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
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
use std::sync::Arc;

use smallvec::SmallVec;

use crate::errors::Error;
use crate::errors::SBSError;

use crate::inversion_tree::InversionTree;
use crate::matrix::Matrix;

use super::Field;
use super::ReconstructShard;

// /// Parameters for parallelism.
// #[derive(PartialEq, Debug, Clone, Copy)]
// pub struct ParallelParam {
//     /// Number of bytes to split the slices into for computations
//     /// which can be done in parallel.
//     ///
//     /// Default is 32768.
//     pub bytes_per_encode: usize,
// }

// impl ParallelParam {
//     /// Create a new `ParallelParam` with the given split arity.
//     pub fn new(bytes_per_encode: usize) -> ParallelParam {
//         ParallelParam { bytes_per_encode }
//     }
// }

// impl Default for ParallelParam {
//     fn default() -> Self {
//         ParallelParam::new(32768)
//     }
// }

/// Bookkeeper for shard by shard encoding.
///
/// This is useful for avoiding incorrect use of
/// `encode_single` and `encode_single_sep`
///
/// # Use cases
///
/// Shard by shard encoding is useful for streamed data encoding
/// where you do not have all the needed data shards immediately,
/// but you want to spread out the encoding workload rather than
/// doing the encoding after everything is ready.
///
/// A concrete example would be network packets encoding,
/// where encoding packet by packet as you receive them may be more efficient
/// than waiting for N packets then encode them all at once.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate reed_solomon_erasure;
/// # use reed_solomon_erasure::*;
/// # fn main () {
/// use reed_solomon_erasure::galois_8::Field;
/// let r: ReedSolomon<Field> = ReedSolomon::new(3, 2).unwrap();
///
/// let mut sbs = ShardByShard::new(&r);
///
/// let mut shards = shards!([0u8,  1,  2,  3,  4],
///                          [5,  6,  7,  8,  9],
///                          // say we don't have the 3rd data shard yet
///                          // and we want to fill it in later
///                          [0,  0,  0,  0,  0],
///                          [0,  0,  0,  0,  0],
///                          [0,  0,  0,  0,  0]);
///
/// // encode 1st and 2nd data shard
/// sbs.encode(&mut shards).unwrap();
/// sbs.encode(&mut shards).unwrap();
///
/// // fill in 3rd data shard
/// shards[2][0] = 10.into();
/// shards[2][1] = 11.into();
/// shards[2][2] = 12.into();
/// shards[2][3] = 13.into();
/// shards[2][4] = 14.into();
///
/// // now do the encoding
/// sbs.encode(&mut shards).unwrap();
///
/// assert!(r.verify(&shards).unwrap());
/// # }
/// ```
#[derive(PartialEq, Debug)]
pub struct ShardByShard<'a, F: 'a + Field> {
    codec: &'a ReedSolomon<F>,
    cur_input: usize,
}

impl<'a, F: 'a + Field> ShardByShard<'a, F> {
    /// Creates a new instance of the bookkeeping struct.
    pub fn new(codec: &'a ReedSolomon<F>) -> ShardByShard<'a, F> {
        ShardByShard {
            codec,
            cur_input: 0,
        }
    }

    /// Checks if the parity shards are ready to use.
    pub fn parity_ready(&self) -> bool {
        self.cur_input == self.codec.data_shard_count
    }

    /// Resets the bookkeeping data.
    ///
    /// You should call this when you have added and encoded
    /// all data shards, and have finished using the parity shards.
    ///
    /// Returns `SBSError::LeftoverShards` when there are shards encoded
    /// but parity shards are not ready to use.
    pub fn reset(&mut self) -> Result<(), SBSError> {
        if self.cur_input > 0 && !self.parity_ready() {
            return Err(SBSError::LeftoverShards);
        }

        self.cur_input = 0;

        Ok(())
    }

    /// Resets the bookkeeping data without checking.
    pub fn reset_force(&mut self) {
        self.cur_input = 0;
    }

