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
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
// Generated from mat.rs.tera template. Edit the template, not the generated file.

use crate::{f64::math, swizzles::*, DMat3, DQuat, DVec3, DVec4, EulerRot, Mat4};
#[cfg(not(target_arch = "spirv"))]
use core::fmt;
use core::iter::{Product, Sum};
use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

/// Creates a 4x4 matrix from four column vectors.
#[inline(always)]
#[must_use]
pub const fn dmat4(x_axis: DVec4, y_axis: DVec4, z_axis: DVec4, w_axis: DVec4) -> DMat4 {
    DMat4::from_cols(x_axis, y_axis, z_axis, w_axis)
}

/// A 4x4 column major matrix.
///
/// This 4x4 matrix type features convenience methods for creating and using affine transforms and
/// perspective projections. If you are primarily dealing with 3D affine transformations
/// considering using [`DAffine3`](crate::DAffine3) which is faster than a 4x4 matrix
/// for some affine operations.
///
/// Affine transformations including 3D translation, rotation and scale can be created
/// using methods such as [`Self::from_translation()`], [`Self::from_quat()`],
/// [`Self::from_scale()`] and [`Self::from_scale_rotation_translation()`].
///
/// Orthographic projections can be created using the methods [`Self::orthographic_lh()`] for
/// left-handed coordinate systems and [`Self::orthographic_rh()`] for right-handed
/// systems. The resulting matrix is also an affine transformation.
///
/// The [`Self::transform_point3()`] and [`Self::transform_vector3()`] convenience methods
/// are provided for performing affine transformations on 3D vectors and points. These
/// multiply 3D inputs as 4D vectors with an implicit `w` value of `1` for points and `0`
/// for vectors respectively. These methods assume that `Self` contains a valid affine
/// transform.
///
/// Perspective projections can be created using methods such as
/// [`Self::perspective_lh()`], [`Self::perspective_infinite_lh()`] and
/// [`Self::perspective_infinite_reverse_lh()`] for left-handed co-ordinate systems and
/// [`Self::perspective_rh()`], [`Self::perspective_infinite_rh()`] and
/// [`Self::perspective_infinite_reverse_rh()`] for right-handed co-ordinate systems.
///
/// The resulting perspective project can be use to transform 3D vectors as points with
/// perspective correction using the [`Self::project_point3()`] convenience method.
#[derive(Clone, Copy)]
#[cfg_attr(feature = "cuda", repr(align(16)))]
#[repr(C)]
pub struct DMat4 {
    pub x_axis: DVec4,
    pub y_axis: DVec4,
    pub z_axis: DVec4,
    pub w_axis: DVec4,
}

impl DMat4 {
    /// A 4x4 matrix with all elements set to `0.0`.
    pub const ZERO: Self = Self::from_cols(DVec4::ZERO, DVec4::ZERO, DVec4::ZERO, DVec4::ZERO);

    /// A 4x4 identity matrix, where all diagonal elements are `1`, and all off-diagonal elements are `0`.
    pub const IDENTITY: Self = Self::from_cols(DVec4::X, DVec4::Y, DVec4::Z, DVec4::W);

    /// All NAN:s.
    pub const NAN: Self = Self::from_cols(DVec4::NAN, DVec4::NAN, DVec4::NAN, DVec4::NAN);

    #[allow(clippy::too_many_arguments)]
    #[inline(always)]
    #[must_use]
    const fn new(
        m00: f64,
        m01: f64,
        m02: f64,
        m03: f64,
        m10: f64,
        m11: f64,
        m12: f64,
        m13: f64,
        m20: f64,
        m21: f64,
        m22: f64,
        m23: f64,
        m30: f64,
        m31: f64,
        m32: f64,
        m33: f64,
    ) -> Self {
        Self {
            x_axis: DVec4::new(m00, m01, m02, m03),
            y_axis: DVec4::new(m10, m11, m12, m13),
            z_axis: DVec4::new(m20, m21, m22, m23),
            w_axis: DVec4::new(m30, m31, m32, m33),
        }
    }

    /// Creates a 4x4 matrix from four column vectors.
    #[inline(always)]
    #[must_use]
    pub const fn from_cols(x_axis: DVec4, y_axis: DVec4, z_axis: DVec4, w_axis: DVec4) -> Self {
        Self {
            x_axis,
            y_axis,
            z_axis,
            w_axis,
        }
    }

    /// Creates a 4x4 matrix from a `[f64; 16]` array stored in column major order.
    /// If your data is stored in row major you will need to `transpose` the returned
    /// matrix.
    #[inline]
    #[must_use]
    pub const fn from_cols_array(m: &[f64; 16]) -> Self {
        Self::new(
            m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8], m[9], m[10], m[11], m[12], m[13],
            m[14], m[15],
        )
    }

    /// Creates a `[f64; 16]` array storing data in column major order.
    /// If you require data in row major order `transpose` the matrix first.
    #[inline]
    #[must_use]
    pub const fn to_cols_array(&self) -> [f64; 16] {
        [
            self.x_axis.x,
            self.x_axis.y,
            self.x_axis.z,
            self.x_axis.w,
            self.y_axis.x,
            self.y_axis.y,
            self.y_axis.z,
            self.y_axis.w,
            self.z_axis.x,
            self.z_axis.y,
            self.z_axis.z,
            self.z_axis.w,
            self.w_axis.x,
            self.w_axis.y,
            self.w_axis.z,
            self.w_axis.w,
        ]
    }

    /// Creates a 4x4 matrix from a `[[f64; 4]; 4]` 4D array stored in column major order.
    /// If your data is in row major order you will need to `transpose` the returned
    /// matrix.
    #[inline]
    #[must_use]
    pub const fn from_cols_array_2d(m: &[[f64; 4]; 4]) -> Self {
        Self::from_cols(
            DVec4::from_array(m[0]),
            DVec4::from_array(m[1]),
            DVec4::from_array(m[2]),
            DVec4::from_array(m[3]),
        )
    }

