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
// Generated from mat.rs.tera template. Edit the template, not the generated file.

use crate::{f32::math, swizzles::*, DMat3, EulerRot, Mat2, Mat3, Mat4, Quat, Vec2, Vec3, Vec3A};
#[cfg(not(target_arch = "spirv"))]
use core::fmt;
use core::iter::{Product, Sum};
use core::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};

/// Creates a 3x3 matrix from three column vectors.
#[inline(always)]
pub const fn mat3a(x_axis: Vec3A, y_axis: Vec3A, z_axis: Vec3A) -> Mat3A {
    Mat3A::from_cols(x_axis, y_axis, z_axis)
}

/// A 3x3 column major matrix.
///
/// This 3x3 matrix type features convenience methods for creating and using linear and
/// affine transformations. If you are primarily dealing with 2D affine transformations the
/// [`Affine2`](crate::Affine2) type is much faster and more space efficient than
/// using a 3x3 matrix.
///
/// Linear transformations including 3D rotation and scale can be created using methods
/// such as [`Self::from_diagonal()`], [`Self::from_quat()`], [`Self::from_axis_angle()`],
/// [`Self::from_rotation_x()`], [`Self::from_rotation_y()`], or
/// [`Self::from_rotation_z()`].
///
/// The resulting matrices can be use to transform 3D vectors using regular vector
/// multiplication.
///
/// Affine transformations including 2D translation, rotation and scale can be created
/// using methods such as [`Self::from_translation()`], [`Self::from_angle()`],
/// [`Self::from_scale()`] and [`Self::from_scale_angle_translation()`].
///
/// The [`Self::transform_point2()`] and [`Self::transform_vector2()`] convenience methods
/// are provided for performing affine transforms on 2D vectors and points. These multiply
/// 2D inputs as 3D vectors with an implicit `z` value of `1` for points and `0` for
/// vectors respectively. These methods assume that `Self` contains a valid affine
/// transform.
#[derive(Clone, Copy)]
#[repr(C)]
pub struct Mat3A {
    pub x_axis: Vec3A,
    pub y_axis: Vec3A,
    pub z_axis: Vec3A,
}

impl Mat3A {
    /// A 3x3 matrix with all elements set to `0.0`.
    pub const ZERO: Self = Self::from_cols(Vec3A::ZERO, Vec3A::ZERO, Vec3A::ZERO);

    /// A 3x3 identity matrix, where all diagonal elements are `1`, and all off-diagonal elements are `0`.
    pub const IDENTITY: Self = Self::from_cols(Vec3A::X, Vec3A::Y, Vec3A::Z);

    /// All NAN:s.
    pub const NAN: Self = Self::from_cols(Vec3A::NAN, Vec3A::NAN, Vec3A::NAN);

    #[allow(clippy::too_many_arguments)]
    #[inline(always)]
    const fn new(
        m00: f32,
        m01: f32,
        m02: f32,
        m10: f32,
        m11: f32,
        m12: f32,
        m20: f32,
        m21: f32,
        m22: f32,
    ) -> Self {
        Self {
            x_axis: Vec3A::new(m00, m01, m02),
            y_axis: Vec3A::new(m10, m11, m12),
            z_axis: Vec3A::new(m20, m21, m22),
        }
    }

    /// Creates a 3x3 matrix from three column vectors.
    #[inline(always)]
    pub const fn from_cols(x_axis: Vec3A, y_axis: Vec3A, z_axis: Vec3A) -> Self {
        Self {
            x_axis,
            y_axis,
            z_axis,
        }
    }

    /// Creates a 3x3 matrix from a `[f32; 9]` array stored in column major order.
    /// If your data is stored in row major you will need to `transpose` the returned
    /// matrix.
    #[inline]
    pub const fn from_cols_array(m: &[f32; 9]) -> Self {
        Self::new(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8])
    }

    /// Creates a `[f32; 9]` array storing data in column major order.
    /// If you require data in row major order `transpose` the matrix first.
    #[inline]
    pub const fn to_cols_array(&self) -> [f32; 9] {
        [
            self.x_axis.x,
            self.x_axis.y,
            self.x_axis.z,
            self.y_axis.x,
            self.y_axis.y,
            self.y_axis.z,
            self.z_axis.x,
            self.z_axis.y,
            self.z_axis.z,
        ]
    }