    /// Returns the current input shard index.
    pub fn cur_input_index(&self) -> usize {
        self.cur_input
    }

    fn return_ok_and_incre_cur_input(&mut self) -> Result<(), SBSError> {
        self.cur_input += 1;
        Ok(())
    }

    fn sbs_encode_checks<U: AsRef<[F::Elem]> + AsMut<[F::Elem]>>(
        &mut self,
        slices: &mut [U],
    ) -> Result<(), SBSError> {
        let internal_checks = |codec: &ReedSolomon<F>, data: &mut [U]| {
            check_piece_count!(all => codec, data);
            check_slices!(multi => data);

            Ok(())
        };

        if self.parity_ready() {
            return Err(SBSError::TooManyCalls);
        }

        match internal_checks(self.codec, slices) {
            Ok(()) => Ok(()),
            Err(e) => Err(SBSError::RSError(e)),
        }
    }

    fn sbs_encode_sep_checks<T: AsRef<[F::Elem]>, U: AsRef<[F::Elem]> + AsMut<[F::Elem]>>(
        &mut self,
        data: &[T],
        parity: &mut [U],
    ) -> Result<(), SBSError> {
        let internal_checks = |codec: &ReedSolomon<F>, data: &[T], parity: &mut [U]| {
            check_piece_count!(data => codec, data);
            check_piece_count!(parity => codec, parity);
            check_slices!(multi => data, multi => parity);

            Ok(())
        };

        if self.parity_ready() {
            return Err(SBSError::TooManyCalls);
        }

        match internal_checks(self.codec, data, parity) {
            Ok(()) => Ok(()),
            Err(e) => Err(SBSError::RSError(e)),
        }
    }

    /// Constructs the parity shards partially using the current input data shard.
    ///
    /// Returns `SBSError::TooManyCalls` when all input data shards
    /// have already been filled in via `encode`
    pub fn encode<T, U>(&mut self, mut shards: T) -> Result<(), SBSError>
    where
        T: AsRef<[U]> + AsMut<[U]>,
        U: AsRef<[F::Elem]> + AsMut<[F::Elem]>,
    {
        let shards = shards.as_mut();
        self.sbs_encode_checks(shards)?;

        self.codec.encode_single(self.cur_input, shards).unwrap();

        self.return_ok_and_incre_cur_input()
    }

    /// Constructs the parity shards partially using the current input data shard.
    ///
    /// Returns `SBSError::TooManyCalls` when all input data shards
    /// have already been filled in via `encode`
    pub fn encode_sep<T: AsRef<[F::Elem]>, U: AsRef<[F::Elem]> + AsMut<[F::Elem]>>(
        &mut self,
        data: &[T],
        parity: &mut [U],
    ) -> Result<(), SBSError> {
        self.sbs_encode_sep_checks(data, parity)?;

        self.codec
            .encode_single_sep(self.cur_input, data[self.cur_input].as_ref(), parity)
            .unwrap();