    /// Creates a `[[f64; 4]; 4]` 4D array storing data in column major order.
    /// If you require data in row major order `transpose` the matrix first.
    #[inline]
    #[must_use]
    pub const fn to_cols_array_2d(&self) -> [[f64; 4]; 4] {
        [
            self.x_axis.to_array(),
            self.y_axis.to_array(),
            self.z_axis.to_array(),
            self.w_axis.to_array(),
        ]
    }

    /// Creates a 4x4 matrix with its diagonal set to `diagonal` and all other entries set to 0.
    #[doc(alias = "scale")]
    #[inline]
    #[must_use]
    pub const fn from_diagonal(diagonal: DVec4) -> Self {
        Self::new(
            diagonal.x, 0.0, 0.0, 0.0, 0.0, diagonal.y, 0.0, 0.0, 0.0, 0.0, diagonal.z, 0.0, 0.0,
            0.0, 0.0, diagonal.w,
        )
    }

    #[inline]
    #[must_use]
    fn quat_to_axes(rotation: DQuat) -> (DVec4, DVec4, DVec4) {
        glam_assert!(rotation.is_normalized());

        let (x, y, z, w) = rotation.into();
        let x2 = x + x;
        let y2 = y + y;
        let z2 = z + z;
        let xx = x * x2;
        let xy = x * y2;
        let xz = x * z2;
        let yy = y * y2;
        let yz = y * z2;
        let zz = z * z2;
        let wx = w * x2;
        let wy = w * y2;
        let wz = w * z2;

        let x_axis = DVec4::new(1.0 - (yy + zz), xy + wz, xz - wy, 0.0);
        let y_axis = DVec4::new(xy - wz, 1.0 - (xx + zz), yz + wx, 0.0);
        let z_axis = DVec4::new(xz + wy, yz - wx, 1.0 - (xx + yy), 0.0);
        (x_axis, y_axis, z_axis)
    }

    /// Creates an affine transformation matrix from the given 3D `scale`, `rotation` and
    /// `translation`.
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    ///
    /// # Panics
    ///
    /// Will panic if `rotation` is not normalized when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn from_scale_rotation_translation(
        scale: DVec3,
        rotation: DQuat,
        translation: DVec3,
    ) -> Self {
        let (x_axis, y_axis, z_axis) = Self::quat_to_axes(rotation);
        Self::from_cols(
            x_axis.mul(scale.x),
            y_axis.mul(scale.y),
            z_axis.mul(scale.z),
            DVec4::from((translation, 1.0)),
        )
    }

    /// Creates an affine transformation matrix from the given 3D `translation`.
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    ///
    /// # Panics
    ///
    /// Will panic if `rotation` is not normalized when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn from_rotation_translation(rotation: DQuat, translation: DVec3) -> Self {
        let (x_axis, y_axis, z_axis) = Self::quat_to_axes(rotation);
        Self::from_cols(x_axis, y_axis, z_axis, DVec4::from((translation, 1.0)))
    }

    /// Extracts `scale`, `rotation` and `translation` from `self`. The input matrix is
    /// expected to be a 3D affine transformation matrix otherwise the output will be invalid.
    ///
    /// # Panics
    ///
    /// Will panic if the determinant of `self` is zero or if the resulting scale vector
    /// contains any zero elements when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn to_scale_rotation_translation(&self) -> (DVec3, DQuat, DVec3) {
        let det = self.determinant();
        glam_assert!(det != 0.0);

        let scale = DVec3::new(
            self.x_axis.length() * math::signum(det),
            self.y_axis.length(),
            self.z_axis.length(),
        );

        glam_assert!(scale.cmpne(DVec3::ZERO).all());

        let inv_scale = scale.recip();

        let rotation = DQuat::from_rotation_axes(
            self.x_axis.mul(inv_scale.x).xyz(),
            self.y_axis.mul(inv_scale.y).xyz(),
            self.z_axis.mul(inv_scale.z).xyz(),
        );

        let translation = self.w_axis.xyz();

        (scale, rotation, translation)
    }

    /// Creates an affine transformation matrix from the given `rotation` quaternion.
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    ///
    /// # Panics
    ///
    /// Will panic if `rotation` is not normalized when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn from_quat(rotation: DQuat) -> Self {
        let (x_axis, y_axis, z_axis) = Self::quat_to_axes(rotation);
        Self::from_cols(x_axis, y_axis, z_axis, DVec4::W)
    }

    /// Creates an affine transformation matrix from the given 3x3 linear transformation
    /// matrix.
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    #[inline]
    #[must_use]
    pub fn from_mat3(m: DMat3) -> Self {
        Self::from_cols(
            DVec4::from((m.x_axis, 0.0)),
            DVec4::from((m.y_axis, 0.0)),
            DVec4::from((m.z_axis, 0.0)),
            DVec4::W,
        )
    }

    /// Creates an affine transformation matrix from the given 3D `translation`.
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    #[inline]
    #[must_use]
    pub fn from_translation(translation: DVec3) -> Self {
        Self::from_cols(
            DVec4::X,
            DVec4::Y,
            DVec4::Z,
            DVec4::new(translation.x, translation.y, translation.z, 1.0),
        )
    }

