macOS 13.3 shipped with an updated Accelerate framework that provides BLAS / LAPACK.  The new version is aligned with Netlib's v3.9.1 and also supports ILP64.  The changes here adopt those new interfaces when available.

- New interfaces are used when ACCELERATE_NEW_LAPACK is defined.
- ILP64 interfaces are used when both ACCELERATE_NEW_LAPACK and ACCELERATE_LAPACK_ILP64 are defined.

macOS 13.3 now ships with 3 different sets of BLAS / LAPACK interfaces:
- LP64 / LAPACK v3.2.1 - legacy interfaces kept for compatibility
- LP64 / LAPACK v3.9.1 - new interfaces
- ILP64 / LAPACK v3.9.1 - new interfaces with ILP64 support

For LP64, we want to support building against macOS 13.3+ SDK, but having it work on pre-13.3 systems.  To that end, we create wrappers for each API that do a runtime check on which set of API is available and should be used.

ILP64 is only supported on macOS 13.3+ and does not use additional wrappers.

We've included support for both distutils and Meson builds.

All tests pass on Apple silicon and Intel based Macs.

Benchmarks
ILP64 Accelerate vs OpenBLAS
       before           after         ratio
     [73f0cf4f]       [d1572653]
     <openblas-ilp64>       <accelerate-ilp64>
              n/a              n/a      n/a  bench_linalg.Linalg.time_op('det', 'float16')
              n/a              n/a      n/a  bench_linalg.Linalg.time_op('pinv', 'float16')
              n/a              n/a      n/a  bench_linalg.Linalg.time_op('svd', 'float16')
           failed           failed      n/a  bench_linalg.LinalgSmallArrays.time_det_small_array
+      3.96±0.1μs       5.04±0.4μs     1.27  bench_linalg.Linalg.time_op('norm', 'float32')
      1.43±0.04ms         1.43±0ms     1.00  bench_linalg.Einsum.time_einsum_outer(<class 'numpy.float32'>)
       12.7±0.4μs       12.7±0.3μs     1.00  bench_linalg.Einsum.time_einsum_sum_mul2(<class 'numpy.float32'>)
       24.1±0.8μs      24.1±0.04μs     1.00  bench_linalg.Linalg.time_op('norm', 'float16')
       9.48±0.2ms       9.48±0.3ms     1.00  bench_linalg.Einsum.time_einsum_outer(<class 'numpy.float64'>)
         609±20μs          609±2μs     1.00  bench_linalg.Einsum.time_einsum_noncon_outer(<class 'numpy.float32'>)
         64.9±2μs      64.7±0.07μs     1.00  bench_linalg.Einsum.time_einsum_contig_outstride0(<class 'numpy.float64'>)
      1.24±0.03ms      1.24±0.01ms     1.00  bench_linalg.Einsum.time_einsum_noncon_outer(<class 'numpy.float64'>)
          102±3μs        102±0.2μs     1.00  bench_linalg.Einsum.time_einsum_contig_contig(<class 'numpy.float64'>)
       21.9±0.8μs      21.8±0.02μs     1.00  bench_linalg.Einsum.time_einsum_multiply(<class 'numpy.float64'>)
       22.8±0.2ms       22.7±0.3ms     0.99  bench_linalg.Eindot.time_einsum_ijk_jil_kl
       13.3±0.4μs      13.3±0.02μs     0.99  bench_linalg.Einsum.time_einsum_sum_mul2(<class 'numpy.float64'>)
       9.56±0.3μs       9.49±0.2μs     0.99  bench_linalg.Einsum.time_einsum_noncon_contig_contig(<class 'numpy.float64'>)
       7.31±0.2μs      7.26±0.08μs     0.99  bench_linalg.Einsum.time_einsum_noncon_contig_outstride0(<class 'numpy.float32'>)
       5.60±0.2ms      5.55±0.02ms     0.99  bench_linalg.Eindot.time_einsum_ij_jk_a_b
         37.1±1μs       36.7±0.1μs     0.99  bench_linalg.Einsum.time_einsum_contig_outstride0(<class 'numpy.float32'>)
       13.5±0.4μs      13.4±0.05μs     0.99  bench_linalg.Einsum.time_einsum_sum_mul(<class 'numpy.float64'>)
      1.03±0.03μs         1.02±0μs     0.99  bench_linalg.LinalgSmallArrays.time_norm_small_array
         51.6±2μs      51.0±0.09μs     0.99  bench_linalg.Einsum.time_einsum_contig_contig(<class 'numpy.float32'>)
       15.2±0.5μs      15.0±0.04μs     0.99  bench_linalg.Einsum.time_einsum_noncon_sum_mul2(<class 'numpy.float64'>)
       13.9±0.4μs      13.7±0.02μs     0.99  bench_linalg.Einsum.time_einsum_noncon_sum_mul2(<class 'numpy.float32'>)
         415±10μs        409±0.4μs     0.99  bench_linalg.Eindot.time_einsum_i_ij_j
       9.29±0.3μs      9.01±0.03μs     0.97  bench_linalg.Einsum.time_einsum_noncon_mul(<class 'numpy.float64'>)
       18.2±0.6μs      17.6±0.04μs     0.97  bench_linalg.Einsum.time_einsum_multiply(<class 'numpy.float32'>)
         509±40μs         492±10μs     0.97  bench_linalg.Einsum.time_einsum_mul(<class 'numpy.float64'>)
       9.63±0.3μs      9.28±0.09μs     0.96  bench_linalg.Einsum.time_einsum_noncon_contig_contig(<class 'numpy.float32'>)
