inline]
    pub(in crate::iter) fn new(iter: I, step: usize) -> StepBy<I> {
        assert!(step != 0);
        let iter = <I as SpecRangeSetup<I>>::setup(iter, step);
        StepBy { iter, step_minus_one: step - 1, first_take: true }
    }

    /// The `step` that was originally passed to `Iterator::step_by(step)`,
    /// aka `self.step_minus_one + 1`.
    #[inline]
    fn original_step(&self) -> NonZero<usize> {
        // SAFETY: By type invariant, `step_minus_one` cannot be `MAX`, which
        // means the addition cannot overflow and the result cannot be zero.
        unsafe { NonZero::new_unchecked(intrinsics::unchecked_add(self.step_minus_one, 1)) }
    }
}

#[stable(feature = "iterator_step_by", since = "1.28.0")]
impl<I> Iterator for StepBy<I>
where
    I: Iterator,
{
    type Item = I::Item;

    #[inline]
    fn next(&mut self) -> Option<Self::Item> {
        self.spec_next()
    }

    #[inline]
    fn size_hint(&self) -> (usize, Option<usize>) {
        self.spec_size_hint()
    }

    #[inline]
    fn nth(&mut self, n: usize) -> Option<Self::Item> {
        self.spec_nth(n)
    }

    fn try_fold<Acc, F, R>(&mut self, acc: Acc, f: F) -> R
    where
        F: FnMut(Acc, Self::Item) -> R,
        R: Try<Output = Acc>,
    {
        self.spec_try_fold(acc, f)
    }

    #[inline]
    fn fold<Acc, F>(self, acc: Acc, f: F) -> Acc
    where
        F: FnMut(Acc, Self::Item) -> Acc,
    {
        self.spec_fold(acc, f)
    }
}

impl<I> StepBy<I>
where
    I: ExactSizeIterator,
{
    // The zero-based index starting from the end of the iterator of the
    // last element. Used in the `DoubleEndedIterator` implementation.
    fn next_back_index(&self) -> usize {
        let rem = self.iter.len() % self.original_step();
        if self.first_take { if rem == 0 { self.step_minus_one } else { rem - 1 } } else { rem }
    }
}

#[stable(feature = "double_ended_step_by_iterator", since = "1.38.0")]
impl<I> DoubleEndedIterator for StepBy<I>
where
    I: DoubleEndedIterator + ExactSizeIterator,
{
    #[inline]
    fn next_back(&mut self) -> Option<Self::Item> {
        self.spec_next_back()
    }

    #[inline]
    fn nth_back(&mut self, n: usize) -> Option<Self::Item> {
        self.spec_nth_back(n)
    }

    fn try_rfold<Acc, F, R>(&mut self, init: Acc, f: F) -> R
    where
        F: FnMut(Acc, Self::Item) -> R,
        R: Try<Output = Acc>,
    {
        self.spec_try_rfold(init, f)
    }

    #[inline]
    fn rfold<Acc, F>(self, init: Acc, f: F) -> Acc
    where
        Self: Sized,
        F: FnMut(Acc, Self::Item) -> Acc,
    {
        self.spec_rfold(init, f)
    }
}

// StepBy can only make the iterator shorter, so the len will still fit.
#[stable(feature = "iterator_step_by", since = "1.28.0")]
impl<I> ExactSizeIterator for StepBy<I> where I: ExactSizeIterator {}

// SAFETY: This adapter is shortening. TrustedLen requires the upper bound to be calculated correctly.
// These requirements can only be satisfied when the upper bound of the inner iterator's upper
// bound is never `None`. I: TrustedRandomAccess happens to provide this guarantee while
// I: TrustedLen would not.
// This also covers the Range specializations since the ranges also implement TRA
#[unstable(feature = "trusted_len", issue = "37572")]
unsafe impl<I> TrustedLen for StepBy<I> where I: Iterator + TrustedRandomAccess {}

trait SpecRangeSetup<T> {
    fn setup(inner: T, step: usize) -> T;
}

impl<T> SpecRangeSetup<T> for T {
    #[inline]
    default fn setup(inner: T, _step: usize) -> T {
        inner
    }
}