    /// Creates a 3x3 matrix from a `[[f32; 3]; 3]` 3D array stored in column major order.
    /// If your data is in row major order you will need to `transpose` the returned
    /// matrix.
    #[inline]
    pub const fn from_cols_array_2d(m: &[[f32; 3]; 3]) -> Self {
        Self::from_cols(
            Vec3A::from_array(m[0]),
            Vec3A::from_array(m[1]),
            Vec3A::from_array(m[2]),
        )
    }

    /// Creates a `[[f32; 3]; 3]` 3D array storing data in column major order.
    /// If you require data in row major order `transpose` the matrix first.
    #[inline]
    pub const fn to_cols_array_2d(&self) -> [[f32; 3]; 3] {
        [
            self.x_axis.to_array(),
            self.y_axis.to_array(),
            self.z_axis.to_array(),
        ]
    }

    /// Creates a 3x3 matrix with its diagonal set to `diagonal` and all other entries set to 0.
    #[doc(alias = "scale")]
    #[inline]
    pub const fn from_diagonal(diagonal: Vec3) -> Self {
        Self::new(
            diagonal.x, 0.0, 0.0, 0.0, diagonal.y, 0.0, 0.0, 0.0, diagonal.z,
        )
    }

    /// Creates a 3x3 matrix from a 4x4 matrix, discarding the 4th row and column.
    pub fn from_mat4(m: Mat4) -> Self {
        Self::from_cols(m.x_axis.into(), m.y_axis.into(), m.z_axis.into())
    }

    /// Creates a 3D rotation matrix from the given quaternion.
    ///
    /// # Panics
    ///
    /// Will panic if `rotation` is not normalized when `glam_assert` is enabled.
    #[inline]
    pub fn from_quat(rotation: Quat) -> Self {
        glam_assert!(rotation.is_normalized());

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

        Self::from_cols(
            Vec3A::new(1.0 - (yy + zz), xy + wz, xz - wy),
            Vec3A::new(xy - wz, 1.0 - (xx + zz), yz + wx),
            Vec3A::new(xz + wy, yz - wx, 1.0 - (xx + yy)),
        )
    }

    /// Creates a 3D rotation matrix from a normalized rotation `axis` and `angle` (in
    /// radians).
    ///
    /// # Panics
    ///
    /// Will panic if `axis` is not normalized when `glam_assert` is enabled.
    #[inline]
    pub fn from_axis_angle(axis: Vec3, angle: f32) -> Self {
        glam_assert!(axis.is_normalized());

        let (sin, cos) = math::sin_cos(angle);
        let (xsin, ysin, zsin) = axis.mul(sin).into();
        let (x, y, z) = axis.into();
        let (x2, y2, z2) = axis.mul(axis).into();
        let omc = 1.0 - cos;
        let xyomc = x * y * omc;
        let xzomc = x * z * omc;
        let yzomc = y * z * omc;
        Self::from_cols(
            Vec3A::new(x2 * omc + cos, xyomc + zsin, xzomc - ysin),
            Vec3A::new(xyomc - zsin, y2 * omc + cos, yzomc + xsin),
            Vec3A::new(xzomc + ysin, yzomc - xsin, z2 * omc + cos),
        )
    }

    #[inline]
    /// Creates a 3D rotation matrix from the given euler rotation sequence and the angles (in
    /// radians).
    pub fn from_euler(order: EulerRot, a: f32, b: f32, c: f32) -> Self {
        let quat = Quat::from_euler(order, a, b, c);
        Self::from_quat(quat)
    }

    /// Creates a 3D rotation matrix from `angle` (in radians) around the x axis.
    #[inline]
    pub fn from_rotation_x(angle: f32) -> Self {
        let (sina, cosa) = math::sin_cos(angle);
        Self::from_cols(
            Vec3A::X,
            Vec3A::new(0.0, cosa, sina),
            Vec3A::new(0.0, -sina, cosa),
        )
    }

    /// Creates a 3D rotation matrix from `angle` (in radians) around the y axis.
    #[inline]
    pub fn from_rotation_y(angle: f32) -> Self {
        let (sina, cosa) = math::sin_cos(angle);
        Self::from_cols(
            Vec3A::new(cosa, 0.0, -sina),
            Vec3A::Y,
            Vec3A::new(sina, 0.0, cosa),
        )
    }

    /// Creates a 3D rotation matrix from `angle` (in radians) around the z axis.
    #[inline]
    pub fn from_rotation_z(angle: f32) -> Self {
        let (sina, cosa) = math::sin_cos(angle);
        Self::from_cols(
            Vec3A::new(cosa, sina, 0.0),
            Vec3A::new(-sina, cosa, 0.0),
            Vec3A::Z,
        )
    }

