forsyth 1.0.1

A pure Rust implementation of Tom Forsyth's 'Linear-Speed Vertex Cache Optimisation'.
Documentation
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
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
#![deny(clippy::all)]
#![forbid(unsafe_code)]

//! This is a clean-room implementation of Tom Forsyth's
//! [`Linear-speed Vertex Cache Optimisation`] in Rust.
//!
//! Two algorithms are provided in this crate.
//! - [`order_triangles_inplace`] and [`order_triangles`] to order triangle indices to maximize data locality.
//! - [`order_vertices`] to order vertex data in such an way, that vertex data locality is maximized when iterating sequentially through index data.
//!
//! Both algorithms can be run independently, but ordering indices first and then ordering vertices provides most benefits.
//!
//! Note that [`Kerbel et al. 2018`] argued that [`GPU caching may not benefit from such ordering`].
//! However, there may be use cases that benefit from improved data locality when sequentially processing index and vertex data,
//! such as when streaming data from persistent storage or when processing geometry with CPUs.
//!
//! Despite the original paper's title, the algorithm is [`not guaranteed to be exactly linear`].
//! There are pathological cases where runtime can be worse, especially when  there are many vertices with many connected edges (ie. high valence).
//! Meshes mostly containing very fine-grained triangle fans are an example. However, one can still expect a throughput of hundreds of thousand indices per second on contemporary CPUs even for these cases.
//!
//! In practice, both algorithms are fast enough to opportunistically apply them to geometry to be processed or read multiple times.
//! Apart from data locality, both algorithms may be useful to improve subsequent compression by producing more contiguous data useful for delta compression and other algorithms.
//!
//! ```rust
//! use forsyth::{order_vertices,order_triangles};
//!
//! let input_vertices = &['a', 'b', 'c', 'd', 'e'];
//! let input_indices = &[0_u32, 1, 2, 0, 1, 3, 0, 3, 4, 2, 1, 4];
//!
//! // order indices first
//! let ordered_indices =
//!     order_triangles(input_indices).unwrap_or_else(|_| input_indices.to_vec());
//!
//! assert_eq!(&ordered_indices, &[0, 3, 4, 0, 1, 3, 2, 1, 4, 0, 1, 2]);
//!
//! // then order vertices and remap indices accordingly
//! let (ordered_vertices, ordered_indices) =
//!     order_vertices(input_vertices, ordered_indices.as_slice())
//!         .unwrap_or_else(|_| (input_vertices.to_vec(), ordered_indices));
//!
//! assert_eq!(&ordered_vertices, &['a', 'd', 'e', 'b', 'c']);
//! assert_eq!(&ordered_indices, &[0, 1, 2, 0, 3, 1, 4, 3, 2, 0, 3, 4]);
//! ```
//!
//! [`Linear-speed Vertex Cache Optimisation`]: https://tomforsyth1000.github.io/papers/fast_vert_cache_opt.html
//! [`Kerbel et al. 2018`]: https://arbook.icg.tugraz.at/schmalstieg/Schmalstieg_351.pdf
//! [`GPU caching may not benefit from such ordering`]: https://www.highperformancegraphics.org/wp-content/uploads/2018/Papers-Session2/HPG2018_RevisitingVertexCache.pdf
//! [`order_triangles_inplace`]: ./fn.order_triangles_inplace.html
//! [`order_triangles`]: ./fn.order_triangles.html
//! [`order_vertices`]: ./fn.order_vertices.html
//! [`not guaranteed to be exactly linear`]: https://kento_asashima.gitlab.io/-/forsyth/-/jobs/1192073834/artifacts/target/criterion/order_triangles/report/index.html

/*
This is a clean-room implementation of Tom Forsyth's
"Linear-speed Vertex Cache Optimisation" into Rust.

Comments and comment blocks starting with "TF:" are
excerpts of the original paper as retrieved from
https://tomforsyth1000.github.io/papers/fast_vert_cache_opt.html
on 5 January 2021.
*/

use std::{
    collections::{HashMap, VecDeque},
    convert::{TryFrom, TryInto},
    fmt::Display,
    u32,
};

const MAX_VERTEX_CACHE_SIZE: u16 = std::u16::MAX - 1;
const NOT_IN_CACHE: u16 = std::u16::MAX;
const NULL_TRI: u32 = std::u32::MAX;

/// The default vertex cache size as suggested by the original paper
pub const DEFAULT_VERTEX_CACHE_SIZE: u16 = 32;

