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
use core::{mem::MaybeUninit, num::NonZeroUsize, ptr};

use awint_internals::*;
use const_fn::const_fn;

use crate::Bits;

/// Rotates a slice range so that `mid` is at element 0.
///
/// Rust's slice rotation function was highly optimized by me, but I had to copy
/// it from https://github.com/rust-lang/rust/blob/master/library/core/src/slice/mod.rs
/// and specialize it to work as `const`.
///
/// # Safety
///
/// The range `[mid-left, mid+right)` must be valid for reading and writing
#[const_fn(cfg(feature = "const_support"))]
const unsafe fn usize_rotate(mut left: usize, mut mid: *mut usize, mut right: usize) {
    unsafe {
        type BufType = [usize; 32];
        loop {
            if (right == 0) || (left == 0) {
                return
            }
            if left + right < 24 {
                // Algorithm 1
                let x = mid.sub(left);
                let mut tmp: usize = x.read();
                let mut i = right;
                let mut gcd = right;
                loop {
                    let tmp_tmp = x.add(i).read();
                    x.add(i).write(tmp);
                    tmp = tmp_tmp;
                    if i >= left {
                        i -= left;
                        if i == 0 {
                            x.write(tmp);
                            break
                        }
                        if i < gcd {
                            gcd = i;
                        }
                    } else {
                        i += right;
                    }
                }
                const_for!(start in {1..gcd} {
                    tmp = x.add(start).read();
                    i = start + right;
                    loop {
                        let tmp_tmp = x.add(i).read();
                        x.add(i).write(tmp);
                        tmp = tmp_tmp;
                        if i >= left {
                            i -= left;
                            if i == start {
                                x.add(start).write(tmp);
                                break;
                            }
                        } else {
                            i += right;
                        }
                    }
                });
                return
            // I have tested this with Miri to make sure it doesn't complain
            } else if left <= 32 || right <= 32 {
                // Algorithm 2
                let mut rawarray = MaybeUninit::<(BufType, [usize; 0])>::uninit();
                let buf = rawarray.as_mut_ptr() as *mut usize;
                let dim = mid.sub(left).add(right);
                if left <= right {
                    ptr::copy_nonoverlapping(mid.sub(left), buf, left);
                    ptr::copy(mid, mid.sub(left), right);
                    ptr::copy_nonoverlapping(buf, dim, left);
                } else {
                    ptr::copy_nonoverlapping(mid, buf, right);
                    ptr::copy(mid.sub(left), dim, left);
                    ptr::copy_nonoverlapping(buf, mid.sub(left), right);
                }
                return
            } else if left >= right {
                // Algorithm 3
                loop {
                    ptr::swap_nonoverlapping(mid.sub(right), mid, right);
                    mid = mid.sub(right);
                    left -= right;
                    if left < right {
                        break
                    }
                }
            } else {
                // Algorithm 3, `left < right`
                loop {
                    ptr::swap_nonoverlapping(mid.sub(left), mid, left);
                    mid = mid.add(left);
                    right -= left;
                    if right < left {
                        break
                    }
                }
            }
        }
    }
}

// `usize_rotate` has some unusually large thresholds for some branches that
// don't get tested well by Miri in fuzz.rs, so test them here
#[test]
fn usize_rotate_test() {
    let mut buf = [123usize; 123];
    for k in 0..123 {
        unsafe { usize_rotate(k, buf.as_mut_ptr().add(k), 123 - k) }
    }
}

/// # Bit permutation
impl Bits {
    /// Shift-left-assigns at the digit level
    #[inline]
    #[const_fn(cfg(feature = "const_support"))]
    pub(crate) const fn digit_shl_assign(&mut self, s: NonZeroUsize) {
        // Should get optimized away when this function is inlined
        assert!(s.get() < self.bw());
        let s = digits(s);
        if s == 0 {
            return
        }
        unsafe {
            // below performs this:
            //const_for!(i in {s..self.len()}.rev() {
            //    *self.get_unchecked_mut(i) = self.get_unchecked(i - s);
            //});
            // If this shift overflows, it does not result in UB because it falls back to
            // the more relaxed `ptr:copy`
            if s.wrapping_shl(1) >= self.len() {
                // We cannot call multiple `as_ptr` or `as_mut_ptr` at the same time, because
                // they come from the same allocation. One would invalidate the other, and we
                // would run into stacked borrow issues.
                let ptr = self.as_mut_ptr();
                ptr::copy_nonoverlapping(ptr, ptr.add(s), self.len() - s);
            } else {
                let ptr = self.as_mut_ptr();
                ptr::copy(ptr, ptr.add(s), self.len() - s);
            }
            self.digit_set(false, 0..s, false);
        }
    }