        self.return_ok_and_incre_cur_input()
    }
}

/// Reed-Solomon erasure code encoder/decoder.
///
/// # Common error handling
///
/// ## For `encode`, `encode_shards`, `verify`, `verify_shards`, `reconstruct`, `reconstruct_data`, `reconstruct_shards`, `reconstruct_data_shards`
///
/// Return `Error::TooFewShards` or `Error::TooManyShards`
/// when the number of provided shards
/// does not match the codec's one.
///
/// Return `Error::EmptyShard` when the first shard provided is
/// of zero length.
///
/// Return `Error::IncorrectShardSize` when the provided shards
/// are of different lengths.
///
/// ## For `reconstruct`, `reconstruct_data`, `reconstruct_shards`, `reconstruct_data_shards`
///
/// Return `Error::TooFewShardsPresent` when there are not
/// enough shards for reconstruction.
///
/// Return `Error::InvalidShardFlags` when the number of flags does not match
/// the total number of shards.
///
/// # Variants of encoding methods
///
/// ## `sep`
///
/// Methods ending in `_sep` takes an immutable reference to data shards,
/// and a mutable reference to parity shards.
///
/// They are useful as they do not need to borrow the data shards mutably,
/// and other work that only needs read-only access to data shards can be done
/// in parallel/concurrently during the encoding.
///
/// Following is a table of all the `sep` variants
///
/// | not `sep` | `sep` |
/// | --- | --- |
/// | `encode_single` | `encode_single_sep` |
/// | `encode`        | `encode_sep` |
///
/// The `sep` variants do similar checks on the provided data shards and
/// parity shards.
///
/// Return `Error::TooFewDataShards`, `Error::TooManyDataShards`,
/// `Error::TooFewParityShards`, or `Error::TooManyParityShards` when applicable.
///
/// ## `single`
///
/// Methods containing `single` facilitate shard by shard encoding, where
/// the parity shards are partially constructed using one data shard at a time.
/// See `ShardByShard` struct for more details on how shard by shard encoding
/// can be useful.
///
/// They are prone to **misuse**, and it is recommended to use the `ShardByShard`
/// bookkeeping struct instead for shard by shard encoding.
///
/// The ones that are also `sep` are **ESPECIALLY** prone to **misuse**.
/// Only use them when you actually need the flexibility.
///
/// Following is a table of all the shard by shard variants
///
/// | all shards at once | shard by shard |
/// | --- | --- |
/// | `encode` | `encode_single` |
/// | `encode_sep` | `encode_single_sep` |
///
/// The `single` variants do similar checks on the provided data shards and parity shards,
/// and also do index check on `i_data`.
///
/// Return `Error::InvalidIndex` if `i_data >= data_shard_count`.
///
/// # Encoding behaviour
/// ## For `encode`
///
/// You do not need to clear the parity shards beforehand, as the methods
/// will overwrite them completely.
///
/// ## For `encode_single`, `encode_single_sep`
///
/// Calling them with `i_data` being `0` will overwrite the parity shards
/// completely. If you are using the methods correctly, then you do not need
/// to clear the parity shards beforehand.
///
/// # Variants of verifying methods
///
/// `verify` allocate sa buffer on the heap of the same size
/// as the parity shards, and encode the input once using the buffer to store
/// the computed parity shards, then check if the provided parity shards
/// match the computed ones.
///
/// `verify_with_buffer`, allows you to provide
/// the buffer to avoid making heap allocation(s) for the buffer in every call.
///
/// The `with_buffer` variants also guarantee that the buffer contains the correct
/// parity shards if the result is `Ok(_)` (i.e. it does not matter whether the
/// verification passed or not, as long as the result is not an error, the buffer
/// will contain the correct parity shards after the call).
///
/// Following is a table of all the `with_buffer` variants
///
/// | not `with_buffer` | `with_buffer` |
/// | --- | --- |
/// | `verify` | `verify_with_buffer` |
///
/// The `with_buffer` variants also check the dimensions of the buffer and return
/// `Error::TooFewBufferShards`, `Error::TooManyBufferShards`, `Error::EmptyShard`,
/// or `Error::IncorrectShardSize` when applicable.
///
#[derive(Debug)]
pub struct ReedSolomon<F: Field> {
    data_shard_count: usize,
    parity_shard_count: usize,
    total_shard_count: usize,
    matrix: Matrix<F>,
    tree: InversionTree<F>,
}

impl<F: Field> Clone for ReedSolomon<F> {
    fn clone(&self) -> ReedSolomon<F> {
        ReedSolomon::new(self.data_shard_count, self.parity_shard_count)
            .expect("basic checks already passed as precondition of existence of self")
    }
}

impl<F: Field> PartialEq for ReedSolomon<F> {
    fn eq(&self, rhs: &ReedSolomon<F>) -> bool {
        self.data_shard_count == rhs.data_shard_count
            && self.parity_shard_count == rhs.parity_shard_count
    }
}