/// An error or invariant violation during an ordering operation
#[derive(Debug, Clone, Copy, PartialEq)]
pub enum Error {
    /// Provided slice of Index cannot represent one or more index triples.
    IndicesNotTriples,
    /// An Index failed to convert to usize.
    IndexToUsizeConversion,
    /// There are more than `limit` triangles involved.
    TooManyTrianglesInTotal { limit: usize },
    /// More than `limit` triangles connect to vertex `vertex_idx`.
    TooManyTrianglesAtVertex { vertex_idx: usize, limit: usize },
    /// The resulting ordered Index draw list was malformed.
    MalformedDrawList,
    /// There was an attempt to refer to an invalid vertex index
    VertexOutOfBounds,
}

impl Display for Error {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        match self {
            Error::IndicesNotTriples => f.write_str("elements are not all triples"),
            Error::IndexToUsizeConversion => f.write_str("cannot convert Index to usize"),
            Error::TooManyTrianglesInTotal { limit } => f.write_fmt(format_args!(
                "too many triangles in total. {} triangles are supported",
                limit,
            )),
            Error::TooManyTrianglesAtVertex { vertex_idx, limit } => f.write_fmt(format_args!(
                "too many triangles connected to vertex {}. {} triangles are supported",
                vertex_idx, limit,
            )),
            Error::MalformedDrawList => {
                f.write_str("the generated ordered Index draw list is malformed")
            }
            Error::VertexOutOfBounds => f.write_str("the vertex index is out of bounds"),
        }
    }
}

/// A struct holding the parameters controlling the algorithm
///
/// Using Config::default() results in a configuration with
/// the parameters set as suggested by the original paper.
///
/// See the paper for further information.

#[derive(Debug, Clone, Copy, PartialEq)]
pub struct Config {
    pub cache_decay_power: f32,
    pub last_tri_score: f32,
    pub valence_boost_scale: f32,
    pub valence_boost_power: f32,
}

impl Default for Config {
    fn default() -> Self {
        Self {
            cache_decay_power: 1.5,
            last_tri_score: 0.75,
            valence_boost_scale: 2.0,
            valence_boost_power: 0.5,
        }
    }
}

/*
TF: Instead, each vertex holds the following data:

Its position in the modelled cache (-1 if it is not in the cache)
Its current score
The total number of triangles that use it
The number of triangles not yet added that use it
The list of triangle indices that use it
*/
#[derive(Clone, Debug)]
struct VertexInfo {
    score: f32,
    tri_list_ofs: u32,
    cache_pos: u16,
    num_tris_active: u16,
}

impl Default for VertexInfo {
    fn default() -> Self {
        Self {
            cache_pos: NOT_IN_CACHE,
            score: 0.0,
            num_tris_active: 0,
            tri_list_ofs: 0,
        }
    }
}

/*
TF: Each triangle in the mesh also stores the following data:

Whether it has been added to the draw list or not
The triangle’s score (the sum of the scores of its vertices)
The indices to the three vertices
*/
#[derive(Debug)]
struct TriangleInfo<Index> {
    verts: [Index; 3],
    score: f32,
    added_to_draw_list: bool,
}

fn calculate_vertex_score(
    config: &Config,
    num_active_tris: u32,
    cache_pos: u16,
    vertex_cache_size: u16,
) -> f32 {
    if num_active_tris == 0 {
        -1.0f32
    } else {
        // TF: Bonus points for having a low number of tris still to
        // use the vert, so we get rid of lone verts quickly.
        let valence_boost = (num_active_tris as f32).powf(-config.valence_boost_power);

        let pos_score = if cache_pos < 3 {
            // TF: This vertex was used in the last triangle,
            // so it has a fixed score, whichever of the three
            // it's in. Otherwise, you can get very different
            // answers depending on whether you add
            // the triangle 1,2,3 or 3,1,2 - which is silly.
            config.last_tri_score
        } else if cache_pos < vertex_cache_size {
            // TF: Points for being high in the cache.
            let scaler = 1.0 / ((vertex_cache_size - 3) as f32);
            (1.0 - ((cache_pos - 3) as f32) * scaler).powf(config.cache_decay_power)
        } else {
            0.0f32
        };