    /// Shift-left-assigns according to extra bits
    #[inline]
    #[const_fn(cfg(feature = "const_support"))]
    pub(crate) const fn subdigit_shl_assign(&mut self, s: NonZeroUsize, clear_unused_bits: bool) {
        let s = extra(s);
        if s != 0 {
            // TODO benchmark this strategy vs dual unroll
            const_for!(i in {1..self.len()}.rev() {
                unsafe {
                    *self.get_unchecked_mut(i) =
                        (self.get_unchecked(i - 1) >> (BITS - s)) | (self.get_unchecked(i) << s);
                }
            });
            *self.first_mut() <<= s;
        }
        if clear_unused_bits {
            self.clear_unused_bits();
        }
    }

    /// Shift-right-assigns at the digit level
    #[inline]
    #[const_fn(cfg(feature = "const_support"))]
    pub(crate) const fn digit_shr_assign(
        &mut self,
        s: NonZeroUsize,
        extension: bool,
        clear_unused_bits: bool,
    ) {
        assert!(s.get() < self.bw());
        let s = digits(s);
        if s == 0 {
            if clear_unused_bits {
                self.clear_unused_bits();
            }
            return
        }
        unsafe {
            // below performs this:
            //const_for!(i in {s..self.len()} {
            //    *self.get_unchecked_mut(i - s) = self.get_unchecked(i);
            //});
            // If this shift overflows, it does not result in UB because it falls back to
            // the more relaxed `ptr:copy`
            if s.wrapping_shl(1) >= self.len() {
                // We cannot call multiple `as_ptr` or `as_mut_ptr` at the same time, because
                // they come from the same allocation. One would invalidate the other, and we
                // would run into stacked borrow issues.
                let ptr = self.as_mut_ptr();
                ptr::copy_nonoverlapping(ptr.add(s), ptr, self.len() - s);
            } else {
                let ptr = self.as_mut_ptr();
                ptr::copy(ptr.add(s), ptr, self.len() - s);
            }
            if extension && (self.unused() != 0) {
                // Safety: There are fewer digit shifts than digits
                *self.get_unchecked_mut(self.len() - 1 - s) |= MAX << (BITS - self.unused());
            }
            self.digit_set(extension, (self.len() - s)..self.len(), clear_unused_bits);
        }
    }

    /// Shift-right-assigns according to extra bits
    #[inline]
    #[const_fn(cfg(feature = "const_support"))]
    pub(crate) const fn subdigit_shr_assign(
        &mut self,
        s: NonZeroUsize,
        extension: bool,
        clear_unused_bits: bool,
    ) {
        let s = extra(s);
        if s == 0 {
            if clear_unused_bits {
                self.clear_unused_bits();
            }
            return
        }
        unsafe {
            // TODO benchmark this strategy vs dual unroll
            const_for!(i in {0..(self.len() - 1)} {
                *self.get_unchecked_mut(i) =
                    (self.get_unchecked(i) >> s) | (self.get_unchecked(i + 1) << (BITS - s));
            });
            *self.last_mut() >>= s;
            if extension {
                if (s + self.unused()) > BITS {
                    *self.last_mut() = MAX;
                    // handle bits that get shifted into the next to last digit
                    // Safety: it is not possible to reach this unless there are enough bits for the
                    // shift which has to be less than the bitwidth
                    *self.get_unchecked_mut(self.len() - 2) |=
                        MAX << ((2 * BITS) - s - self.unused());
                } else {
                    *self.last_mut() |= MAX << (BITS - s - self.unused());
                }
            }
            if clear_unused_bits {
                self.clear_unused_bits();
            }
        }
    }