    /// Creates an affine transformation matrix from the given 2D `translation`.
    ///
    /// The resulting matrix can be used to transform 2D points and vectors. See
    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
    #[inline]
    pub fn from_translation(translation: Vec2) -> Self {
        Self::from_cols(
            Vec3A::X,
            Vec3A::Y,
            Vec3A::new(translation.x, translation.y, 1.0),
        )
    }

    /// Creates an affine transformation matrix from the given 2D rotation `angle` (in
    /// radians).
    ///
    /// The resulting matrix can be used to transform 2D points and vectors. See
    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
    #[inline]
    pub fn from_angle(angle: f32) -> Self {
        let (sin, cos) = math::sin_cos(angle);
        Self::from_cols(
            Vec3A::new(cos, sin, 0.0),
            Vec3A::new(-sin, cos, 0.0),
            Vec3A::Z,
        )
    }

    /// Creates an affine transformation matrix from the given 2D `scale`, rotation `angle` (in
    /// radians) and `translation`.
    ///
    /// The resulting matrix can be used to transform 2D points and vectors. See
    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
    #[inline]
    pub fn from_scale_angle_translation(scale: Vec2, angle: f32, translation: Vec2) -> Self {
        let (sin, cos) = math::sin_cos(angle);
        Self::from_cols(
            Vec3A::new(cos * scale.x, sin * scale.x, 0.0),
            Vec3A::new(-sin * scale.y, cos * scale.y, 0.0),
            Vec3A::new(translation.x, translation.y, 1.0),
        )
    }

    /// Creates an affine transformation matrix from the given non-uniform 2D `scale`.
    ///
    /// The resulting matrix can be used to transform 2D points and vectors. See
    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
    ///
    /// # Panics
    ///
    /// Will panic if all elements of `scale` are zero when `glam_assert` is enabled.
    #[inline]
    pub fn from_scale(scale: Vec2) -> Self {
        // Do not panic as long as any component is non-zero
        glam_assert!(scale.cmpne(Vec2::ZERO).any());

        Self::from_cols(
            Vec3A::new(scale.x, 0.0, 0.0),
            Vec3A::new(0.0, scale.y, 0.0),
            Vec3A::Z,
        )
    }

    /// Creates an affine transformation matrix from the given 2x2 matrix.
    ///
    /// The resulting matrix can be used to transform 2D points and vectors. See
    /// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
    #[inline]
    pub fn from_mat2(m: Mat2) -> Self {
        Self::from_cols((m.x_axis, 0.0).into(), (m.y_axis, 0.0).into(), Vec3A::Z)
    }

    /// Creates a 3x3 matrix from the first 9 values in `slice`.
    ///
    /// # Panics
    ///
    /// Panics if `slice` is less than 9 elements long.
    #[inline]
    pub const fn from_cols_slice(slice: &[f32]) -> Self {
        Self::new(
            slice[0], slice[1], slice[2], slice[3], slice[4], slice[5], slice[6], slice[7],
            slice[8],
        )
    }

    /// Writes the columns of `self` to the first 9 elements in `slice`.
    ///
    /// # Panics
    ///
    /// Panics if `slice` is less than 9 elements long.
    #[inline]
    pub fn write_cols_to_slice(self, slice: &mut [f32]) {
        slice[0] = self.x_axis.x;
        slice[1] = self.x_axis.y;
        slice[2] = self.x_axis.z;
        slice[3] = self.y_axis.x;
        slice[4] = self.y_axis.y;
        slice[5] = self.y_axis.z;
        slice[6] = self.z_axis.x;
        slice[7] = self.z_axis.y;
        slice[8] = self.z_axis.z;
    }

    /// Returns the matrix column for the given `index`.
    ///
    /// # Panics
    ///
    /// Panics if `index` is greater than 2.
    #[inline]
    pub fn col(&self, index: usize) -> Vec3A {
        match index {
            0 => self.x_axis,
            1 => self.y_axis,
            2 => self.z_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 2.
    #[inline]
    pub fn col_mut(&mut self, index: usize) -> &mut Vec3A {
        match index {
            0 => &mut self.x_axis,
            1 => &mut self.y_axis,
            2 => &mut self.z_axis,
            _ => panic!("index out of bounds"),
        }
    }