        pos_score + (config.valence_boost_scale * valence_boost)
    }
}

/// Orders a slice of triangle indices in place.
///
/// The configuration in `config` can be used to tweak the algorithm's parameters.
/// No checks for sanity and/or validity of the provided values is done.
///
/// The slice `indices` is assumed to contain the index triples making
/// up the triangles to be ordered.
///
/// `vertex_cache_size` controls the size of the simulated LRU cache that
/// is used to drive the optimization. A size often used is 32.
///
/// Smaller cache sizes result in faster but worse ordering, whereas larger size
/// increase hit rates at the cost of runtime.
/// [`This size-performance-relationship may be sub-linear`]
/// Cache size is clamped internally to implementation-specific ranges.
///
///
/// Returns a reference to `indices`
///
/// ```
/// use forsyth::{Config, order_triangles_inplace};
///
/// let mut indices = [0_u16, 1, 2, 3, 2, 0, 0, 1, 3, 0, 1, 4, 0, 1, 5];
/// assert!(
///     order_triangles_inplace(Config::default(), &mut indices, 32) ==
///     Ok(&[0_u16, 1, 4, 0, 1, 5, 0, 1, 2, 3, 2, 0, 0, 1, 3])
/// );
/// ```
///
/// [`This size-performance-relationship may be sub-linear`]: https://kento_asashima.gitlab.io/-/forsyth/-/jobs/1192073834/artifacts/target/criterion/caches/report/index.html

pub fn order_triangles_inplace<Index>(
    config: Config,
    indices: &mut [Index],
    vertex_cache_size: u16,
) -> Result<&[Index], Error>
where
    Index: TryInto<usize> + std::default::Default + std::cmp::PartialEq + Copy,
{
    let vertex_cache_size =
        std::cmp::max(4, std::cmp::min(vertex_cache_size, MAX_VERTEX_CACHE_SIZE));

    if indices.is_empty() || (indices.len() % 3) != 0 {
        return Err(Error::IndexToUsizeConversion);
    }

    let num_tris = indices.len() / 3;

    let (mut tris, mut verts, mut vertex_tri_list) = {
        let mut tris: Vec<TriangleInfo<Index>> = Vec::with_capacity(num_tris);
        let mut verts: Vec<VertexInfo> = Vec::with_capacity(indices.len());

        /*
        TF: Initialisation of the data is fairly straightforward, with two passes over the triangle data.
        The first simply increments the counter of the number of triangles that use each vertex,
        the second allocates the lists of triangles for each vertex and fills them in.
        After that, the score of each vertex is found using the above code,
        and then the score of each triangle is found by summing the scores of each vertex the triangle uses.
        These scores are simply cached values of the computed scores, and are updated when necessary as the algorithm runs.
        */

        let mut total_vertex_tris = 0;

        for tri_idx in 0..num_tris {
            let mut tri_verts = [Index::default(), Index::default(), Index::default()];

            for (v, tri_vert) in tri_verts.iter_mut().enumerate() {
                let element = (tri_idx * 3) + v;
                let vertex_idx = indices[element];
                *tri_vert = vertex_idx;

                let vertex_idx: usize = if let Ok(vertex_idx) = vertex_idx.try_into() {
                    vertex_idx
                } else {
                    return Err(Error::IndexToUsizeConversion);
                };

                if verts.len() < vertex_idx + 1 {
                    verts.resize(vertex_idx + 1, VertexInfo::default());
                }
                let vert: &mut VertexInfo = &mut verts[vertex_idx];
                if vert.num_tris_active == std::u16::MAX {
                    return Err(Error::TooManyTrianglesAtVertex {
                        vertex_idx,
                        limit: std::u16::MAX as usize,
                    });
                }
                vert.num_tris_active += 1;

                if total_vertex_tris == std::u32::MAX {
                    return Err(Error::TooManyTrianglesInTotal {
                        limit: std::usize::MAX,
                    });
                }

                total_vertex_tris += 1;
            }

            tris.push(TriangleInfo {
                verts: tri_verts,
                score: 0.0,
                added_to_draw_list: false,
            });
        }

        let mut vertex_tri_list = Vec::with_capacity(total_vertex_tris as usize);

        for vert in &mut verts {
            vert.tri_list_ofs = vertex_tri_list.len() as u32;
            vertex_tri_list.resize(vertex_tri_list.len() + vert.num_tris_active as usize, 0u32);
            vert.num_tris_active = 0;
        }

        for tri_idx in 0..num_tris {
            for v in 0..3 {
                let element = (tri_idx * 3) + v;

                let vertex_idx = indices[element]
                    .try_into()
                    .map_err(|_| Error::IndexToUsizeConversion)?;
                let vert: &mut VertexInfo = &mut verts[vertex_idx];
                let tri_list = &mut vertex_tri_list[vert.tri_list_ofs as usize..];
                tri_list[vert.num_tris_active as usize] = tri_idx as u32;
                // We already checked that this is below u16::MAX
                vert.num_tris_active += 1;
            }
        }

