[Type] Matrix: clean, templated functions and add double benchmarks

[fredroy]

For reference:

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Benchmark                                                   Time             CPU   Iterations
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BM_Matrix_typemat3x3_construct<float>/512               0.579 us        0.579 us      1189106
BM_Matrix_typemat3x3_construct<float>/1024               1.16 us         1.16 us       597386
BM_Matrix_typemat3x3_construct<float>/2048               2.32 us         2.32 us       301394
BM_Matrix_typemat3x3_construct<double>/512              0.496 us        0.496 us      1408265
BM_Matrix_typemat3x3_construct<double>/1024             0.988 us        0.988 us       707940
BM_Matrix_typemat3x3_construct<double>/2048              1.97 us         1.97 us       355088
BM_Matrix_typemat3x3_construct_noinit<float>/512        0.579 us        0.579 us      1222639
BM_Matrix_typemat3x3_construct_noinit<float>/1024        1.16 us         1.16 us       602978
BM_Matrix_typemat3x3_construct_noinit<float>/2048        2.32 us         2.32 us       301552
BM_Matrix_typemat3x3_construct_noinit<double>/512       0.487 us        0.487 us      1432345
BM_Matrix_typemat3x3_construct_noinit<double>/1024      0.971 us        0.970 us       722325
BM_Matrix_typemat3x3_construct_noinit<double>/2048       1.92 us         1.92 us       361677
BM_Matrix_typemat3x3_transpose<float>/512               0.588 us        0.588 us      1184440
BM_Matrix_typemat3x3_transpose<float>/1024               1.17 us         1.17 us       596101
BM_Matrix_typemat3x3_transpose<float>/2048               2.65 us         2.64 us       265830
BM_Matrix_typemat3x3_transpose<double>/512              0.873 us        0.873 us       797691
BM_Matrix_typemat3x3_transpose<double>/1024              1.97 us         1.97 us       353188
BM_Matrix_typemat3x3_transpose<double>/2048              3.97 us         3.97 us       176653
BM_Matrix_typemat3x3_invert<float>/512                   2.62 us         2.62 us       268439
BM_Matrix_typemat3x3_invert<float>/1024                  5.21 us         5.21 us       133543
BM_Matrix_typemat3x3_invert<float>/2048                  10.4 us         10.4 us        66940
BM_Matrix_typemat3x3_invert<double>/512                  3.47 us         3.47 us       200442
BM_Matrix_typemat3x3_invert<double>/1024                 6.92 us         6.92 us       100351
BM_Matrix_typemat3x3_invert<double>/2048                 13.9 us         13.9 us        50062
BM_Matrix_typemat3x3_determinant<float>/512             0.649 us        0.649 us      1073947
BM_Matrix_typemat3x3_determinant<float>/1024             1.30 us         1.30 us       539439
BM_Matrix_typemat3x3_determinant<float>/2048             2.60 us         2.60 us       268295
BM_Matrix_typemat3x3_determinant<double>/512            0.646 us        0.646 us      1089623
BM_Matrix_typemat3x3_determinant<double>/1024            1.34 us         1.34 us       516699
BM_Matrix_typemat3x3_determinant<double>/2048            2.67 us         2.67 us       260411
BM_Matrix_typemat_matmult<float, 3>/512                  1.54 us         1.54 us       452324
BM_Matrix_typemat_matmult<float, 3>/1024                 3.08 us         3.08 us       226642
BM_Matrix_typemat_matmult<float, 3>/2048                 6.16 us         6.16 us       112635
BM_Matrix_typemat_matmult<double, 3>/512                 1.73 us         1.73 us       401970
BM_Matrix_typemat_matmult<double, 3>/1024                3.47 us         3.47 us       201947