impl<F: Field> ReedSolomon<F> {
    // AUDIT
    //
    // Error detection responsibilities
    //
    // Terminologies and symbols:
    //   X =A, B, C=> Y: X delegates error checking responsibilities A, B, C to Y
    //   X:= A, B, C: X needs to handle responsibilities A, B, C
    //
    // Encode methods
    //
    // `encode_single`:=
    //   - check index `i_data` within range [0, data shard count)
    //   - check length of `slices` matches total shard count exactly
    //   - check consistency of length of individual slices
    // `encode_single_sep`:=
    //   - check index `i_data` within range [0, data shard count)
    //   - check length of `parity` matches parity shard count exactly
    //   - check consistency of length of individual parity slices
    //   - check length of `single_data` matches length of first parity slice
    // `encode`:=
    //   - check length of `slices` matches total shard count exactly
    //   - check consistency of length of individual slices
    // `encode_sep`:=
    //   - check length of `data` matches data shard count exactly
    //   - check length of `parity` matches parity shard count exactly
    //   - check consistency of length of individual data slices
    //   - check consistency of length of individual parity slices
    //   - check length of first parity slice matches length of first data slice
    //
    // Verify methods
    //
    // `verify`:=
    //   - check length of `slices` matches total shard count exactly
    //   - check consistency of length of individual slices
    //
    //   Generates buffer then passes control to verify_with_buffer
    //
    // `verify_with_buffer`:=
    //   - check length of `slices` matches total shard count exactly
    //   - check length of `buffer` matches parity shard count exactly
    //   - check consistency of length of individual slices
    //   - check consistency of length of individual slices in buffer
    //   - check length of first slice in buffer matches length of first slice
    //
    // Reconstruct methods
    //
    // `reconstruct` =ALL=> `reconstruct_internal`
    // `reconstruct_data`=ALL=> `reconstruct_internal`
    // `reconstruct_internal`:=
    //   - check length of `slices` matches total shard count exactly
    //   - check consistency of length of individual slices
    //   - check length of `slice_present` matches length of `slices`

    fn get_parity_rows(&self) -> SmallVec<[&[F::Elem]; 32]> {
        let mut parity_rows = SmallVec::with_capacity(self.parity_shard_count);
        let matrix = &self.matrix;
        for i in self.data_shard_count..self.total_shard_count {
            parity_rows.push(matrix.get_row(i));
        }

        parity_rows
    }

    fn build_matrix(data_shards: usize, total_shards: usize) -> Matrix<F> {
        let vandermonde = Matrix::vandermonde(total_shards, data_shards);

        let top = vandermonde.sub_matrix(0, 0, data_shards, data_shards);

        vandermonde.multiply(&top.invert().unwrap())
    }

    /// Creates a new instance of Reed-Solomon erasure code encoder/decoder.
    ///
    /// Returns `Error::TooFewDataShards` if `data_shards == 0`.
    ///
    /// Returns `Error::TooFewParityShards` if `parity_shards == 0`.
    ///
    /// Returns `Error::TooManyShards` if `data_shards + parity_shards > F::ORDER`.
    pub fn new(data_shards: usize, parity_shards: usize) -> Result<ReedSolomon<F>, Error> {
        if data_shards == 0 {
            return Err(Error::TooFewDataShards);
        }
        if parity_shards == 0 {
            return Err(Error::TooFewParityShards);
        }
        if data_shards + parity_shards > F::ORDER {
            return Err(Error::TooManyShards);
        }

        let total_shards = data_shards + parity_shards;

        let matrix = Self::build_matrix(data_shards, total_shards);