        (tris, verts, vertex_tri_list)
    };

    let mut best_score_tri = (NULL_TRI, 0.0_f32);

    for vert in &mut verts {
        vert.score = calculate_vertex_score(
            &config,
            vert.num_tris_active as u32,
            NOT_IN_CACHE,
            vertex_cache_size,
        );
        for i in 0..vert.num_tris_active {
            let tri_idx = vertex_tri_list[vert.tri_list_ofs as usize + i as usize];
            let mut tri = &mut tris[tri_idx as usize];
            tri.score += vert.score;
            if best_score_tri.0 == NULL_TRI || tri.score > best_score_tri.1 {
                best_score_tri = (tri_idx, tri.score);
            }
        }
    }

    let mut draw_list_cursor = 0;

    /*
    TF: Then comes the main body of the algorithm, which picks one triangle at a time to add to the list of drawn triangles, until there are no more triangles left to draw.
    Usually, the algorithm knows from the previous iteration which triangle has the highest score, and simply picks that one.
    In some cases, for example the first time the algorithm runs, it does not already know the best triangle, or the supposed best triangle has an unusually low score (implying that there may be others in the mesh that are better).
    In those rare circumstances, it runs through all the remaining triangles in the mesh searching for the best score.
    */
    let mut lru_cache: VecDeque<Index> = VecDeque::with_capacity(vertex_cache_size as usize + 3);

    while best_score_tri.0 != NULL_TRI {
        let mut best_tri = &mut tris[best_score_tri.0 as usize];
        if best_tri.added_to_draw_list {
            break;
        }
        best_tri.added_to_draw_list = true;

        for v in &best_tri.verts {
            /*
            TF: The best triangle is then added to the draw list. For each vertex the triangle used,
            the valence of that vertex (the number of triangles not yet drawn that use it) is reduced by one,
            and the list of triangle indices in the vertex is updated appropriately.
            */
            let vertex_idx = *v;
            let vertex_idx_usize: usize = vertex_idx
                .try_into()
                .map_err(|_| Error::IndexToUsizeConversion)?;

            let vert = &mut verts[vertex_idx_usize];

            let tri_list = &mut vertex_tri_list[vert.tri_list_ofs as usize
                ..vert.tri_list_ofs as usize + vert.num_tris_active as usize];

            for (i, ti) in tri_list.iter().enumerate() {
                if *ti == best_score_tri.0 {
                    vert.num_tris_active -= 1;
                    for rot in i..vert.num_tris_active as usize {
                        tri_list[rot] = tri_list[rot + 1];
                    }

                    break;
                }
            }

            // Add vertex to draw list
            if let Some(draw_list_idx) = indices.get_mut(draw_list_cursor) {
                *draw_list_idx = vertex_idx;
                draw_list_cursor += 1;
            } else {
                return Err(Error::MalformedDrawList);
            }

            /*
            TF: The three vertices used by the triangle are either moved to the head of the LRU modelled cache,
            or added to the head if they were not already in it.
            */
            lru_cache.retain(|&i| i != vertex_idx);
            lru_cache.push_front(vertex_idx);
        }

        /*
        TF: The cache is temporarily grown in size by three vertices to include all vertices that were previously in the cache,
        and up to the three new ones of this triangle.
        Then the new positions of the vertices in the cache are updated, their corresponding scores are found using the code given above,
        and the scores of all their still-to-be-added triangles are also updated.
        */
        best_score_tri = (NULL_TRI, 0.0);

        for (cache_pos, vertex_idx) in lru_cache.iter().enumerate() {
            let cache_pos = std::cmp::min(cache_pos, (MAX_VERTEX_CACHE_SIZE - 1) as usize) as u16;
            let (new_score, old_score, tri_list_ofs, num_tris_active) = {
                let vertex_idx: usize = (*vertex_idx)
                    .try_into()
                    .map_err(|_| Error::IndexToUsizeConversion)?;
                let vert: &mut VertexInfo = &mut verts[vertex_idx];
                vert.cache_pos = if cache_pos < vertex_cache_size {
                    cache_pos
                } else {
                    NOT_IN_CACHE
                };
                let old_score = vert.score;
                vert.score = calculate_vertex_score(
                    &config,
                    vert.num_tris_active as u32,
                    cache_pos,
                    vertex_cache_size,
                );