BM_Matrix_typemat_matmult<double, 3>/2048                6.92 us         6.92 us        99931
BM_Matrix_typemat_matmult<float, 6>/512                  23.9 us         23.9 us        29448
BM_Matrix_typemat_matmult<float, 6>/1024                 47.9 us         47.9 us        14537
BM_Matrix_typemat_matmult<float, 6>/2048                 95.3 us         95.3 us         7270
BM_Matrix_typemat_matmult<double, 6>/512                 24.6 us         24.6 us        28482
BM_Matrix_typemat_matmult<double, 6>/1024                49.3 us         49.3 us        14211
BM_Matrix_typemat_matmult<double, 6>/2048                98.6 us         98.5 us         7065
BM_Matrix_typemat_matmult<float, 24>/512                 2088 us         2088 us          333
BM_Matrix_typemat_matmult<float, 24>/1024                4281 us         4281 us          166
BM_Matrix_typemat_matmult<float, 24>/2048                8496 us         8495 us           79
BM_Matrix_typemat_matmult<double, 24>/512                1880 us         1879 us          371
BM_Matrix_typemat_matmult<double, 24>/1024               3784 us         3784 us          185
BM_Matrix_typemat_matmult<double, 24>/2048               7746 us         7745 us           89
BM_Matrix_typemat_vecmult<float, 3>/512                 0.722 us        0.722 us       957334
BM_Matrix_typemat_vecmult<float, 3>/1024                 1.52 us         1.52 us       459710
BM_Matrix_typemat_vecmult<float, 3>/2048                 3.02 us         3.02 us       230703
BM_Matrix_typemat_vecmult<double, 3>/512                0.809 us        0.809 us       854849
BM_Matrix_typemat_vecmult<double, 3>/1024                1.67 us         1.67 us       416414
BM_Matrix_typemat_vecmult<double, 3>/2048                3.34 us         3.34 us       209030
BM_Matrix_typemat_vecmult<float, 6>/512                  2.78 us         2.78 us       270710
BM_Matrix_typemat_vecmult<float, 6>/1024                 5.52 us         5.52 us       103825
BM_Matrix_typemat_vecmult<float, 6>/2048                 10.4 us         10.4 us        67237
BM_Matrix_typemat_vecmult<double, 6>/512                 2.90 us         2.90 us       241592
BM_Matrix_typemat_vecmult<double, 6>/1024                5.82 us         5.82 us       119400
BM_Matrix_typemat_vecmult<double, 6>/2048                11.6 us         11.6 us        59630
BM_Matrix_typemat_vecmult<float, 24>/512                 84.2 us         84.2 us         8626
BM_Matrix_typemat_vecmult<float, 24>/1024                 168 us          168 us         4030
BM_Matrix_typemat_vecmult<float, 24>/2048                 337 us          337 us         2099
BM_Matrix_typemat_vecmult<double, 24>/512                85.3 us         85.3 us         8111
BM_Matrix_typemat_vecmult<double, 24>/1024                170 us          170 us         4139
BM_Matrix_typemat_vecmult<double, 24>/2048                342 us          342 us         2041
BM_Matrix_typemat3x3_assign<float>/512                  0.575 us        0.575 us      1206089
BM_Matrix_typemat3x3_assign<float>/1024                  1.16 us         1.16 us       603018
BM_Matrix_typemat3x3_assign<float>/2048                  2.31 us         2.31 us       302253
BM_Matrix_typemat3x3_assign<double>/512                 0.488 us        0.488 us      1434481
BM_Matrix_typemat3x3_assign<double>/1024                0.963 us        0.963 us       721575
BM_Matrix_typemat3x3_assign<double>/2048                 1.89 us         1.89 us       368600
BM_Matrix_typemat3x3_multTranspose<float>/512            2.50 us         2.50 us       280416
BM_Matrix_typemat3x3_multTranspose<float>/1024           5.12 us         5.12 us       135750