    /// Left-shifts-assigns by `s` bits. If `s >= self.bw()`, then
    /// `None` is returned and the `Bits` are left unchanged.
    ///
    /// Left shifts can act as a very fast multiplication by a power of two for
    /// both the signed and unsigned interpretation of `Bits`.
    #[const_fn(cfg(feature = "const_support"))]
    #[must_use]
    pub const fn shl_assign(&mut self, s: usize) -> Option<()> {
        match NonZeroUsize::new(s) {
            None => Some(()),
            Some(s) if s.get() < self.bw() => {
                self.digit_shl_assign(s);
                self.subdigit_shl_assign(s, true);
                Some(())
            }
            _ => None,
        }
    }

    /// Logically-right-shift-assigns by `s` bits. If `s >= self.bw()`, then
    /// `None` is returned and the `Bits` are left unchanged.
    ///
    /// Logical right shifts do not copy the sign bit, and thus can act as a
    /// very fast floored division by a power of two for the unsigned
    /// interpretation of `Bits`.
    #[const_fn(cfg(feature = "const_support"))]
    #[must_use]
    pub const fn lshr_assign(&mut self, s: usize) -> Option<()> {
        match NonZeroUsize::new(s) {
            None => Some(()),
            Some(s) if s.get() < self.bw() => {
                self.digit_shr_assign(s, false, false);
                self.subdigit_shr_assign(s, false, true);
                Some(())
            }
            _ => None,
        }
    }

    /// Arithmetically-right-shift-assigns by `s` bits. If `s >= self.bw()`,
    /// then `None` is returned and the `Bits` are left unchanged.
    ///
    /// Arithmetic right shifts copy the sign bit, and thus can act as a very
    /// fast _floored_ division by a power of two for the signed interpretation
    /// of `Bits`.
    #[const_fn(cfg(feature = "const_support"))]
    #[must_use]
    pub const fn ashr_assign(&mut self, s: usize) -> Option<()> {
        match NonZeroUsize::new(s) {
            None => Some(()),
            Some(s) if s.get() < self.bw() => {
                let extension = self.msb();
                self.digit_shr_assign(s, extension, false);
                self.subdigit_shr_assign(s, extension, true);
                Some(())
            }
            _ => None,
        }
    }

    /// Left-rotate-assigns by `s` bits. If `s >= self.bw()`, then
    /// `None` is returned and the `Bits` are left unchanged.
    ///
    /// This function is equivalent to the following:
    /// ```
    /// use awint::prelude::*;
    /// let mut input = inlawi!(0x4321u16);
    /// let mut output = inlawi!(0u16);
    /// // rotate left by 4 bits or one hexadecimal digit
    /// let shift = 4;
    ///
    /// // temporary clone of the input
    /// let mut tmp = ExtAwi::from(input);
    /// cc!(input; output).unwrap();
    /// if shift != 0 {
    ///     if shift >= input.bw() {
    ///         // the actual function would return `None`
    ///         panic!();
    ///     }
    ///     output.shl_assign(shift).unwrap();
    ///     tmp.lshr_assign(input.bw() - shift).unwrap();
    ///     output.or_assign(&tmp);
    /// };
    ///
    /// assert_eq!(output, inlawi!(0x3214u16));
    /// let mut using_rotate = ExtAwi::from(input);
    /// using_rotate.rotl_assign(shift).unwrap();
    /// assert_eq!(using_rotate, extawi!(0x3214u16));
    ///
    /// // Note that slices are typed in a little-endian order opposite of
    /// // how integers are typed, but they still visually rotate in the
    /// // same way. This means `Rust`s built in slice rotation is in the
    /// // opposite direction to integers and `Bits`
    /// let mut array = [4, 3, 2, 1];
    /// array.rotate_left(1);
    /// assert_eq!(array, [3, 2, 1, 4]);
    /// assert_eq!(0x4321u16.rotate_left(4), 0x3214);
    /// let mut x = inlawi!(0x4321u16);
    /// x.rotl_assign(4).unwrap();
    /// // `Bits` has the preferred endianness
    /// assert_eq!(x, inlawi!(0x3214u16));
    /// ```
    ///
    /// Unlike the example above which needs cloning, this function avoids any
    /// allocation and has many optimized branches for different input sizes and
    /// shifts.
    #[const_fn(cfg(feature = "const_support"))]
    #[must_use]
    pub const fn rotl_assign(&mut self, s: usize) -> Option<()> {
        match NonZeroUsize::new(s) {
            None => Some(()),
            Some(s) if s.get() < self.bw() => {
                let x = self;
                // fast path and simplifies other code paths
                if x.len() == 1 {
                    *x.last_mut() = ((x.last() >> (x.bw() - s.get())) | (x.last() << s.get()))
                        & (MAX >> (BITS - x.bw()));
                    return Some(())
                }
                // TODO implement faster `subdigit_rotate_right` branch for certain cases