    /// Creates an affine transformation matrix containing a 3D rotation around a normalized
    /// rotation `axis` of `angle` (in radians).
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    ///
    /// # Panics
    ///
    /// Will panic if `axis` is not normalized when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn from_axis_angle(axis: DVec3, angle: f64) -> Self {
        glam_assert!(axis.is_normalized());

        let (sin, cos) = math::sin_cos(angle);
        let axis_sin = axis.mul(sin);
        let axis_sq = axis.mul(axis);
        let omc = 1.0 - cos;
        let xyomc = axis.x * axis.y * omc;
        let xzomc = axis.x * axis.z * omc;
        let yzomc = axis.y * axis.z * omc;
        Self::from_cols(
            DVec4::new(
                axis_sq.x * omc + cos,
                xyomc + axis_sin.z,
                xzomc - axis_sin.y,
                0.0,
            ),
            DVec4::new(
                xyomc - axis_sin.z,
                axis_sq.y * omc + cos,
                yzomc + axis_sin.x,
                0.0,
            ),
            DVec4::new(
                xzomc + axis_sin.y,
                yzomc - axis_sin.x,
                axis_sq.z * omc + cos,
                0.0,
            ),
            DVec4::W,
        )
    }

    /// Creates a affine transformation matrix containing a rotation from the given euler
    /// rotation sequence and angles (in radians).
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    #[inline]
    #[must_use]
    pub fn from_euler(order: EulerRot, a: f64, b: f64, c: f64) -> Self {
        let quat = DQuat::from_euler(order, a, b, c);
        Self::from_quat(quat)
    }

    /// Creates an affine transformation matrix containing a 3D rotation around the x axis of
    /// `angle` (in radians).
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    #[inline]
    #[must_use]
    pub fn from_rotation_x(angle: f64) -> Self {
        let (sina, cosa) = math::sin_cos(angle);
        Self::from_cols(
            DVec4::X,
            DVec4::new(0.0, cosa, sina, 0.0),
            DVec4::new(0.0, -sina, cosa, 0.0),
            DVec4::W,
        )
    }

    /// Creates an affine transformation matrix containing a 3D rotation around the y axis of
    /// `angle` (in radians).
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    #[inline]
    #[must_use]
    pub fn from_rotation_y(angle: f64) -> Self {
        let (sina, cosa) = math::sin_cos(angle);
        Self::from_cols(
            DVec4::new(cosa, 0.0, -sina, 0.0),
            DVec4::Y,
            DVec4::new(sina, 0.0, cosa, 0.0),
            DVec4::W,
        )
    }

    /// Creates an affine transformation matrix containing a 3D rotation around the z axis of
    /// `angle` (in radians).
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    #[inline]
    #[must_use]
    pub fn from_rotation_z(angle: f64) -> Self {
        let (sina, cosa) = math::sin_cos(angle);
        Self::from_cols(
            DVec4::new(cosa, sina, 0.0, 0.0),
            DVec4::new(-sina, cosa, 0.0, 0.0),
            DVec4::Z,
            DVec4::W,
        )
    }

    /// Creates an affine transformation matrix containing the given 3D non-uniform `scale`.
    ///
    /// The resulting matrix can be used to transform 3D points and vectors. See
    /// [`Self::transform_point3()`] and [`Self::transform_vector3()`].
    ///
    /// # Panics
    ///
    /// Will panic if all elements of `scale` are zero when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn from_scale(scale: DVec3) -> Self {
        // Do not panic as long as any component is non-zero
        glam_assert!(scale.cmpne(DVec3::ZERO).any());

        Self::from_cols(
            DVec4::new(scale.x, 0.0, 0.0, 0.0),
            DVec4::new(0.0, scale.y, 0.0, 0.0),
            DVec4::new(0.0, 0.0, scale.z, 0.0),
            DVec4::W,
        )
    }

    /// Creates a 4x4 matrix from the first 16 values in `slice`.
    ///
    /// # Panics
    ///
    /// Panics if `slice` is less than 16 elements long.
    #[inline]
    #[must_use]
    pub const fn from_cols_slice(slice: &[f64]) -> Self {
        Self::new(
            slice[0], slice[1], slice[2], slice[3], slice[4], slice[5], slice[6], slice[7],
            slice[8], slice[9], slice[10], slice[11], slice[12], slice[13], slice[14], slice[15],
        )
    }

    /// Writes the columns of `self` to the first 16 elements in `slice`.
    ///
    /// # Panics
    ///
    /// Panics if `slice` is less than 16 elements long.
    #[inline]
    pub fn write_cols_to_slice(self, slice: &mut [f64]) {
        slice[0] = self.x_axis.x;
        slice[1] = self.x_axis.y;
        slice[2] = self.x_axis.z;
        slice[3] = self.x_axis.w;
        slice[4] = self.y_axis.x;
        slice[5] = self.y_axis.y;
        slice[6] = self.y_axis.z;
        slice[7] = self.y_axis.w;
        slice[8] = self.z_axis.x;
        slice[9] = self.z_axis.y;
        slice[10] = self.z_axis.z;
        slice[11] = self.z_axis.w;
        slice[12] = self.w_axis.x;
        slice[13] = self.w_axis.y;
        slice[14] = self.w_axis.z;
        slice[15] = self.w_axis.w;
    }

    /// Returns the matrix column for the given `index`.
    ///
    /// # Panics
    ///
    /// Panics if `index` is greater than 3.
    #[inline]
    #[must_use]
    pub fn col(&self, index: usize) -> DVec4 {
        match index {
            0 => self.x_axis,
            1 => self.y_axis,
            2 => self.z_axis,
            3 => self.w_axis,
            _ => panic!("index out of bounds"),
        }
    }

    /// Returns a mutable reference to the matrix column for the given `index`.
    ///
    /// # Panics
    ///
    /// Panics if `index` is greater than 3.
    #[inline]
    pub fn col_mut(&mut self, index: usize) -> &mut DVec4 {
        match index {
            0 => &mut self.x_axis,
            1 => &mut self.y_axis,
            2 => &mut self.z_axis,
            3 => &mut self.w_axis,
            _ => panic!("index out of bounds"),
        }
    }