                (
                    vert.score,
                    old_score,
                    vert.tri_list_ofs,
                    vert.num_tris_active,
                )
            };

            for tri_idx in &vertex_tri_list
                [tri_list_ofs as usize..tri_list_ofs as usize + num_tris_active as usize]
            {
                let tri_idx = *tri_idx;
                if tri_idx != NULL_TRI {
                    let tri = &mut tris[tri_idx as usize];

                    tri.score -= old_score;
                    tri.score += new_score;

                    if tri.added_to_draw_list {
                        continue;
                    }

                    //TF: As this is done, the score and index of the highest-scoring triangle so far are noted.
                    if best_score_tri.0 == NULL_TRI || tri.score > best_score_tri.1 {
                        best_score_tri = (tri_idx, tri.score);
                    }
                }
            }
        }

        /*
        TF: Finally, the cache is shrunk back to its normal size, with up to three vertices falling out of it.
        Their cache positions have already been updated appropriately.
        */
        while lru_cache.len() > vertex_cache_size as usize {
            lru_cache.pop_back();
        }

        /*
        TF: The algorithm repeats until there are no triangles left to add.
        */

        if best_score_tri.0 == NULL_TRI {
            if draw_list_cursor >= num_tris * 3 {
                break;
            }

            for (tri_idx, tri) in tris.iter().enumerate() {
                if tri.added_to_draw_list {
                    continue;
                }
                // TF: As this is done, the score and index of the highest-scoring triangle so far are noted.
                if best_score_tri.0 == NULL_TRI || tri.score > best_score_tri.1 {
                    best_score_tri = (tri_idx as u32, tri.score);
                }
            }

            if best_score_tri.0 == NULL_TRI {
                break;
            }
        }
    }

    if draw_list_cursor != num_tris * 3 {
        return Err(Error::MalformedDrawList);
    }

    Ok(&indices[0..draw_list_cursor])
}

/// Creates an ordered triangle index buffer.
///
/// A convenience function that wraps [`order_triangles_in_place`] to return a newly
/// allocated ordered index buffer.
///
/// This is equivalent to calling [`order_triangles_in_place`] with default [`Config`] and `cache_size` of 32.
///
/// ```
/// use forsyth::{Error,order_triangles};
///
/// // a triangle
/// assert_eq!(order_triangles(&[0, 1, 2]), Ok(vec![0, 1, 2]));
/// // a quad
/// assert_eq!(
///     order_triangles(&[0_u32, 1, 2, 0, 2, 3]),
///     Ok(vec![0, 1, 2, 0, 2, 3]),
/// );
///
/// assert_eq!(
///     order_triangles(&Vec::<u32>::new()),
///     Err(Error::IndicesNotTriples)
/// );
/// assert_eq!(
///     order_triangles(&[0, 1]),
///     Err(Error::IndicesNotTriples)
/// );
/// assert_eq!(
///     order_triangles(&[0, 1, 2, 3]),
///     Err(Error::IndicesNotTriples)
/// );
///
/// // Works with all (un-)signed integers
/// assert_eq!(
///     order_triangles(&[0_u8, 1, 2, 3, 4, 5]),
///     Ok(vec![0, 1, 2, 3, 4, 5])
/// );
/// assert_eq!(
///     order_triangles(&[0_i16, 1, 2, 3, 4, 5]),
///     Ok(vec![0, 1, 2, 3, 4, 5])
/// );
/// assert_eq!(
///     order_triangles(&[0_u32, 1, 2, 3, 4, 5]),
///     Ok(vec![0, 1, 2, 3, 4, 5])
/// );
/// assert_eq!(
///     order_triangles(&[0_i64, 1, 2, 3, 4, 5]),
///     Ok(vec![0, 1, 2, 3, 4, 5])
/// );
/// assert_eq!(
///     order_triangles(&[0_usize, 1, 2, 3, 4, 5]),
///     Ok(vec![0, 1, 2, 3, 4, 5])
/// );
///
/// // Indices can be sparse
/// assert_eq!(
///     order_triangles(&[0_i8, 1, 2, 63, 64, 65]),
///     Ok(vec![0, 1, 2, 63, 64, 65])
/// );
///
/// // Indices cannot be negative
/// assert_eq!(
///    order_triangles(&[0_i8, -1, -2, 63, 64, 65]),
///    Err(Error::IndexToUsizeConversion)
/// );
/// ```
///
/// [`order_triangles_in_place`]: ./fn.order_triangles_inplace.html
/// [`Config`]: ./struct.Config.html

pub fn order_triangles<Index>(indices: &[Index]) -> Result<Vec<Index>, Error>
where
    Index: std::convert::TryInto<usize> + std::default::Default + std::cmp::PartialEq + Copy,
{
    if indices.is_empty() || (indices.len() % 3) != 0 {
        return Err(Error::IndicesNotTriples);
    }