        Ok(ReedSolomon {
            data_shard_count: data_shards,
            parity_shard_count: parity_shards,
            total_shard_count: total_shards,
            matrix,
            tree: InversionTree::new(data_shards, parity_shards),
        })
    }

    pub fn data_shard_count(&self) -> usize {
        self.data_shard_count
    }

    pub fn parity_shard_count(&self) -> usize {
        self.parity_shard_count
    }

    pub fn total_shard_count(&self) -> usize {
        self.total_shard_count
    }

    fn code_some_slices<T: AsRef<[F::Elem]>, U: AsMut<[F::Elem]>>(
        &self,
        matrix_rows: &[&[F::Elem]],
        inputs: &[T],
        outputs: &mut [U],
    ) {
        for i_input in 0..self.data_shard_count {
            self.code_single_slice(matrix_rows, i_input, inputs[i_input].as_ref(), outputs);
        }
    }

    fn code_single_slice<U: AsMut<[F::Elem]>>(
        &self,
        matrix_rows: &[&[F::Elem]],
        i_input: usize,
        input: &[F::Elem],
        outputs: &mut [U],
    ) {
        outputs.iter_mut().enumerate().for_each(|(i_row, output)| {
            let matrix_row_to_use = matrix_rows[i_row][i_input];
            let output = output.as_mut();

            if i_input == 0 {
                F::mul_slice(matrix_row_to_use, input, output);
            } else {
                F::mul_slice_add(matrix_row_to_use, input, output);
            }
        })
    }

    fn check_some_slices_with_buffer<T, U>(
        &self,
        matrix_rows: &[&[F::Elem]],
        inputs: &[T],
        to_check: &[T],
        buffer: &mut [U],
    ) -> bool
    where
        T: AsRef<[F::Elem]>,
        U: AsRef<[F::Elem]> + AsMut<[F::Elem]>,
    {
        self.code_some_slices(matrix_rows, inputs, buffer);

        let at_least_one_mismatch_present = buffer
            .iter_mut()
            .enumerate()
            .map(|(i, expected_parity_shard)| {
                expected_parity_shard.as_ref() == to_check[i].as_ref()
            })
            .any(|x| !x); // find the first false (some slice is different from the expected one)
        !at_least_one_mismatch_present
    }

    /// Constructs the parity shards partially using only the data shard
    /// indexed by `i_data`.
    ///
    /// The slots where the parity shards sit at will be overwritten.
    ///
    /// # Warning
    ///
    /// You must apply this method on the data shards in strict sequential order (0..data shard count),
    /// otherwise the parity shards will be incorrect.
    ///
    /// It is recommended to use the `ShardByShard` bookkeeping struct instead of this method directly.
    pub fn encode_single<T, U>(&self, i_data: usize, mut shards: T) -> Result<(), Error>
    where
        T: AsRef<[U]> + AsMut<[U]>,
        U: AsRef<[F::Elem]> + AsMut<[F::Elem]>,
    {
        let slices = shards.as_mut();

        check_slice_index!(data => self, i_data);
        check_piece_count!(all=> self, slices);
        check_slices!(multi => slices);

        // Get the slice of output buffers.
        let (mut_input, output) = slices.split_at_mut(self.data_shard_count);

        let input = mut_input[i_data].as_ref();

        self.encode_single_sep(i_data, input, output)
    }

    /// Constructs the parity shards partially using only the data shard provided.
    ///
    /// The data shard must match the index `i_data`.
    ///
    /// The slots where the parity shards sit at will be overwritten.
    ///
    /// # Warning
    ///
    /// You must apply this method on the data shards in strict sequential order (0..data shard count),
    /// otherwise the parity shards will be incorrect.
    ///
    /// It is recommended to use the `ShardByShard` bookkeeping struct instead of this method directly.
    pub fn encode_single_sep<U: AsRef<[F::Elem]> + AsMut<[F::Elem]>>(
        &self,
        i_data: usize,
        single_data: &[F::Elem],
        parity: &mut [U],
    ) -> Result<(), Error> {
        check_slice_index!(data => self, i_data);
        check_piece_count!(parity => self, parity);
        check_slices!(multi => parity, single => single_data);

        let parity_rows = self.get_parity_rows();

        // Do the coding.
        self.code_single_slice(&parity_rows, i_data, single_data, parity);