/// Specialization trait to optimize `StepBy<Range<{integer}>>` iteration.
///
/// # Safety
///
/// Technically this is safe to implement (look ma, no unsafe!), but in reality
/// a lot of unsafe code relies on ranges over integers being correct.
///
/// For correctness *all* public StepBy methods must be specialized
/// because `setup` drastically alters the meaning of the struct fields so that mixing
/// different implementations would lead to incorrect results.
unsafe trait StepByImpl<I> {
    type Item;

    fn spec_next(&mut self) -> Option<Self::Item>;

    fn spec_size_hint(&self) -> (usize, Option<usize>);

    fn spec_nth(&mut self, n: usize) -> Option<Self::Item>;

    fn spec_try_fold<Acc, F, R>(&mut self, acc: Acc, f: F) -> R
    where
        F: FnMut(Acc, Self::Item) -> R,
        R: Try<Output = Acc>;

    fn spec_fold<Acc, F>(self, acc: Acc, f: F) -> Acc
    where
        F: FnMut(Acc, Self::Item) -> Acc;
}

/// Specialization trait for double-ended iteration.
///
/// See also: `StepByImpl`
///
/// # Safety
///
/// The specializations must be implemented together with `StepByImpl`
/// where applicable. I.e. if `StepBy` does support backwards iteration
/// for a given iterator and that is specialized for forward iteration then
/// it must also be specialized for backwards iteration.
unsafe trait StepByBackImpl<I> {
    type Item;

    fn spec_next_back(&mut self) -> Option<Self::Item>
    where
        I: DoubleEndedIterator + ExactSizeIterator;

    fn spec_nth_back(&mut self, n: usize) -> Option<Self::Item>
    where
        I: DoubleEndedIterator + ExactSizeIterator;

    fn spec_try_rfold<Acc, F, R>(&mut self, init: Acc, f: F) -> R
    where
        I: DoubleEndedIterator + ExactSizeIterator,
        F: FnMut(Acc, Self::Item) -> R,
        R: Try<Output = Acc>;

    fn spec_rfold<Acc, F>(self, init: Acc, f: F) -> Acc
    where
        I: DoubleEndedIterator + ExactSizeIterator,
        F: FnMut(Acc, Self::Item) -> Acc;
}

unsafe impl<I: Iterator> StepByImpl<I> for StepBy<I> {
    type Item = I::Item;

    #[inline]
    default fn spec_next(&mut self) -> Option<I::Item> {
        let step_size = if self.first_take { 0 } else { self.step_minus_one };
        self.first_take = false;
        self.iter.nth(step_size)
    }

    #[inline]
    default fn spec_size_hint(&self) -> (usize, Option<usize>) {
        #[inline]
        fn first_size(step: NonZero<usize>) -> impl Fn(usize) -> usize {
            move |n| if n == 0 { 0 } else { 1 + (n - 1) / step }
        }

        #[inline]
        fn other_size(step: NonZero<usize>) -> impl Fn(usize) -> usize {
            move |n| n / step
        }

        let (low, high) = self.iter.size_hint();

        if self.first_take {
            let f = first_size(self.original_step());
            (f(low), high.map(f))
        } else {
            let f = other_size(self.original_step());
            (f(low), high.map(f))
        }
    }

    #[inline]
    default fn spec_nth(&mut self, mut n: usize) -> Option<I::Item> {
        if self.first_take {
            self.first_take = false;
            let first = self.iter.next();
            if n == 0 {
                return first;
            }
            n -= 1;
        }
        // n and self.step_minus_one are indices, we need to add 1 to get the amount of elements
        // When calling `.nth`, we need to subtract 1 again to convert back to an index
        let mut step = self.original_step().get();
        // n + 1 could overflow
        // thus, if n is usize::MAX, instead of adding one, we call .nth(step)
        if n == usize::MAX {
            self.iter.nth(step - 1);
        } else {
            n += 1;
        }

        // overflow handling
        loop {
            let mul = n.checked_mul(step);
            {
                if intrinsics::likely(mul.is_some()) {
                    return self.iter.nth(mul.unwrap() - 1);
                }
            }
            let div_n = usize::MAX / n;
            let div_step = usize::MAX / step;
            let nth_n = div_n * n;
            let nth_step = div_step * step;
            let nth = if nth_n > nth_step {
                step -= div_n;
                nth_n
            } else {
                n -= div_step;
                nth_step
            };
            self.iter.nth(nth - 1);
        }
    }

    default fn spec_try_fold<Acc, F, R>(&mut self, mut acc: Acc, mut f: F) -> R
    where
        F: FnMut(Acc, Self::Item) -> R,
        R: Try<Output = Acc>,
    {
        #[inline]
        fn nth<I: Iterator>(
            iter: &mut I,
            step_minus_one: usize,
        ) -> impl FnMut() -> Option<I::Item> + '_ {
            move || iter.nth(step_minus_one)
        }