                let digits = digits(s);
                // Note: this is not a bitwidth but a shift
                let s0 = extra(s);
                let extra = x.extra();

                let mid_digit = x.len() - digits;
                let p = x.as_mut_ptr();
                // Safety: this satisfies the requirements of `usize_rotate`
                unsafe {
                    usize_rotate(mid_digit, p.add(mid_digit), digits);
                }

                if extra != 0 && digits != 0 {
                    // fix unused bits left in the middle from the rotation
                    let wrap = x.last() >> extra;
                    unsafe {
                        subdigits_mut!(x, 0..digits, y, {
                            y.subdigit_shl_assign(NonZeroUsize::new_unchecked(BITS - extra), false)
                        });
                    }
                    *x.first_mut() |= wrap;
                    x.clear_unused_bits();
                }
                if s0 != 0 {
                    // apply subdigit rotation
                    let wrap = if extra == 0 {
                        x.last() >> (BITS - s0)
                    } else if s0 <= extra {
                        x.last() >> (extra - s0)
                    } else {
                        // bits from the second to last digit get rotated all the way through the
                        // extra bits. We have already handled `x.len() == 1`.
                        unsafe {
                            (x.last() << (s0 - extra))
                                | (x.get_unchecked(x.len() - 2) >> (BITS - s0 + extra))
                        }
                    };
                    x.subdigit_shl_assign(s, true);
                    *x.first_mut() |= wrap;
                }

                Some(())
            }
            _ => None,
        }
    }

    /// Right-rotate-assigns by `s` bits. If `s >= self.bw()`, then
    /// `None` is returned and the `Bits` are left unchanged.
    ///
    /// See `Bits::rotl_assign` for more details.
    #[const_fn(cfg(feature = "const_support"))]
    #[must_use]
    pub const fn rotr_assign(&mut self, s: usize) -> Option<()> {
        let bw = self.bw();
        if s == 0 {
            return Some(())
        } else if s >= bw {
            return None
        }
        self.rotl_assign(bw - s)
    }

    /// Reverse-bit-order-assigns `self`. The least significant bit becomes the
    /// most significant bit, the second least significant bit becomes the
    /// second most significant bit, etc.
    #[const_fn(cfg(feature = "const_support"))]
    pub const fn rev_assign(&mut self) {
        let len = self.len();
        if len == 1 {
            *self.last_mut() = self.last().reverse_bits() >> self.unused();
            return
        }
        let halfway = len >> 1;
        let odd = (len & 1) != 0;
        if self.extra() == 0 {
            unsafe {
                const_for!(i in {0..halfway} {
                    // swap opposite reversed digits until reaching the halfway point
                    let tmp = self.get_unchecked(i).reverse_bits();
                    *self.get_unchecked_mut(i) = self.get_unchecked_mut(len - 1 - i).reverse_bits();
                    *self.get_unchecked_mut(len - 1 - i) = tmp;
                });
                if odd {
                    // reverse the digit in the middle inplace
                    let tmp = self.get_unchecked_mut(halfway);
                    *tmp = tmp.reverse_bits();
                }
            }
        } else {
            if len == 2 {
                let tmp0 = self.first().reverse_bits();
                let tmp1 = self.last().reverse_bits();
                *self.first_mut() = tmp1 >> self.unused() | tmp0 << self.extra();
                *self.last_mut() = tmp0 >> self.unused();
                return
            }
            unsafe {
                let unused = self.unused();
                let extra = self.extra();
                // There are four temporaries, two starting in the least significant digits and
                // two starting in the most significant digits. `tmp0` starts initialized with
                // zero, so that the new unused bits are set to zero. If there are 7 digits,
                // then the temporary assignments look like:
                //
                // tmp0=0 | .... | .... | .... | .... | .... | .... | tmp3 |
                // tmp0=0 | tmp1 | .... | .... | .... | .... | tmp2 | tmp3 |
                //        | done | tmp0 | .... | .... | .... | tmp2 | done |
                //        | done | tmp0 | tmp1 | .... | tmp3 | tmp2 | done |
                //        | done | done | tmp1 | .... | tmp3 | done | done |
                //        | done | done | tmp1 |tmp0&2| tmp3 | done | done |
                //        | done | done | done |tmp0&2| done | done | done |
                //        | done | done | done |bridge| done | done | done |
                let mut i0 = 0;
                let mut tmp0 = 0;
                let mut tmp1;
                let mut i2 = len - 1;
                let mut tmp2;
                let mut tmp3 = self.get_unchecked(i2).reverse_bits();
                loop {
                    if i0 == halfway {
                        // bridge between the converging indexes
                        if odd {
                            *self.get_unchecked_mut(i2) = (tmp3 >> unused) | (tmp0 << extra);
                        }
                        break
                    }
                    tmp1 = self.get_unchecked(i0).reverse_bits();
                    tmp2 = self.get_unchecked(i2 - 1).reverse_bits();
                    *self.get_unchecked_mut(i0) = (tmp3 >> unused) | (tmp2 << extra);
                    *self.get_unchecked_mut(i2) = (tmp1 >> unused) | (tmp0 << extra);
                    i0 += 1;
                    i2 -= 1;
                    if i0 == halfway {
                        if odd {
                            *self.get_unchecked_mut(i0) = (tmp2 >> unused) | (tmp1 << extra);
                        }
                        break
                    }
                    tmp0 = self.get_unchecked(i0).reverse_bits();
                    tmp3 = self.get_unchecked(i2 - 1).reverse_bits();
                    *self.get_unchecked_mut(i0) = (tmp2 >> unused) | (tmp3 << extra);
                    *self.get_unchecked_mut(i2) = (tmp0 >> unused) | (tmp1 << extra);
                    i0 += 1;
                    i2 -= 1;
                }
            }
        }
    }