    /// Returns the matrix row for the given `index`.
    ///
    /// # Panics
    ///
    /// Panics if `index` is greater than 3.
    #[inline]
    #[must_use]
    pub fn row(&self, index: usize) -> DVec4 {
        match index {
            0 => DVec4::new(self.x_axis.x, self.y_axis.x, self.z_axis.x, self.w_axis.x),
            1 => DVec4::new(self.x_axis.y, self.y_axis.y, self.z_axis.y, self.w_axis.y),
            2 => DVec4::new(self.x_axis.z, self.y_axis.z, self.z_axis.z, self.w_axis.z),
            3 => DVec4::new(self.x_axis.w, self.y_axis.w, self.z_axis.w, self.w_axis.w),
            _ => panic!("index out of bounds"),
        }
    }

    /// Returns `true` if, and only if, all elements are finite.
    /// If any element is either `NaN`, positive or negative infinity, this will return `false`.
    #[inline]
    #[must_use]
    pub fn is_finite(&self) -> bool {
        self.x_axis.is_finite()
            && self.y_axis.is_finite()
            && self.z_axis.is_finite()
            && self.w_axis.is_finite()
    }

    /// Returns `true` if any elements are `NaN`.
    #[inline]
    #[must_use]
    pub fn is_nan(&self) -> bool {
        self.x_axis.is_nan() || self.y_axis.is_nan() || self.z_axis.is_nan() || self.w_axis.is_nan()
    }

    /// Returns the transpose of `self`.
    #[inline]
    #[must_use]
    pub fn transpose(&self) -> Self {
        Self {
            x_axis: DVec4::new(self.x_axis.x, self.y_axis.x, self.z_axis.x, self.w_axis.x),
            y_axis: DVec4::new(self.x_axis.y, self.y_axis.y, self.z_axis.y, self.w_axis.y),
            z_axis: DVec4::new(self.x_axis.z, self.y_axis.z, self.z_axis.z, self.w_axis.z),
            w_axis: DVec4::new(self.x_axis.w, self.y_axis.w, self.z_axis.w, self.w_axis.w),
        }
    }

    /// Returns the determinant of `self`.
    #[must_use]
    pub fn determinant(&self) -> f64 {
        let (m00, m01, m02, m03) = self.x_axis.into();
        let (m10, m11, m12, m13) = self.y_axis.into();
        let (m20, m21, m22, m23) = self.z_axis.into();
        let (m30, m31, m32, m33) = self.w_axis.into();

        let a2323 = m22 * m33 - m23 * m32;
        let a1323 = m21 * m33 - m23 * m31;
        let a1223 = m21 * m32 - m22 * m31;
        let a0323 = m20 * m33 - m23 * m30;
        let a0223 = m20 * m32 - m22 * m30;
        let a0123 = m20 * m31 - m21 * m30;

        m00 * (m11 * a2323 - m12 * a1323 + m13 * a1223)
            - m01 * (m10 * a2323 - m12 * a0323 + m13 * a0223)
            + m02 * (m10 * a1323 - m11 * a0323 + m13 * a0123)
            - m03 * (m10 * a1223 - m11 * a0223 + m12 * a0123)
    }

    /// Returns the inverse of `self`.
    ///
    /// If the matrix is not invertible the returned matrix will be invalid.
    ///
    /// # Panics
    ///
    /// Will panic if the determinant of `self` is zero when `glam_assert` is enabled.
    #[must_use]
    pub fn inverse(&self) -> Self {
        let (m00, m01, m02, m03) = self.x_axis.into();
        let (m10, m11, m12, m13) = self.y_axis.into();
        let (m20, m21, m22, m23) = self.z_axis.into();
        let (m30, m31, m32, m33) = self.w_axis.into();

        let coef00 = m22 * m33 - m32 * m23;
        let coef02 = m12 * m33 - m32 * m13;
        let coef03 = m12 * m23 - m22 * m13;

        let coef04 = m21 * m33 - m31 * m23;
        let coef06 = m11 * m33 - m31 * m13;
        let coef07 = m11 * m23 - m21 * m13;

        let coef08 = m21 * m32 - m31 * m22;
        let coef10 = m11 * m32 - m31 * m12;
        let coef11 = m11 * m22 - m21 * m12;

        let coef12 = m20 * m33 - m30 * m23;
        let coef14 = m10 * m33 - m30 * m13;
        let coef15 = m10 * m23 - m20 * m13;

        let coef16 = m20 * m32 - m30 * m22;
        let coef18 = m10 * m32 - m30 * m12;
        let coef19 = m10 * m22 - m20 * m12;

        let coef20 = m20 * m31 - m30 * m21;
        let coef22 = m10 * m31 - m30 * m11;
        let coef23 = m10 * m21 - m20 * m11;

        let fac0 = DVec4::new(coef00, coef00, coef02, coef03);
        let fac1 = DVec4::new(coef04, coef04, coef06, coef07);
        let fac2 = DVec4::new(coef08, coef08, coef10, coef11);
        let fac3 = DVec4::new(coef12, coef12, coef14, coef15);
        let fac4 = DVec4::new(coef16, coef16, coef18, coef19);
        let fac5 = DVec4::new(coef20, coef20, coef22, coef23);

        let vec0 = DVec4::new(m10, m00, m00, m00);
        let vec1 = DVec4::new(m11, m01, m01, m01);
        let vec2 = DVec4::new(m12, m02, m02, m02);
        let vec3 = DVec4::new(m13, m03, m03, m03);

        let inv0 = vec1.mul(fac0).sub(vec2.mul(fac1)).add(vec3.mul(fac2));
        let inv1 = vec0.mul(fac0).sub(vec2.mul(fac3)).add(vec3.mul(fac4));
        let inv2 = vec0.mul(fac1).sub(vec1.mul(fac3)).add(vec3.mul(fac5));
        let inv3 = vec0.mul(fac2).sub(vec1.mul(fac4)).add(vec2.mul(fac5));

        let sign_a = DVec4::new(1.0, -1.0, 1.0, -1.0);
        let sign_b = DVec4::new(-1.0, 1.0, -1.0, 1.0);