    let vertex_cache_size = DEFAULT_VERTEX_CACHE_SIZE;

    let buffer = {
        let mut buffer = Vec::with_capacity(indices.len());
        buffer.extend_from_slice(indices);

        order_triangles_inplace(Config::default(), buffer.as_mut_slice(), vertex_cache_size)?;

        buffer
    };
    Ok(buffer)
}

/// Orders a vertex buffer to maximize data locality.
///
/// The returned vertex buffer contains the referenced vertices from `vertices` and is ordered to maximize data locality when being read sequentially.
/// The accompanying index buffer contains the mapped `indices` to match the new vertex ordering.
///
/// This function can also be used to consolidate sparse index and vertex data as unreferenced vertices are not copied.
/// ```
/// use forsyth::{Error,order_vertices};
///
/// assert_eq!(
///     order_vertices(&['d', 'c', 'b', 'a'], &[3, 2, 0, 2, 1, 0]),
///     Ok((vec!['a', 'b', 'd', 'c'], vec![0, 1, 2, 1, 3, 2]))
/// );
///
/// // Vertices not referenced by any index are removed
/// assert_eq!(
///     order_vertices(&['x', 'x', 'a', 'b', 'y', 'c'], &[2, 3, 5]),
///     Ok((vec!['a', 'b', 'c'], vec![0, 1, 2]))
/// );
///
/// // Indices must be in valid range
/// assert_eq!(
///     order_vertices(&['a', 'b', 'c'], &[0_i8, 1, 99]),
///     Err(Error::VertexOutOfBounds)
/// );
/// assert_eq!(
///     order_vertices(&['a', 'b', 'c'], &[0_i8, -1, 2]),
///     Err(Error::IndexToUsizeConversion)
/// );

/// ```
/// [`This size-performance-relationship may be sub-linear`]: https://kento_asashima.gitlab.io/-/forsyth/-/jobs/1192073834/artifacts/target/criterion/caches/report/index.html

pub fn order_vertices<Index, Vertex>(
    vertices: &[Vertex],
    indices: &[Index],
) -> Result<(Vec<Vertex>, Vec<Index>), Error>
where
    Index: Copy + Eq + TryInto<usize> + TryFrom<usize> + std::hash::Hash,
    Vertex: Copy,
{
    let mut ordered_vertices = Vec::with_capacity(vertices.len());
    let mut ordered_indices = Vec::with_capacity(indices.len());
    let mut index_map: HashMap<Index, Index> = HashMap::with_capacity(indices.len());

    for index in indices {
        let mapped_idx = match index_map.entry(*index) {
            std::collections::hash_map::Entry::Occupied(mapped) => *mapped.get(),
            std::collections::hash_map::Entry::Vacant(vacant) => {
                let index = (*index)
                    .try_into()
                    .map_err(|_| Error::IndexToUsizeConversion)?;
                if let Some(vertex) = vertices.get(index) {
                    ordered_vertices.push(*vertex);
                    let mapped = (ordered_vertices.len() - 1)
                        .try_into()
                        .map_err(|_| Error::IndexToUsizeConversion)?;
                    *vacant.insert(mapped)
                } else {
                    return Err(Error::VertexOutOfBounds);
                }
            }
        };
        ordered_indices.push(mapped_idx);
    }

    Ok((ordered_vertices, ordered_indices))
}

#[cfg(test)]
mod tests {

    use super::*;

    use proptest::collection::vec;
    use proptest::prelude::*;

    #[test]
    fn error_formatting() {
        for e in [
            Error::IndexToUsizeConversion,
            Error::IndicesNotTriples,
            Error::TooManyTrianglesAtVertex {
                vertex_idx: 123,
                limit: 42,
            },
            Error::TooManyTrianglesInTotal { limit: 42 },
            Error::MalformedDrawList,
            Error::VertexOutOfBounds,
        ] {
            assert_eq!(
                format!("{}", e),
                match e {
                    Error::IndicesNotTriples => "elements are not all triples",
                    Error::IndexToUsizeConversion => "cannot convert Index to usize",
                    Error::TooManyTrianglesInTotal { .. } =>
                        "too many triangles in total. 42 triangles are supported",
                    Error::TooManyTrianglesAtVertex { .. } =>
                        "too many triangles connected to vertex 123. 42 triangles are supported",
                    Error::MalformedDrawList =>
                        "the generated ordered Index draw list is malformed",
                    Error::VertexOutOfBounds => "the vertex index is out of bounds",
                }
                .to_string()
            );
        }
    }