    /// Funnel shift with power-of-two bitwidths. Returns `None` if
    /// `2*self.bw() != rhs.bw() || 2^s.bw() != self.bw()`. A `self.bw()` sized
    /// field is assigned to `self` from `rhs` starting from the bit position
    /// `s`. The shift cannot overflow because of the restriction on the
    /// bitwidth of `s`.
    ///
    /// ```
    /// use awint::prelude::*;
    /// let mut lhs = inlawi!(0xffff_ffffu32);
    /// let mut rhs = inlawi!(0xfedc_ba98_7654_3210u64);
    /// // `lhs.bw()` must be a power of two, `s.bw()` here is
    /// // `log_2(32) == 5`. The value of `s` is set to what bit
    /// // of `rhs` should be the starting bit for `lhs`.
    /// let mut s = inlawi!(12u5);
    /// lhs.funnel(&rhs, &s).unwrap();
    /// assert_eq!(lhs, inlawi!(0xa9876543_u32))
    /// ```
    #[const_fn(cfg(feature = "const_support"))]
    #[must_use]
    pub const fn funnel(&mut self, rhs: &Self, s: &Self) -> Option<()> {
        // because we later call `s.to_usize()` and assume it fits within `s.bw()`
        s.assert_cleared_unused_bits();
        // We avoid overflow by checking in this order and with `BITS - 1` instead of
        // `BITS`
        if (s.bw() >= (BITS - 1))
            || ((1usize << s.bw()) != self.bw())
            || ((self.bw() << 1) != rhs.bw())
        {
            return None
        }
        let s = s.to_usize();
        let digits = digits_u(s);
        let bits = extra_u(s);
        if bits == 0 {
            // Safety: there are two nonoverlapping `Bits`, and no out-of-bounds can occur
            // because of strict checks
            unsafe {
                ptr::copy_nonoverlapping(rhs.as_ptr().add(digits), self.as_mut_ptr(), self.len());
            }
        } else if self.bw() < BITS {
            *self.first_mut() = rhs.first() >> bits;
        } else {
            // Safety: When `self.bw() >= BITS`, `digits + i + 1` can be at most
            // `self.len() + digits` which cannot reach `rhs.len()`.
            unsafe {
                const_for!(i in {0..self.len()} {
                    *self.get_unchecked_mut(i) = (rhs.get_unchecked(digits + i) >> bits)
                        | (rhs.get_unchecked(digits + i + 1) << (BITS - bits));
                });
            }
        }
        self.clear_unused_bits();
        Some(())
    }
}