    /// Returns the matrix row for the given `index`.
    ///
    /// # Panics
    ///
    /// Panics if `index` is greater than 2.
    #[inline]
    pub fn row(&self, index: usize) -> Vec3A {
        match index {
            0 => Vec3A::new(self.x_axis.x, self.y_axis.x, self.z_axis.x),
            1 => Vec3A::new(self.x_axis.y, self.y_axis.y, self.z_axis.y),
            2 => Vec3A::new(self.x_axis.z, self.y_axis.z, self.z_axis.z),
            _ => 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]
    pub fn is_finite(&self) -> bool {
        self.x_axis.is_finite() && self.y_axis.is_finite() && self.z_axis.is_finite()
    }

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

    /// Returns the transpose of `self`.
    #[must_use]
    #[inline]
    pub fn transpose(&self) -> Self {
        Self {
            x_axis: Vec3A::new(self.x_axis.x, self.y_axis.x, self.z_axis.x),
            y_axis: Vec3A::new(self.x_axis.y, self.y_axis.y, self.z_axis.y),
            z_axis: Vec3A::new(self.x_axis.z, self.y_axis.z, self.z_axis.z),
        }
    }

    /// Returns the determinant of `self`.
    #[inline]
    pub fn determinant(&self) -> f32 {
        self.z_axis.dot(self.x_axis.cross(self.y_axis))
    }

    /// 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]
    #[inline]
    pub fn inverse(&self) -> Self {
        let tmp0 = self.y_axis.cross(self.z_axis);
        let tmp1 = self.z_axis.cross(self.x_axis);
        let tmp2 = self.x_axis.cross(self.y_axis);
        let det = self.z_axis.dot(tmp2);
        glam_assert!(det != 0.0);
        let inv_det = Vec3A::splat(det.recip());
        Self::from_cols(tmp0.mul(inv_det), tmp1.mul(inv_det), tmp2.mul(inv_det)).transpose()
    }

    /// Transforms the given 2D vector as a point.
    ///
    /// This is the equivalent of multiplying `rhs` as a 3D vector where `z` is `1`.
    ///
    /// This method assumes that `self` contains a valid affine transform.
    ///
    /// # Panics
    ///
    /// Will panic if the 2nd row of `self` is not `(0, 0, 1)` when `glam_assert` is enabled.
    #[inline]
    pub fn transform_point2(&self, rhs: Vec2) -> Vec2 {
        glam_assert!(self.row(2).abs_diff_eq(Vec3A::Z, 1e-6));
        Mat2::from_cols(self.x_axis.xy(), self.y_axis.xy()) * rhs + self.z_axis.xy()
    }

    /// Rotates the given 2D vector.
    ///
    /// This is the equivalent of multiplying `rhs` as a 3D vector where `z` is `0`.
    ///
    /// This method assumes that `self` contains a valid affine transform.
    ///
    /// # Panics
    ///
    /// Will panic if the 2nd row of `self` is not `(0, 0, 1)` when `glam_assert` is enabled.
    #[inline]
    pub fn transform_vector2(&self, rhs: Vec2) -> Vec2 {
        glam_assert!(self.row(2).abs_diff_eq(Vec3A::Z, 1e-6));
        Mat2::from_cols(self.x_axis.xy(), self.y_axis.xy()) * rhs
    }

    /// Transforms a 3D vector.
    #[inline]
    pub fn mul_vec3(&self, rhs: Vec3) -> Vec3 {
        self.mul_vec3a(rhs.into()).into()
    }

    /// Transforms a [`Vec3A`].
    #[inline]
    pub fn mul_vec3a(&self, rhs: Vec3A) -> Vec3A {
        let mut res = self.x_axis.mul(rhs.xxx());
        res = res.add(self.y_axis.mul(rhs.yyy()));
        res = res.add(self.z_axis.mul(rhs.zzz()));
        res
    }

    /// Multiplies two 3x3 matrices.
    #[inline]
    pub fn mul_mat3(&self, rhs: &Self) -> Self {
        Self::from_cols(
            self.mul(rhs.x_axis),
            self.mul(rhs.y_axis),
            self.mul(rhs.z_axis),
        )
    }

    /// Adds two 3x3 matrices.
    #[inline]
    pub fn add_mat3(&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),
        )
    }

    /// Subtracts two 3x3 matrices.
    #[inline]
    pub fn sub_mat3(&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),
        )
    }