BM_Matrix_typemat3x3_multTranspose<float>/2048           10.2 us         10.2 us        68247
BM_Matrix_typemat3x3_multTranspose<double>/512           2.65 us         2.65 us       266250
BM_Matrix_typemat3x3_multTranspose<double>/1024          5.26 us         5.26 us       131820
BM_Matrix_typemat3x3_multTranspose<double>/2048          10.4 us         10.4 us        66779
BM_Matrix_eigenmat3x3_construct<float>/512              0.575 us        0.575 us      1210528
BM_Matrix_eigenmat3x3_construct<float>/1024              1.15 us         1.15 us       604338
BM_Matrix_eigenmat3x3_construct<float>/2048              2.31 us         2.31 us       304021
BM_Matrix_eigenmat3x3_construct<double>/512             0.579 us        0.578 us      1205414
BM_Matrix_eigenmat3x3_construct<double>/1024             1.15 us         1.15 us       603990
BM_Matrix_eigenmat3x3_construct<double>/2048             2.30 us         2.30 us       302897
BM_Matrix_eigenmat3x3_transpose<float>/512              0.577 us        0.577 us      1205916
BM_Matrix_eigenmat3x3_transpose<float>/1024              1.16 us         1.16 us       603725
BM_Matrix_eigenmat3x3_transpose<float>/2048              2.31 us         2.31 us       300089
BM_Matrix_eigenmat3x3_transpose<double>/512             0.418 us        0.418 us      1670150
BM_Matrix_eigenmat3x3_transpose<double>/1024             1.02 us         1.02 us       683479
BM_Matrix_eigenmat3x3_transpose<double>/2048             2.05 us         2.05 us       343103
BM_Matrix_eigenmat3x3_invert<float>/512                  2.22 us         2.22 us       316699
BM_Matrix_eigenmat3x3_invert<float>/1024                 4.42 us         4.42 us       157892
BM_Matrix_eigenmat3x3_invert<float>/2048                 8.87 us         8.87 us        78670
BM_Matrix_eigenmat3x3_invert<double>/512                 1.61 us         1.61 us       435067
BM_Matrix_eigenmat3x3_invert<double>/1024                3.23 us         3.23 us       215697
BM_Matrix_eigenmat3x3_invert<double>/2048                6.45 us         6.45 us       107563
BM_Matrix_eigenmat3x3_determinant<float>/512            0.523 us        0.523 us      1330224
BM_Matrix_eigenmat3x3_determinant<float>/1024            1.04 us         1.04 us       668177
BM_Matrix_eigenmat3x3_determinant<float>/2048            2.13 us         2.13 us       326373
BM_Matrix_eigenmat3x3_determinant<double>/512           0.524 us        0.524 us      1331359
BM_Matrix_eigenmat3x3_determinant<double>/1024           1.09 us         1.09 us       636367
BM_Matrix_eigenmat3x3_determinant<double>/2048           2.20 us         2.20 us       317365
BM_Matrix_eigenmat_matmult<float, 3>/512                 2.06 us         2.06 us       337531
BM_Matrix_eigenmat_matmult<float, 3>/1024                4.20 us         4.19 us       166559
BM_Matrix_eigenmat_matmult<float, 3>/2048                8.40 us         8.40 us        83194
BM_Matrix_eigenmat_matmult<double, 3>/512                1.75 us         1.75 us       400442
BM_Matrix_eigenmat_matmult<double, 3>/1024               3.48 us         3.48 us       199876
BM_Matrix_eigenmat_matmult<double, 3>/2048               6.99 us         6.99 us        99800
BM_Matrix_eigenmat_matmult<float, 6>/512                 10.9 us         10.9 us        59584
BM_Matrix_eigenmat_matmult<float, 6>/1024                21.2 us         21.2 us        33112
BM_Matrix_eigenmat_matmult<float, 6>/2048                43.2 us         43.2 us        16582
BM_Matrix_eigenmat_matmult<double, 6>/512                11.9 us         11.9 us        58446