        Ok(())
    }

    /// Constructs the parity shards.
    ///
    /// The slots where the parity shards sit at will be overwritten.
    pub fn encode<T, U>(&self, mut shards: T) -> Result<(), Error>
    where
        T: AsRef<[U]> + AsMut<[U]>,
        U: AsRef<[F::Elem]> + AsMut<[F::Elem]>,
    {
        let slices: &mut [U] = shards.as_mut();

        check_piece_count!(all => self, slices);
        check_slices!(multi => slices);

        // Get the slice of output buffers.
        let (input, output) = slices.split_at_mut(self.data_shard_count);

        self.encode_sep(&*input, output)
    }

    /// Constructs the parity shards using a read-only view into the
    /// data shards.
    ///
    /// The slots where the parity shards sit at will be overwritten.
    pub fn encode_sep<T: AsRef<[F::Elem]>, U: AsRef<[F::Elem]> + AsMut<[F::Elem]>>(
        &self,
        data: &[T],
        parity: &mut [U],
    ) -> Result<(), Error> {
        check_piece_count!(data => self, data);
        check_piece_count!(parity => self, parity);
        check_slices!(multi => data, multi => parity);

        let parity_rows = self.get_parity_rows();

        // Do the coding.
        self.code_some_slices(&parity_rows, data, parity);

        Ok(())
    }

    /// Checks if the parity shards are correct.
    ///
    /// This is a wrapper of `verify_with_buffer`.
    pub fn verify<T: AsRef<[F::Elem]>>(&self, slices: &[T]) -> Result<bool, Error> {
        check_piece_count!(all => self, slices);
        check_slices!(multi => slices);

        let slice_len = slices[0].as_ref().len();

        let mut buffer: SmallVec<[Vec<F::Elem>; 32]> =
            SmallVec::with_capacity(self.parity_shard_count);

        for _ in 0..self.parity_shard_count {
            buffer.push(vec![F::zero(); slice_len]);
        }

        self.verify_with_buffer(slices, &mut buffer)
    }

    /// Checks if the parity shards are correct.
    pub fn verify_with_buffer<T, U>(&self, slices: &[T], buffer: &mut [U]) -> Result<bool, Error>
    where
        T: AsRef<[F::Elem]>,
        U: AsRef<[F::Elem]> + AsMut<[F::Elem]>,
    {
        check_piece_count!(all => self, slices);
        check_piece_count!(parity_buf => self, buffer);
        check_slices!(multi => slices, multi => buffer);

        let data = &slices[0..self.data_shard_count];
        let to_check = &slices[self.data_shard_count..];

        let parity_rows = self.get_parity_rows();

        Ok(self.check_some_slices_with_buffer(&parity_rows, data, to_check, buffer))
    }

    /// Reconstructs all shards.
    ///
    /// The shards marked not present are only overwritten when no error
    /// is detected. All provided shards must have the same length.
    ///
    /// This means if the method returns an `Error`, then nothing is touched.
    ///
    /// `reconstruct`, `reconstruct_data`, `reconstruct_shards`,
    /// `reconstruct_data_shards` share the same core code base.
    pub fn reconstruct<T: ReconstructShard<F>>(&self, slices: &mut [T]) -> Result<(), Error> {
        self.reconstruct_internal(slices, false)
    }

    /// Reconstructs only the data shards.
    ///
    /// The shards marked not present are only overwritten when no error
    /// is detected. All provided shards must have the same length.
    ///
    /// This means if the method returns an `Error`, then nothing is touched.
    ///
    /// `reconstruct`, `reconstruct_data`, `reconstruct_shards`,
    /// `reconstruct_data_shards` share the same core code base.
    pub fn reconstruct_data<T: ReconstructShard<F>>(&self, slices: &mut [T]) -> Result<(), Error> {
        self.reconstruct_internal(slices, true)
    }