    #[test]
    fn config() {
        assert_eq!(
            Config {
                cache_decay_power: 1.5,
                last_tri_score: 0.75,
                valence_boost_scale: 2.0,
                valence_boost_power: 0.5,
            },
            Config::default()
        );
    }

    #[test]
    fn combined() {
        let input_vertices = &['a', 'b', 'c', 'd', 'e'];
        let input_indices = &[0_u32, 1, 2, 0, 1, 3, 0, 3, 4, 2, 1, 4];

        // order indices first
        let ordered_indices =
            order_triangles(input_indices).unwrap_or_else(|_| input_indices.to_vec());

        assert_eq!(&ordered_indices, &[0, 3, 4, 0, 1, 3, 2, 1, 4, 0, 1, 2]);

        // then order vertices and remap indices accordingly
        let (ordered_vertices, ordered_indices) =
            order_vertices(&input_vertices[..], ordered_indices.as_slice())
                .unwrap_or_else(|_| (input_vertices.to_vec(), ordered_indices));

        assert_eq!(&ordered_vertices, &['a', 'd', 'e', 'b', 'c']);
        assert_eq!(&ordered_indices, &[0, 1, 2, 0, 3, 1, 4, 3, 2, 0, 3, 4]);
    }

    #[test]
    fn fuzz_regressions() {
        {
            assert_eq!(
                order_triangles(&[i16::from_be_bytes([130_u8, 246])]),
                Err(Error::IndicesNotTriples)
            );
        }
    }

    #[test]
    fn sanity_checks() {
        let mut cache = VecDeque::new();
        cache.push_back(0);
        cache.push_back(1);
        cache.push_back(2);
        cache.push_back(3);
        cache.retain(|i| *i != 3);
        assert_eq!(cache.len(), 3);
        cache.push_front(3);
        assert_eq!(cache, [3, 0, 1, 2]);
    }

    #[test]
    fn test_vertex_score() {
        const MAX_VERTEX_CACHE_SIZE: u16 = 32;

        let config = Config::default();

        for (cache_pos, ref_score) in [
            (-2, config.valence_boost_scale),
            (-1, config.valence_boost_scale),
            (0, config.last_tri_score + config.valence_boost_scale),
            (1, config.last_tri_score + config.valence_boost_scale),
            (2, config.last_tri_score + config.valence_boost_scale),
            (3, 3.0),
            (4, 2.9487243),
            (5, 2.8983564),
            (6, 2.8489127),
            (MAX_VERTEX_CACHE_SIZE as i32 - 1, 2.0064032),
            (MAX_VERTEX_CACHE_SIZE as i32, config.valence_boost_scale),
            (2 * MAX_VERTEX_CACHE_SIZE as i32, config.valence_boost_scale),
        ]
        .iter()
        {
            let score = calculate_vertex_score(
                &config,
                1,
                if *cache_pos < 0 {
                    MAX_VERTEX_CACHE_SIZE + 1
                } else {
                    *cache_pos as u16
                },
                MAX_VERTEX_CACHE_SIZE,
            );
            assert!(
                (score - ref_score).abs() <= f32::EPSILON,
                "Score ({},{}) != ({},{})",
                &cache_pos,
                score,
                &cache_pos,
                &ref_score
            );
        }
    }

    #[test]
    fn basic_triangle_ordering() {
        {
            let mut indices = [0_u16, 1, 2, 3, 2, 0, 0, 1, 3, 0, 1, 4, 0, 1, 5];
            assert_eq!(
                order_triangles_inplace(Config::default(), &mut indices, 32).unwrap(),
                &[0, 1, 4, 0, 1, 5, 0, 1, 2, 3, 2, 0, 0, 1, 3]
            );
        }

        assert_eq!(
            order_triangles_inplace::<u32>(Config::default(), &mut [], 32),
            Err(Error::IndexToUsizeConversion)
        );

        assert_eq!(
            order_triangles_inplace(Config::default(), &mut [-1_i32, 0, 2], 32),
            Err(Error::IndexToUsizeConversion)
        );

        // 1 shared edge - quad
        assert_eq!(
            order_triangles(&[0_u32, 1, 2, 0, 2, 3]).unwrap(),
            [0, 1, 2, 0, 2, 3]
        );

        assert_eq!(
            order_triangles(&Vec::<u32>::new()),
            Err(Error::IndicesNotTriples)
        );
        assert_eq!(order_triangles(&[0]), Err(Error::IndicesNotTriples));
        assert_eq!(order_triangles(&[0, 1]), Err(Error::IndicesNotTriples));
        assert_eq!(order_triangles(&[0, 1, 2]).unwrap(), [0, 1, 2]);
        assert_eq!(
            order_triangles(&[0, 1, 2, 3]),
            Err(Error::IndicesNotTriples)
        );