BM_Matrix_eigenmat_matmult<double, 6>/1024               23.9 us         23.9 us        29227
BM_Matrix_eigenmat_matmult<double, 6>/2048               48.1 us         48.0 us        14585
BM_Matrix_eigenmat_matmult<float, 24>/512                 361 us          361 us         1937
BM_Matrix_eigenmat_matmult<float, 24>/1024                722 us          722 us          969
BM_Matrix_eigenmat_matmult<float, 24>/2048               1476 us         1476 us          474
BM_Matrix_eigenmat_matmult<double, 24>/512                712 us          712 us          975
BM_Matrix_eigenmat_matmult<double, 24>/1024              1437 us         1437 us          480
BM_Matrix_eigenmat_matmult<double, 24>/2048              3081 us         3081 us          227
BM_Matrix_eigenmat_vecmult<float, 3>/512                0.802 us        0.801 us       864473
BM_Matrix_eigenmat_vecmult<float, 3>/1024                1.66 us         1.66 us       422782
BM_Matrix_eigenmat_vecmult<float, 3>/2048                3.28 us         3.28 us       213442
BM_Matrix_eigenmat_vecmult<double, 3>/512               0.732 us        0.732 us       951869
BM_Matrix_eigenmat_vecmult<double, 3>/1024               1.49 us         1.49 us       467593
BM_Matrix_eigenmat_vecmult<double, 3>/2048               2.99 us         2.99 us       234730
BM_Matrix_eigenmat_vecmult<float, 6>/512                 1.79 us         1.79 us       388093
BM_Matrix_eigenmat_vecmult<float, 6>/1024                3.60 us         3.60 us       194217
BM_Matrix_eigenmat_vecmult<float, 6>/2048                7.04 us         7.04 us        96671
BM_Matrix_eigenmat_vecmult<double, 6>/512                1.95 us         1.95 us       358813
BM_Matrix_eigenmat_vecmult<double, 6>/1024               3.91 us         3.91 us       180632
BM_Matrix_eigenmat_vecmult<double, 6>/2048               7.79 us         7.79 us        88419
BM_Matrix_eigenmat_vecmult<float, 24>/512                18.8 us         18.8 us        37207
BM_Matrix_eigenmat_vecmult<float, 24>/1024               40.1 us         40.1 us        17504
BM_Matrix_eigenmat_vecmult<float, 24>/2048               80.6 us         80.6 us         8431
BM_Matrix_eigenmat_vecmult<double, 24>/512               32.2 us         32.2 us        21553
BM_Matrix_eigenmat_vecmult<double, 24>/1024              69.1 us         69.1 us        10038
BM_Matrix_eigenmat_vecmult<double, 24>/2048               143 us          143 us         4845
BM_Matrix_eigenmat3x3_assign<float>/512                 0.580 us        0.579 us      1200527
BM_Matrix_eigenmat3x3_assign<float>/1024                 1.15 us         1.15 us       603957
BM_Matrix_eigenmat3x3_assign<float>/2048                 2.31 us         2.31 us       302645
BM_Matrix_eigenmat3x3_assign<double>/512                0.492 us        0.492 us      1423180
BM_Matrix_eigenmat3x3_assign<double>/1024               0.981 us        0.981 us       714472
BM_Matrix_eigenmat3x3_assign<double>/2048                1.95 us         1.95 us       357253
BM_Matrix_eigenmat3x3_multTranspose<float>/512           2.04 us         2.04 us       343530
BM_Matrix_eigenmat3x3_multTranspose<float>/1024          4.07 us         4.07 us       171680
BM_Matrix_eigenmat3x3_multTranspose<float>/2048          8.16 us         8.16 us        84007
BM_Matrix_eigenmat3x3_multTranspose<double>/512          1.96 us         1.96 us       356372
BM_Matrix_eigenmat3x3_multTranspose<double>/1024         3.99 us         3.99 us       179840
BM_Matrix_eigenmat3x3_multTranspose<double>/2048         9.08 us         9.08 us        74699

(On a i7 13700k, Ubuntu 22.04, gcc12, LTO, -O3)