    fn get_data_decode_matrix(
        &self,
        valid_indices: &[usize],
        invalid_indices: &[usize],
    ) -> Arc<Matrix<F>> {
        // Attempt to get the cached inverted matrix out of the tree
        // based on the indices of the invalid rows.
        match self.tree.get_inverted_matrix(&invalid_indices) {
            // If the inverted matrix isn't cached in the tree yet we must
            // construct it ourselves and insert it into the tree for the
            // future.  In this way the inversion tree is lazily loaded.
            None => {
                // Pull out the rows of the matrix that correspond to the
                // shards that we have and build a square matrix.  This
                // matrix could be used to generate the shards that we have
                // from the original data.
                let mut sub_matrix = Matrix::new(self.data_shard_count, self.data_shard_count);
                for (sub_matrix_row, &valid_index) in valid_indices.into_iter().enumerate() {
                    for c in 0..self.data_shard_count {
                        sub_matrix.set(sub_matrix_row, c, self.matrix.get(valid_index, c));
                    }
                }
                // Invert the matrix, so we can go from the encoded shards
                // back to the original data.  Then pull out the row that
                // generates the shard that we want to decode.  Note that
                // since this matrix maps back to the original data, it can
                // be used to create a data shard, but not a parity shard.
                let data_decode_matrix = Arc::new(sub_matrix.invert().unwrap());

                // Cache the inverted matrix in the tree for future use keyed on the
                // indices of the invalid rows.
                self.tree
                    .insert_inverted_matrix(&invalid_indices, &data_decode_matrix)
                    .unwrap();

                data_decode_matrix
            }
            Some(m) => m,
        }
    }

    fn reconstruct_internal<T: ReconstructShard<F>>(
        &self,
        shards: &mut [T],
        data_only: bool,
    ) -> Result<(), Error> {
        check_piece_count!(all => self, shards);

        let data_shard_count = self.data_shard_count;

        // Quick check: are all of the shards present?  If so, there's
        // nothing to do.
        let mut number_present = 0;
        let mut shard_len = None;

        for shard in shards.iter_mut() {
            if let Some(len) = shard.len() {
                if len == 0 {
                    return Err(Error::EmptyShard);
                }
                number_present += 1;
                if let Some(old_len) = shard_len {
                    if len != old_len {
                        // mismatch between shards.
                        return Err(Error::IncorrectShardSize);
                    }
                }
                shard_len = Some(len);
            }
        }

        if number_present == self.total_shard_count {
            // Cool.  All of the shards are there.  We don't
            // need to do anything.
            return Ok(());
        }

        // More complete sanity check
        if number_present < data_shard_count {
            return Err(Error::TooFewShardsPresent);
        }

        let shard_len = shard_len.expect("at least one shard present; qed");

        // Pull out an array holding just the shards that
        // correspond to the rows of the submatrix.  These shards
        // will be the input to the decoding process that re-creates
        // the missing data shards.
        //
        // Also, create an array of indices of the valid rows we do have
        // and the invalid rows we don't have.
        //
        // The valid indices are used to construct the data decode matrix,
        // the invalid indices are used to key the data decode matrix
        // in the inversion tree.
        //
        // We only need exactly N valid indices, where N = `data_shard_count`,
        // as the data decode matrix is a N x N matrix, thus only needs
        // N valid indices for determining the N rows to pick from
        // `self.matrix`.
        let mut sub_shards: SmallVec<[&[F::Elem]; 32]> = SmallVec::with_capacity(data_shard_count);
        let mut missing_data_slices: SmallVec<[&mut [F::Elem]; 32]> =
            SmallVec::with_capacity(self.parity_shard_count);
        let mut missing_parity_slices: SmallVec<[&mut [F::Elem]; 32]> =
            SmallVec::with_capacity(self.parity_shard_count);
        let mut valid_indices: SmallVec<[usize; 32]> = SmallVec::with_capacity(data_shard_count);
        let mut invalid_indices: SmallVec<[usize; 32]> = SmallVec::with_capacity(data_shard_count);