    /// Multiplies a 3x3 matrix by a scalar.
    #[inline]
    pub fn mul_scalar(&self, rhs: f32) -> Self {
        Self::from_cols(
            self.x_axis.mul(rhs),
            self.y_axis.mul(rhs),
            self.z_axis.mul(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]
    pub fn abs_diff_eq(&self, rhs: Self, max_abs_diff: f32) -> 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)
    }

    #[inline]
    pub fn as_dmat3(&self) -> DMat3 {
        DMat3::from_cols(
            self.x_axis.as_dvec3(),
            self.y_axis.as_dvec3(),
            self.z_axis.as_dvec3(),
        )
    }
}

impl Default for Mat3A {
    #[inline]
    fn default() -> Self {
        Self::IDENTITY
    }
}

impl Add<Mat3A> for Mat3A {
    type Output = Self;
    #[inline]
    fn add(self, rhs: Self) -> Self::Output {
        self.add_mat3(&rhs)
    }
}

impl AddAssign<Mat3A> for Mat3A {
    #[inline]
    fn add_assign(&mut self, rhs: Self) {
        *self = self.add_mat3(&rhs);
    }
}

impl Sub<Mat3A> for Mat3A {
    type Output = Self;
    #[inline]
    fn sub(self, rhs: Self) -> Self::Output {
        self.sub_mat3(&rhs)
    }
}

impl SubAssign<Mat3A> for Mat3A {
    #[inline]
    fn sub_assign(&mut self, rhs: Self) {
        *self = self.sub_mat3(&rhs);
    }
}

impl Neg for Mat3A {
    type Output = Self;
    #[inline]
    fn neg(self) -> Self::Output {
        Self::from_cols(self.x_axis.neg(), self.y_axis.neg(), self.z_axis.neg())
    }
}

impl Mul<Mat3A> for Mat3A {
    type Output = Self;
    #[inline]
    fn mul(self, rhs: Self) -> Self::Output {
        self.mul_mat3(&rhs)
    }
}

impl MulAssign<Mat3A> for Mat3A {
    #[inline]
    fn mul_assign(&mut self, rhs: Self) {
        *self = self.mul_mat3(&rhs);
    }
}

impl Mul<Vec3A> for Mat3A {
    type Output = Vec3A;
    #[inline]
    fn mul(self, rhs: Vec3A) -> Self::Output {
        self.mul_vec3a(rhs)
    }
}

impl Mul<Mat3A> for f32 {
    type Output = Mat3A;
    #[inline]
    fn mul(self, rhs: Mat3A) -> Self::Output {
        rhs.mul_scalar(self)
    }
}

impl Mul<f32> for Mat3A {
    type Output = Self;
    #[inline]
    fn mul(self, rhs: f32) -> Self::Output {
        self.mul_scalar(rhs)
    }
}

impl MulAssign<f32> for Mat3A {
    #[inline]
    fn mul_assign(&mut self, rhs: f32) {
        *self = self.mul_scalar(rhs);
    }
}

impl Mul<Vec3> for Mat3A {
    type Output = Vec3;
    #[inline]
    fn mul(self, rhs: Vec3) -> Vec3 {
        self.mul_vec3a(rhs.into()).into()
    }
}

impl From<Mat3> for Mat3A {
    #[inline]
    fn from(m: Mat3) -> Self {
        Self {
            x_axis: m.x_axis.into(),
            y_axis: m.y_axis.into(),
            z_axis: m.z_axis.into(),
        }
    }
}

impl Sum<Self> for Mat3A {
    fn sum<I>(iter: I) -> Self
    where
        I: Iterator<Item = Self>,
    {
        iter.fold(Self::ZERO, Self::add)
    }
}

impl<'a> Sum<&'a Self> for Mat3A {
    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 Mat3A {
    fn product<I>(iter: I) -> Self
    where
        I: Iterator<Item = Self>,
    {
        iter.fold(Self::IDENTITY, Self::mul)
    }
}

impl<'a> Product<&'a Self> for Mat3A {
    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 Mat3A {
    #[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)
    }
}

#[cfg(not(target_arch = "spirv"))]
impl fmt::Debug for Mat3A {
    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
        fmt.debug_struct(stringify!(Mat3A))
            .field("x_axis", &self.x_axis)
            .field("y_axis", &self.y_axis)
            .field("z_axis", &self.z_axis)
            .finish()
    }
}

#[cfg(not(target_arch = "spirv"))]
impl fmt::Display for Mat3A {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(f, "[{}, {}, {}]", self.x_axis, self.y_axis, self.z_axis)
    }
}