        if self.first_take {
            self.first_take = false;
            match self.iter.next() {
                None => return try { acc },
                Some(x) => acc = f(acc, x)?,
            }
        }
        from_fn(nth(&mut self.iter, self.step_minus_one)).try_fold(acc, f)
    }

    default fn spec_fold<Acc, F>(mut self, mut acc: Acc, mut f: F) -> Acc
    where
        F: FnMut(Acc, Self::Item) -> Acc,
    {
        #[inline]
        fn nth<I: Iterator>(
            iter: &mut I,
            step_minus_one: usize,
        ) -> impl FnMut() -> Option<I::Item> + '_ {
            move || iter.nth(step_minus_one)
        }

        if self.first_take {
            self.first_take = false;
            match self.iter.next() {
                None => return acc,
                Some(x) => acc = f(acc, x),
            }
        }
        from_fn(nth(&mut self.iter, self.step_minus_one)).fold(acc, f)
    }
}

unsafe impl<I: DoubleEndedIterator + ExactSizeIterator> StepByBackImpl<I> for StepBy<I> {
    type Item = I::Item;

    #[inline]
    default fn spec_next_back(&mut self) -> Option<Self::Item> {
        self.iter.nth_back(self.next_back_index())
    }

    #[inline]
    default fn spec_nth_back(&mut self, n: usize) -> Option<I::Item> {
        // `self.iter.nth_back(usize::MAX)` does the right thing here when `n`
        // is out of bounds because the length of `self.iter` does not exceed
        // `usize::MAX` (because `I: ExactSizeIterator`) and `nth_back` is
        // zero-indexed
        let n = n.saturating_mul(self.original_step().get()).saturating_add(self.next_back_index());
        self.iter.nth_back(n)
    }

    default fn spec_try_rfold<Acc, F, R>(&mut self, init: Acc, mut f: F) -> R
    where
        F: FnMut(Acc, Self::Item) -> R,
        R: Try<Output = Acc>,
    {
        #[inline]
        fn nth_back<I: DoubleEndedIterator>(
            iter: &mut I,
            step_minus_one: usize,
        ) -> impl FnMut() -> Option<I::Item> + '_ {
            move || iter.nth_back(step_minus_one)
        }

        match self.next_back() {
            None => try { init },
            Some(x) => {
                let acc = f(init, x)?;
                from_fn(nth_back(&mut self.iter, self.step_minus_one)).try_fold(acc, f)
            }
        }
    }

    #[inline]
    default fn spec_rfold<Acc, F>(mut self, init: Acc, mut f: F) -> Acc
    where
        Self: Sized,
        F: FnMut(Acc, I::Item) -> Acc,
    {
        #[inline]
        fn nth_back<I: DoubleEndedIterator>(
            iter: &mut I,
            step_minus_one: usize,
        ) -> impl FnMut() -> Option<I::Item> + '_ {
            move || iter.nth_back(step_minus_one)
        }

        match self.next_back() {
            None => init,
            Some(x) => {
                let acc = f(init, x);
                from_fn(nth_back(&mut self.iter, self.step_minus_one)).fold(acc, f)
            }
        }
    }
}

/// For these implementations, `SpecRangeSetup` calculates the number
/// of iterations that will be needed and stores that in `iter.end`.
///
/// The various iterator implementations then rely on that to not need
/// overflow checking, letting loops just be counted instead.
///
/// These only work for unsigned types, and will need to be reworked
/// if you want to use it to specialize on signed types.
///
/// Currently these are only implemented for integers up to `usize` due to
/// correctness issues around `ExactSizeIterator` impls on 16bit platforms.
/// And since `ExactSizeIterator` is a prerequisite for backwards iteration
/// and we must consistently specialize backwards and forwards iteration
/// that makes the situation complicated enough that it's not covered
/// for now.
macro_rules! spec_int_ranges {
    ($($t:ty)*) => ($(

        const _: () = assert!(usize::BITS >= <$t>::BITS);

        impl SpecRangeSetup<Range<$t>> for Range<$t> {
            #[inline]
            fn setup(mut r: Range<$t>, step: usize) -> Range<$t> {
                let inner_len = r.size_hint().0;
                // If step exceeds $t::MAX, then the count will be at most 1 and
                // thus always fit into $t.
                let yield_count = inner_len.div_ceil(step);
                // Turn the range end into an iteration counter
                r.end = yield_count as $t;
                r
            }
        }

        unsafe impl StepByImpl<Range<$t>> for StepBy<Range<$t>> {
            #[inline]
            fn spec_next(&mut self) -> Option<$t> {
                // if a step size larger than the type has been specified fall back to
                // t::MAX, in which case remaining will be at most 1.
                let step = <$t>::try_from(self.original_step().get()).unwrap_or(<$t>::MAX);
                let remaining = self.iter.end;
                if remaining > 0 {
                    let val = self.iter.start;
                    // this can only overflow during the last step, after which the value
                    // will not be used
                    self.iter.start = val.wrapping_add(step);
                    self.iter.end = remaining - 1;
                    Some(val)
                } else {
                    None
                }
            }