        // Separate the shards into groups
        for (matrix_row, shard) in shards.into_iter().enumerate() {
            // get or initialize the shard so we can reconstruct in-place,
            // but if we are only reconstructing data shard,
            // do not initialize if the shard is not a data shard
            let shard_data = if matrix_row >= data_shard_count && data_only {
                shard.get().ok_or(None)
            } else {
                shard.get_or_initialize(shard_len).map_err(Some)
            };

            match shard_data {
                Ok(shard) => {
                    if sub_shards.len() < data_shard_count {
                        sub_shards.push(shard);
                        valid_indices.push(matrix_row);
                    } else {
                        // Already have enough shards in `sub_shards`
                        // as we only need N shards, where N = `data_shard_count`,
                        // for the data decode matrix
                        //
                        // So nothing to do here
                    }
                }
                Err(None) => {
                    // the shard data is not meant to be initialized here,
                    // but we should still note it missing.
                    invalid_indices.push(matrix_row);
                }
                Err(Some(x)) => {
                    // initialized missing shard data.
                    let shard = x?;
                    if matrix_row < data_shard_count {
                        missing_data_slices.push(shard);
                    } else {
                        missing_parity_slices.push(shard);
                    }

                    invalid_indices.push(matrix_row);
                }
            }
        }

        let data_decode_matrix = self.get_data_decode_matrix(&valid_indices, &invalid_indices);

        // Re-create any data shards that were missing.
        //
        // The input to the coding is all of the shards we actually
        // have, and the output is the missing data shards. The computation
        // is done using the special decode matrix we just built.
        let mut matrix_rows: SmallVec<[&[F::Elem]; 32]> =
            SmallVec::with_capacity(self.parity_shard_count);

        for i_slice in invalid_indices
            .iter()
            .cloned()
            .take_while(|i| i < &data_shard_count)
        {
            matrix_rows.push(data_decode_matrix.get_row(i_slice));
        }

        self.code_some_slices(&matrix_rows, &sub_shards, &mut missing_data_slices);

        if data_only {
            Ok(())
        } else {
            // Now that we have all of the data shards intact, we can
            // compute any of the parity that is missing.
            //
            // The input to the coding is ALL of the data shards, including
            // any that we just calculated.  The output is whichever of the
            // parity shards were missing.
            let mut matrix_rows: SmallVec<[&[F::Elem]; 32]> =
                SmallVec::with_capacity(self.parity_shard_count);
            let parity_rows = self.get_parity_rows();

            for i_slice in invalid_indices
                .iter()
                .cloned()
                .skip_while(|i| i < &data_shard_count)
            {
                matrix_rows.push(parity_rows[i_slice - data_shard_count]);
            }
            {
                // Gather up all the data shards.
                // old data shards are in `sub_shards`,
                // new ones are in `missing_data_slices`.
                let mut i_old_data_slice = 0;
                let mut i_new_data_slice = 0;

                let mut all_data_slices: SmallVec<[&[F::Elem]; 32]> =
                    SmallVec::with_capacity(data_shard_count);

                let mut next_maybe_good = 0;
                let mut push_good_up_to = move |data_slices: &mut SmallVec<_>, up_to| {
                    // if next_maybe_good == up_to, this loop is a no-op.
                    for _ in next_maybe_good..up_to {
                        // push all good indices we just skipped.
                        data_slices.push(sub_shards[i_old_data_slice]);
                        i_old_data_slice += 1;
                    }

                    next_maybe_good = up_to + 1;
                };

                for i_slice in invalid_indices
                    .iter()
                    .cloned()
                    .take_while(|i| i < &data_shard_count)
                {
                    push_good_up_to(&mut all_data_slices, i_slice);
                    all_data_slices.push(missing_data_slices[i_new_data_slice]);
                    i_new_data_slice += 1;
                }
                push_good_up_to(&mut all_data_slices, data_shard_count);

                // Now do the actual computation for the missing
                // parity shards
                self.code_some_slices(&matrix_rows, &all_data_slices, &mut missing_parity_slices);
            }

            Ok(())
        }
    }
}