        let inverse = Self::from_cols(
            inv0.mul(sign_a),
            inv1.mul(sign_b),
            inv2.mul(sign_a),
            inv3.mul(sign_b),
        );

        let col0 = DVec4::new(
            inverse.x_axis.x,
            inverse.y_axis.x,
            inverse.z_axis.x,
            inverse.w_axis.x,
        );

        let dot0 = self.x_axis.mul(col0);
        let dot1 = dot0.x + dot0.y + dot0.z + dot0.w;

        glam_assert!(dot1 != 0.0);

        let rcp_det = dot1.recip();
        inverse.mul(rcp_det)
    }

    /// Creates a left-handed view matrix using a camera position, an up direction, and a facing
    /// direction.
    ///
    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=forward`.
    #[inline]
    #[must_use]
    pub fn look_to_lh(eye: DVec3, dir: DVec3, up: DVec3) -> Self {
        Self::look_to_rh(eye, -dir, up)
    }

    /// Creates a right-handed view matrix using a camera position, an up direction, and a facing
    /// direction.
    ///
    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=back`.
    #[inline]
    #[must_use]
    pub fn look_to_rh(eye: DVec3, dir: DVec3, up: DVec3) -> Self {
        let f = dir.normalize();
        let s = f.cross(up).normalize();
        let u = s.cross(f);

        Self::from_cols(
            DVec4::new(s.x, u.x, -f.x, 0.0),
            DVec4::new(s.y, u.y, -f.y, 0.0),
            DVec4::new(s.z, u.z, -f.z, 0.0),
            DVec4::new(-eye.dot(s), -eye.dot(u), eye.dot(f), 1.0),
        )
    }

    /// Creates a left-handed view matrix using a camera position, an up direction, and a focal
    /// point.
    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=forward`.
    ///
    /// # Panics
    ///
    /// Will panic if `up` is not normalized when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn look_at_lh(eye: DVec3, center: DVec3, up: DVec3) -> Self {
        glam_assert!(up.is_normalized());
        Self::look_to_lh(eye, center.sub(eye), up)
    }

    /// Creates a right-handed view matrix using a camera position, an up direction, and a focal
    /// point.
    /// For a view coordinate system with `+X=right`, `+Y=up` and `+Z=back`.
    ///
    /// # Panics
    ///
    /// Will panic if `up` is not normalized when `glam_assert` is enabled.
    #[inline]
    pub fn look_at_rh(eye: DVec3, center: DVec3, up: DVec3) -> Self {
        glam_assert!(up.is_normalized());
        Self::look_to_rh(eye, center.sub(eye), up)
    }

    /// Creates a right-handed perspective projection matrix with [-1,1] depth range.
    /// This is the same as the OpenGL `gluPerspective` function.
    /// See <https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluPerspective.xml>
    #[inline]
    #[must_use]
    pub fn perspective_rh_gl(
        fov_y_radians: f64,
        aspect_ratio: f64,
        z_near: f64,
        z_far: f64,
    ) -> Self {
        let inv_length = 1.0 / (z_near - z_far);
        let f = 1.0 / math::tan(0.5 * fov_y_radians);
        let a = f / aspect_ratio;
        let b = (z_near + z_far) * inv_length;
        let c = (2.0 * z_near * z_far) * inv_length;
        Self::from_cols(
            DVec4::new(a, 0.0, 0.0, 0.0),
            DVec4::new(0.0, f, 0.0, 0.0),
            DVec4::new(0.0, 0.0, b, -1.0),
            DVec4::new(0.0, 0.0, c, 0.0),
        )
    }

    /// Creates a left-handed perspective projection matrix with `[0,1]` depth range.
    ///
    /// # Panics
    ///
    /// Will panic if `z_near` or `z_far` are less than or equal to zero when `glam_assert` is
    /// enabled.
    #[inline]
    #[must_use]
    pub fn perspective_lh(fov_y_radians: f64, aspect_ratio: f64, z_near: f64, z_far: f64) -> Self {
        glam_assert!(z_near > 0.0 && z_far > 0.0);
        let (sin_fov, cos_fov) = math::sin_cos(0.5 * fov_y_radians);
        let h = cos_fov / sin_fov;
        let w = h / aspect_ratio;
        let r = z_far / (z_far - z_near);
        Self::from_cols(
            DVec4::new(w, 0.0, 0.0, 0.0),
            DVec4::new(0.0, h, 0.0, 0.0),
            DVec4::new(0.0, 0.0, r, 1.0),
            DVec4::new(0.0, 0.0, -r * z_near, 0.0),
        )
    }

    /// Creates a right-handed perspective projection matrix with `[0,1]` depth range.
    ///
    /// # Panics
    ///
    /// Will panic if `z_near` or `z_far` are less than or equal to zero when `glam_assert` is
    /// enabled.
    #[inline]
    #[must_use]
    pub fn perspective_rh(fov_y_radians: f64, aspect_ratio: f64, z_near: f64, z_far: f64) -> Self {
        glam_assert!(z_near > 0.0 && z_far > 0.0);
        let (sin_fov, cos_fov) = math::sin_cos(0.5 * fov_y_radians);
        let h = cos_fov / sin_fov;
        let w = h / aspect_ratio;
        let r = z_far / (z_near - z_far);
        Self::from_cols(
            DVec4::new(w, 0.0, 0.0, 0.0),
            DVec4::new(0.0, h, 0.0, 0.0),
            DVec4::new(0.0, 0.0, r, -1.0),
            DVec4::new(0.0, 0.0, r * z_near, 0.0),
        )
    }