            #[inline]
            fn spec_size_hint(&self) -> (usize, Option<usize>) {
                let remaining = self.iter.end as usize;
                (remaining, Some(remaining))
            }

            // The methods below are all copied from the Iterator trait default impls.
            // We have to repeat them here so that the specialization overrides the StepByImpl defaults

            #[inline]
            fn spec_nth(&mut self, n: usize) -> Option<Self::Item> {
                self.advance_by(n).ok()?;
                self.next()
            }

            #[inline]
            fn spec_try_fold<Acc, F, R>(&mut self, init: Acc, mut f: F) -> R
                where
                    F: FnMut(Acc, Self::Item) -> R,
                    R: Try<Output = Acc>
            {
                let mut accum = init;
                while let Some(x) = self.next() {
                    accum = f(accum, x)?;
                }
                try { accum }
            }

            #[inline]
            fn spec_fold<Acc, F>(self, init: Acc, mut f: F) -> Acc
                where
                    F: FnMut(Acc, Self::Item) -> Acc
            {
                // if a step size larger than the type has been specified fall back to
                // t::MAX, in which case remaining will be at most 1.
                let step = <$t>::try_from(self.original_step().get()).unwrap_or(<$t>::MAX);
                let remaining = self.iter.end;
                let mut acc = init;
                let mut val = self.iter.start;
                for _ in 0..remaining {
                    acc = f(acc, val);
                    // this can only overflow during the last step, after which the value
                    // will no longer be used
                    val = val.wrapping_add(step);
                }
                acc
            }
        }
    )*)
}

macro_rules! spec_int_ranges_r {
    ($($t:ty)*) => ($(
        const _: () = assert!(usize::BITS >= <$t>::BITS);

        unsafe impl StepByBackImpl<Range<$t>> for StepBy<Range<$t>> {

            #[inline]
            fn spec_next_back(&mut self) -> Option<Self::Item> {
                let step = self.original_step().get() as $t;
                let remaining = self.iter.end;
                if remaining > 0 {
                    let start = self.iter.start;
                    self.iter.end = remaining - 1;
                    Some(start + step * (remaining - 1))
                } else {
                    None
                }
            }

            // The methods below are all copied from the Iterator trait default impls.
            // We have to repeat them here so that the specialization overrides the StepByImplBack defaults

            #[inline]
            fn spec_nth_back(&mut self, n: usize) -> Option<Self::Item> {
                if self.advance_back_by(n).is_err() {
                    return None;
                }
                self.next_back()
            }

            #[inline]
            fn spec_try_rfold<Acc, F, R>(&mut self, init: Acc, mut f: F) -> R
            where
                F: FnMut(Acc, Self::Item) -> R,
                R: Try<Output = Acc>
            {
                let mut accum = init;
                while let Some(x) = self.next_back() {
                    accum = f(accum, x)?;
                }
                try { accum }
            }

            #[inline]
            fn spec_rfold<Acc, F>(mut self, init: Acc, mut f: F) -> Acc
            where
                F: FnMut(Acc, Self::Item) -> Acc
            {
                let mut accum = init;
                while let Some(x) = self.next_back() {
                    accum = f(accum, x);
                }
                accum
            }
        }
    )*)
}

#[cfg(target_pointer_width = "64")]
spec_int_ranges!(u8 u16 u32 u64 usize);
// DoubleEndedIterator requires ExactSizeIterator, which isn't implemented for Range<u64>
#[cfg(target_pointer_width = "64")]
spec_int_ranges_r!(u8 u16 u32 usize);

#[cfg(target_pointer_width = "32")]
spec_int_ranges!(u8 u16 u32 usize);
#[cfg(target_pointer_width = "32")]
spec_int_ranges_r!(u8 u16 u32 usize);

#[cfg(target_pointer_width = "16")]
spec_int_ranges!(u8 u16 usize);
#[cfg(target_pointer_width = "16")]
spec_int_ranges_r!(u8 u16 usize);