        // Two disjunctive tris in multiple types
        assert_eq!(
            order_triangles(&[0_u32, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_u16, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_u8, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_u64, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );

        assert_eq!(
            order_triangles(&[0_i32, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_i16, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_i8, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_i64, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_usize, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_isize, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_u128, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );
        assert_eq!(
            order_triangles(&[0_i128, 1, 2, 3, 4, 5]).unwrap(),
            [0, 1, 2, 3, 4, 5]
        );

        // Indices are sparse
        assert_eq!(
            order_triangles(&[0_i8, 1, 2, 63, 64, 65]).unwrap(),
            [0, 1, 2, 63, 64, 65]
        );

        // Indices are negative
        assert_eq!(
            order_triangles(&[0_i8, -1, -2, 63, 64, 65]),
            Err(Error::IndexToUsizeConversion)
        );

        {
            let num_indices = 3 * 256;
            let mut indices = Vec::with_capacity(num_indices);
            for _ in 0..num_indices {
                indices.push(indices.len());
            }

            for cs in [
                0,
                1,
                2,
                3,
                4,
                8,
                16,
                32,
                64,
                128,
                256,
                257,
                std::u16::MAX - 1,
                std::u16::MAX,
            ] {
                let mut indices = indices.clone();
                let result = order_triangles_inplace(Config::default(), indices.as_mut_slice(), cs);
                assert!(result.is_ok(), "result is {:?}", result);
            }
        }

        {
            let mut indices = Vec::with_capacity((std::u16::MAX as usize) + 1);
            for _ in 0..(std::u16::MAX as usize) + 1 {
                indices.push(0);
                indices.push(1);
                indices.push(2);
            }

            assert_eq!(
                order_triangles(indices.as_slice()),
                Err(Error::TooManyTrianglesAtVertex {
                    vertex_idx: 0,
                    limit: 65535
                })
            );
        }
    }

    #[test]
    fn basic_vertex_ordering() {
        assert_eq!(
            order_vertices(&['a', 'b', 'c'], &[0, 1, 2]),
            Ok((vec!['a', 'b', 'c'], vec![0, 1, 2]))
        );

        assert_eq!(
            order_vertices(&['x', 'x', 'a', 'b', 'y', 'c'], &[2, 3, 5]),
            Ok((vec!['a', 'b', 'c'], vec![0, 1, 2]))
        );

        assert_eq!(
            order_vertices(&['a', 'b', 'c'], &[-1, 0, 2]),
            Err(Error::IndexToUsizeConversion)
        );

        assert_eq!(
            order_vertices(&['a', 'b', 'c'], &[0, 1, 3]),
            Err(Error::VertexOutOfBounds)
        );
    }

    #[test]
    fn readme_test() {
        let input_vertices = &['a', 'b', 'c', 'd', 'e'];
        let input_indices = &[0_u32, 1, 2, 0, 1, 3, 0, 3, 4, 2, 1, 4];

        // order indices first
        let ordered_indices =
            order_triangles(input_indices).unwrap_or_else(|_| input_indices.to_vec());

        assert_eq!(&ordered_indices, &[0, 3, 4, 0, 1, 3, 2, 1, 4, 0, 1, 2]);

        // then order vertices and remap indices accordingly
        let (ordered_vertices, ordered_indices) =
            order_vertices(input_vertices, ordered_indices.as_slice())
                .unwrap_or_else(|_| (input_vertices.to_vec(), ordered_indices));

        assert_eq!(&ordered_vertices, &['a', 'd', 'e', 'b', 'c']);
        assert_eq!(&ordered_indices, &[0, 1, 2, 0, 3, 1, 4, 3, 2, 0, 3, 4]);
    }

    proptest! {

        #![proptest_config(ProptestConfig::with_cases(20000))]
        #[test]
        fn fuzz_order_triangles(mut indices in vec(0u8..32,3..32))
        {
            while indices.len() < 3 || indices.len() % 3 != 0 {
                indices.push(0);
            }

            let mut ordered = order_triangles(&indices).expect("does not panic!");
            assert_eq!(indices.len(),ordered.len());
            indices.sort_unstable();
            ordered.sort_unstable();
            assert_eq!(indices,ordered);
        }
    }
}