    /// Creates an infinite left-handed perspective projection matrix with `[0,1]` depth range.
    ///
    /// # Panics
    ///
    /// Will panic if `z_near` is less than or equal to zero when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn perspective_infinite_lh(fov_y_radians: f64, aspect_ratio: f64, z_near: f64) -> Self {
        glam_assert!(z_near > 0.0);
        let (sin_fov, cos_fov) = math::sin_cos(0.5 * fov_y_radians);
        let h = cos_fov / sin_fov;
        let w = h / aspect_ratio;
        Self::from_cols(
            DVec4::new(w, 0.0, 0.0, 0.0),
            DVec4::new(0.0, h, 0.0, 0.0),
            DVec4::new(0.0, 0.0, 1.0, 1.0),
            DVec4::new(0.0, 0.0, -z_near, 0.0),
        )
    }

    /// Creates an infinite left-handed perspective projection matrix with `[0,1]` depth range.
    ///
    /// # Panics
    ///
    /// Will panic if `z_near` is less than or equal to zero when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn perspective_infinite_reverse_lh(
        fov_y_radians: f64,
        aspect_ratio: f64,
        z_near: f64,
    ) -> Self {
        glam_assert!(z_near > 0.0);
        let (sin_fov, cos_fov) = math::sin_cos(0.5 * fov_y_radians);
        let h = cos_fov / sin_fov;
        let w = h / aspect_ratio;
        Self::from_cols(
            DVec4::new(w, 0.0, 0.0, 0.0),
            DVec4::new(0.0, h, 0.0, 0.0),
            DVec4::new(0.0, 0.0, 0.0, 1.0),
            DVec4::new(0.0, 0.0, z_near, 0.0),
        )
    }

    /// Creates an infinite right-handed perspective projection matrix with
    /// `[0,1]` depth range.
    #[inline]
    #[must_use]
    pub fn perspective_infinite_rh(fov_y_radians: f64, aspect_ratio: f64, z_near: f64) -> Self {
        glam_assert!(z_near > 0.0);
        let f = 1.0 / math::tan(0.5 * fov_y_radians);
        Self::from_cols(
            DVec4::new(f / aspect_ratio, 0.0, 0.0, 0.0),
            DVec4::new(0.0, f, 0.0, 0.0),
            DVec4::new(0.0, 0.0, -1.0, -1.0),
            DVec4::new(0.0, 0.0, -z_near, 0.0),
        )
    }

    /// Creates an infinite reverse right-handed perspective projection matrix
    /// with `[0,1]` depth range.
    #[inline]
    #[must_use]
    pub fn perspective_infinite_reverse_rh(
        fov_y_radians: f64,
        aspect_ratio: f64,
        z_near: f64,
    ) -> Self {
        glam_assert!(z_near > 0.0);
        let f = 1.0 / math::tan(0.5 * fov_y_radians);
        Self::from_cols(
            DVec4::new(f / aspect_ratio, 0.0, 0.0, 0.0),
            DVec4::new(0.0, f, 0.0, 0.0),
            DVec4::new(0.0, 0.0, 0.0, -1.0),
            DVec4::new(0.0, 0.0, z_near, 0.0),
        )
    }

    /// Creates a right-handed orthographic projection matrix with `[-1,1]` depth
    /// range.  This is the same as the OpenGL `glOrtho` function in OpenGL.
    /// See
    /// <https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glOrtho.xml>
    #[inline]
    #[must_use]
    pub fn orthographic_rh_gl(
        left: f64,
        right: f64,
        bottom: f64,
        top: f64,
        near: f64,
        far: f64,
    ) -> Self {
        let a = 2.0 / (right - left);
        let b = 2.0 / (top - bottom);
        let c = -2.0 / (far - near);
        let tx = -(right + left) / (right - left);
        let ty = -(top + bottom) / (top - bottom);
        let tz = -(far + near) / (far - near);

        Self::from_cols(
            DVec4::new(a, 0.0, 0.0, 0.0),
            DVec4::new(0.0, b, 0.0, 0.0),
            DVec4::new(0.0, 0.0, c, 0.0),
            DVec4::new(tx, ty, tz, 1.0),
        )
    }

    /// Creates a left-handed orthographic projection matrix with `[0,1]` depth range.
    #[inline]
    #[must_use]
    pub fn orthographic_lh(
        left: f64,
        right: f64,
        bottom: f64,
        top: f64,
        near: f64,
        far: f64,
    ) -> Self {
        let rcp_width = 1.0 / (right - left);
        let rcp_height = 1.0 / (top - bottom);
        let r = 1.0 / (far - near);
        Self::from_cols(
            DVec4::new(rcp_width + rcp_width, 0.0, 0.0, 0.0),
            DVec4::new(0.0, rcp_height + rcp_height, 0.0, 0.0),
            DVec4::new(0.0, 0.0, r, 0.0),
            DVec4::new(
                -(left + right) * rcp_width,
                -(top + bottom) * rcp_height,
                -r * near,
                1.0,
            ),
        )
    }

    /// Creates a right-handed orthographic projection matrix with `[0,1]` depth range.
    #[inline]
    #[must_use]
    pub fn orthographic_rh(
        left: f64,
        right: f64,
        bottom: f64,
        top: f64,
        near: f64,
        far: f64,
    ) -> Self {
        let rcp_width = 1.0 / (right - left);
        let rcp_height = 1.0 / (top - bottom);
        let r = 1.0 / (near - far);
        Self::from_cols(
            DVec4::new(rcp_width + rcp_width, 0.0, 0.0, 0.0),
            DVec4::new(0.0, rcp_height + rcp_height, 0.0, 0.0),
            DVec4::new(0.0, 0.0, r, 0.0),
            DVec4::new(
                -(left + right) * rcp_width,
                -(top + bottom) * rcp_height,
                r * near,
                1.0,
            ),
        )
    }

    /// Transforms the given 3D vector as a point, applying perspective correction.
    ///
    /// This is the equivalent of multiplying the 3D vector as a 4D vector where `w` is `1.0`.
    /// The perspective divide is performed meaning the resulting 3D vector is divided by `w`.
    ///
    /// This method assumes that `self` contains a projective transform.
    #[inline]
    #[must_use]
    pub fn project_point3(&self, rhs: DVec3) -> DVec3 {
        let mut res = self.x_axis.mul(rhs.x);
        res = self.y_axis.mul(rhs.y).add(res);
        res = self.z_axis.mul(rhs.z).add(res);
        res = self.w_axis.add(res);
        res = res.mul(res.wwww().recip());
        res.xyz()
    }

    /// Transforms the given 3D vector as a point.
    ///
    /// This is the equivalent of multiplying the 3D vector as a 4D vector where `w` is
    /// `1.0`.
    ///
    /// This method assumes that `self` contains a valid affine transform. It does not perform
    /// a perspective divide, if `self` contains a perspective transform, or if you are unsure,
    /// the [`Self::project_point3()`] method should be used instead.
    ///
    /// # Panics
    ///
    /// Will panic if the 3rd row of `self` is not `(0, 0, 0, 1)` when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn transform_point3(&self, rhs: DVec3) -> DVec3 {
        glam_assert!(self.row(3).abs_diff_eq(DVec4::W, 1e-6));
        let mut res = self.x_axis.mul(rhs.x);
        res = self.y_axis.mul(rhs.y).add(res);
        res = self.z_axis.mul(rhs.z).add(res);
        res = self.w_axis.add(res);
        res.xyz()
    }

    /// Transforms the give 3D vector as a direction.
    ///
    /// This is the equivalent of multiplying the 3D vector as a 4D vector where `w` is
    /// `0.0`.
    ///
    /// This method assumes that `self` contains a valid affine transform.
    ///
    /// # Panics
    ///
    /// Will panic if the 3rd row of `self` is not `(0, 0, 0, 1)` when `glam_assert` is enabled.
    #[inline]
    #[must_use]
    pub fn transform_vector3(&self, rhs: DVec3) -> DVec3 {
        glam_assert!(self.row(3).abs_diff_eq(DVec4::W, 1e-6));
        let mut res = self.x_axis.mul(rhs.x);
        res = self.y_axis.mul(rhs.y).add(res);
        res = self.z_axis.mul(rhs.z).add(res);
        res.xyz()
    }

    /// Transforms a 4D vector.
    #[inline]
    #[must_use]
    pub fn mul_vec4(&self, rhs: DVec4) -> DVec4 {
        let mut res = self.x_axis.mul(rhs.x);
        res = res.add(self.y_axis.mul(rhs.y));
        res = res.add(self.z_axis.mul(rhs.z));
        res = res.add(self.w_axis.mul(rhs.w));
        res
    }

    /// Multiplies two 4x4 matrices.
    #[inline]
    #[must_use]
    pub fn mul_mat4(&self, rhs: &Self) -> Self {
        Self::from_cols(
            self.mul(rhs.x_axis),
            self.mul(rhs.y_axis),
            self.mul(rhs.z_axis),
            self.mul(rhs.w_axis),
        )
    }

    /// Adds two 4x4 matrices.
    #[inline]
    #[must_use]
    pub fn add_mat4(&self, rhs: &Self) -> Self {
        Self::from_cols(
            self.x_axis.add(rhs.x_axis),
            self.y_axis.add(rhs.y_axis),
            self.z_axis.add(rhs.z_axis),
            self.w_axis.add(rhs.w_axis),
        )
    }

    /// Subtracts two 4x4 matrices.
    #[inline]
    #[must_use]
    pub fn sub_mat4(&self, rhs: &Self) -> Self {
        Self::from_cols(
            self.x_axis.sub(rhs.x_axis),
            self.y_axis.sub(rhs.y_axis),
            self.z_axis.sub(rhs.z_axis),
            self.w_axis.sub(rhs.w_axis),
        )
    }

    /// Multiplies a 4x4 matrix by a scalar.
    #[inline]
    #[must_use]
    pub fn mul_scalar(&self, rhs: f64) -> Self {
        Self::from_cols(
            self.x_axis.mul(rhs),
            self.y_axis.mul(rhs),
            self.z_axis.mul(rhs),
            self.w_axis.mul(rhs),
        )
    }

    /// Divides a 4x4 matrix by a scalar.
    #[inline]
    #[must_use]
    pub fn div_scalar(&self, rhs: f64) -> Self {
        let rhs = DVec4::splat(rhs);
        Self::from_cols(
            self.x_axis.div(rhs),
            self.y_axis.div(rhs),
            self.z_axis.div(rhs),
            self.w_axis.div(rhs),
        )
    }

    /// Returns true if the absolute difference of all elements between `self` and `rhs`
    /// is less than or equal to `max_abs_diff`.
    ///
    /// This can be used to compare if two matrices contain similar elements. It works best
    /// when comparing with a known value. The `max_abs_diff` that should be used used
    /// depends on the values being compared against.
    ///
    /// For more see
    /// [comparing floating point numbers](https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/).
    #[inline]
    #[must_use]
    pub fn abs_diff_eq(&self, rhs: Self, max_abs_diff: f64) -> bool {
        self.x_axis.abs_diff_eq(rhs.x_axis, max_abs_diff)
            && self.y_axis.abs_diff_eq(rhs.y_axis, max_abs_diff)
            && self.z_axis.abs_diff_eq(rhs.z_axis, max_abs_diff)
            && self.w_axis.abs_diff_eq(rhs.w_axis, max_abs_diff)
    }

    /// Takes the absolute value of each element in `self`
    #[inline]
    #[must_use]
    pub fn abs(&self) -> Self {
        Self::from_cols(
            self.x_axis.abs(),
            self.y_axis.abs(),
            self.z_axis.abs(),
            self.w_axis.abs(),
        )
    }

    #[inline]
    pub fn as_mat4(&self) -> Mat4 {
        Mat4::from_cols(
            self.x_axis.as_vec4(),
            self.y_axis.as_vec4(),
            self.z_axis.as_vec4(),
            self.w_axis.as_vec4(),
        )
    }
}

impl Default for DMat4 {
    #[inline]
    fn default() -> Self {
        Self::IDENTITY
    }
}

impl Add<DMat4> for DMat4 {
    type Output = Self;
    #[inline]
    fn add(self, rhs: Self) -> Self::Output {
        self.add_mat4(&rhs)
    }
}

impl AddAssign<DMat4> for DMat4 {
    #[inline]
    fn add_assign(&mut self, rhs: Self) {
        *self = self.add_mat4(&rhs);
    }
}

impl Sub<DMat4> for DMat4 {
    type Output = Self;
    #[inline]
    fn sub(self, rhs: Self) -> Self::Output {
        self.sub_mat4(&rhs)
    }
}

impl SubAssign<DMat4> for DMat4 {
    #[inline]
    fn sub_assign(&mut self, rhs: Self) {
        *self = self.sub_mat4(&rhs);
    }
}

impl Neg for DMat4 {
    type Output = Self;
    #[inline]
    fn neg(self) -> Self::Output {
        Self::from_cols(
            self.x_axis.neg(),
            self.y_axis.neg(),
            self.z_axis.neg(),
            self.w_axis.neg(),
        )
    }
}

impl Mul<DMat4> for DMat4 {
    type Output = Self;
    #[inline]
    fn mul(self, rhs: Self) -> Self::Output {
        self.mul_mat4(&rhs)
    }
}

impl MulAssign<DMat4> for DMat4 {
    #[inline]
    fn mul_assign(&mut self, rhs: Self) {
        *self = self.mul_mat4(&rhs);
    }
}

impl Mul<DVec4> for DMat4 {
    type Output = DVec4;
    #[inline]
    fn mul(self, rhs: DVec4) -> Self::Output {
        self.mul_vec4(rhs)
    }
}

impl Mul<DMat4> for f64 {
    type Output = DMat4;
    #[inline]
    fn mul(self, rhs: DMat4) -> Self::Output {
        rhs.mul_scalar(self)
    }
}

impl Mul<f64> for DMat4 {
    type Output = Self;
    #[inline]
    fn mul(self, rhs: f64) -> Self::Output {
        self.mul_scalar(rhs)
    }
}

impl MulAssign<f64> for DMat4 {
    #[inline]
    fn mul_assign(&mut self, rhs: f64) {
        *self = self.mul_scalar(rhs);
    }
}

impl Div<DMat4> for f64 {
    type Output = DMat4;
    #[inline]
    fn div(self, rhs: DMat4) -> Self::Output {
        rhs.div_scalar(self)
    }
}

impl Div<f64> for DMat4 {
    type Output = Self;
    #[inline]
    fn div(self, rhs: f64) -> Self::Output {
        self.div_scalar(rhs)
    }
}

impl DivAssign<f64> for DMat4 {
    #[inline]
    fn div_assign(&mut self, rhs: f64) {
        *self = self.div_scalar(rhs);
    }
}

impl Sum<Self> for DMat4 {
    fn sum<I>(iter: I) -> Self
    where
        I: Iterator<Item = Self>,
    {
        iter.fold(Self::ZERO, Self::add)
    }
}

impl<'a> Sum<&'a Self> for DMat4 {
    fn sum<I>(iter: I) -> Self
    where
        I: Iterator<Item = &'a Self>,
    {
        iter.fold(Self::ZERO, |a, &b| Self::add(a, b))
    }
}

impl Product for DMat4 {
    fn product<I>(iter: I) -> Self
    where
        I: Iterator<Item = Self>,
    {
        iter.fold(Self::IDENTITY, Self::mul)
    }
}

impl<'a> Product<&'a Self> for DMat4 {
    fn product<I>(iter: I) -> Self
    where
        I: Iterator<Item = &'a Self>,
    {
        iter.fold(Self::IDENTITY, |a, &b| Self::mul(a, b))
    }
}

impl PartialEq for DMat4 {
    #[inline]
    fn eq(&self, rhs: &Self) -> bool {
        self.x_axis.eq(&rhs.x_axis)
            && self.y_axis.eq(&rhs.y_axis)
            && self.z_axis.eq(&rhs.z_axis)
            && self.w_axis.eq(&rhs.w_axis)
    }
}

#[cfg(not(target_arch = "spirv"))]
impl AsRef<[f64; 16]> for DMat4 {
    #[inline]
    fn as_ref(&self) -> &[f64; 16] {
        unsafe { &*(self as *const Self as *const [f64; 16]) }
    }
}

#[cfg(not(target_arch = "spirv"))]
impl AsMut<[f64; 16]> for DMat4 {
    #[inline]
    fn as_mut(&mut self) -> &mut [f64; 16] {
        unsafe { &mut *(self as *mut Self as *mut [f64; 16]) }
    }
}

#[cfg(not(target_arch = "spirv"))]
impl fmt::Debug for DMat4 {
    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
        fmt.debug_struct(stringify!(DMat4))
            .field("x_axis", &self.x_axis)
            .field("y_axis", &self.y_axis)
            .field("z_axis", &self.z_axis)
            .field("w_axis", &self.w_axis)
            .finish()
    }
}

#[cfg(not(target_arch = "spirv"))]
impl fmt::Display for DMat4 {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        if let Some(p) = f.precision() {
            write!(
                f,
                "[{:.*}, {:.*}, {:.*}, {:.*}]",
                p, self.x_axis, p, self.y_axis, p, self.z_axis, p, self.w_axis
            )
        } else {
            write!(
                f,
                "[{}, {}, {}, {}]",
                self.x_axis, self.y_axis, self.z_axis, self.w_axis
            )
        }
    }
}