       9.08±0.2μs      8.73±0.02μs     0.96  bench_linalg.Einsum.time_einsum_noncon_mul(<class 'numpy.float32'>)
       15.6±0.5μs      15.0±0.04μs     0.96  bench_linalg.Einsum.time_einsum_noncon_sum_mul(<class 'numpy.float64'>)
       7.74±0.2μs      7.39±0.04μs     0.95  bench_linalg.Einsum.time_einsum_noncon_contig_outstride0(<class 'numpy.float64'>)
       18.6±0.6μs      17.7±0.03μs     0.95  bench_linalg.Einsum.time_einsum_noncon_multiply(<class 'numpy.float32'>)
       14.5±0.4μs      13.7±0.03μs     0.95  bench_linalg.Einsum.time_einsum_noncon_sum_mul(<class 'numpy.float32'>)
       13.3±0.6μs       12.5±0.3μs     0.94  bench_linalg.Einsum.time_einsum_sum_mul(<class 'numpy.float32'>)
       23.5±0.5μs      21.9±0.05μs     0.93  bench_linalg.Einsum.time_einsum_noncon_multiply(<class 'numpy.float64'>)
         264±20μs          243±4μs     0.92  bench_linalg.Einsum.time_einsum_mul(<class 'numpy.float32'>)
-        177±50μs        132±0.6μs     0.75  bench_linalg.Eindot.time_dot_trans_at_a
-      10.7±0.3μs      7.13±0.01μs     0.67  bench_linalg.Linalg.time_op('norm', 'int16')
-        97.5±2μs       64.7±0.1μs     0.66  bench_linalg.Eindot.time_matmul_trans_a_at
-      8.87±0.3μs         5.76±0μs     0.65  bench_linalg.Linalg.time_op('norm', 'longfloat')
-      8.90±0.3μs      5.77±0.01μs     0.65  bench_linalg.Linalg.time_op('norm', 'float64')
-      8.48±0.3μs      5.40±0.01μs     0.64  bench_linalg.Linalg.time_op('norm', 'int64')
-         106±2μs         66.5±8μs     0.63  bench_linalg.Eindot.time_inner_trans_a_a
-      8.25±0.3μs         5.16±0μs     0.62  bench_linalg.Linalg.time_op('norm', 'int32')
-         103±5ms       64.6±0.5ms     0.62  bench_import.Import.time_linalg
-         106±3μs       66.0±0.1μs     0.62  bench_linalg.Eindot.time_dot_trans_a_at
-        202±20μs        124±0.6μs     0.61  bench_linalg.Eindot.time_matmul_trans_at_a
-       31.5±10μs      19.3±0.02μs     0.61  bench_linalg.Eindot.time_dot_d_dot_b_c
-       32.4±20μs      19.7±0.03μs     0.61  bench_linalg.Eindot.time_matmul_d_matmul_b_c
-        5.05±1ms      3.06±0.09ms     0.61  bench_linalg.Linalg.time_op('svd', 'complex128')
-      5.35±0.9ms      3.09±0.09ms     0.58  bench_linalg.Linalg.time_op('svd', 'complex64')
-        6.37±3ms       3.27±0.1ms     0.51  bench_linalg.Linalg.time_op('pinv', 'complex128')
-        7.26±8ms       3.24±0.1ms     0.45  bench_linalg.Linalg.time_op('pinv', 'complex64')
-       519±100μs        219±0.8μs     0.42  bench_linalg.Linalg.time_op('det', 'complex64')
-      31.3±0.9μs       12.8±0.1μs     0.41  bench_linalg.Linalg.time_op('norm', 'complex128')
-      2.44±0.7ms          924±1μs     0.38  bench_linalg.Linalg.time_op('pinv', 'float64')
-      29.9±0.8μs      10.8±0.01μs     0.36  bench_linalg.Linalg.time_op('norm', 'complex64')
-      2.56±0.5ms          924±1μs     0.36  bench_linalg.Linalg.time_op('pinv', 'float32')
-      2.63±0.5ms        924±0.6μs     0.35  bench_linalg.Linalg.time_op('pinv', 'int64')
-      2.68±0.7ms         927±10μs     0.35  bench_linalg.Linalg.time_op('pinv', 'int32')
-      2.68±0.5ms         927±10μs     0.35  bench_linalg.Linalg.time_op('pinv', 'int16')
-      2.93±0.6ms          925±2μs     0.32  bench_linalg.Linalg.time_op('pinv', 'longfloat')
-       809±500μs        215±0.2μs     0.27  bench_linalg.Linalg.time_op('det', 'complex128')
-      3.67±0.9ms         895±20μs     0.24  bench_linalg.Eindot.time_tensordot_a_b_axes_1_0_0_1
-       489±100μs         114±20μs     0.23  bench_linalg.Eindot.time_inner_trans_a_ac
-      3.64±0.7ms        777±0.3μs     0.21  bench_linalg.Lstsq.time_numpy_linalg_lstsq_a__b_float64
-        755±90μs         157±10μs     0.21  bench_linalg.Eindot.time_dot_a_b
-        4.63±1ms          899±9μs     0.19  bench_linalg.Linalg.time_op('svd', 'longfloat')
-        5.19±1ms         922±10μs     0.18  bench_linalg.Linalg.time_op('svd', 'float64')
-       599±200μs         89.4±2μs     0.15  bench_linalg.Eindot.time_matmul_trans_atc_a
-       956±200μs         140±10μs     0.15  bench_linalg.Eindot.time_matmul_a_b
-        6.45±3ms         903±10μs     0.14  bench_linalg.Linalg.time_op('svd', 'float32')
-        6.42±3ms        896±0.7μs     0.14  bench_linalg.Linalg.time_op('svd', 'int32')
-        6.47±4ms          902±5μs     0.14  bench_linalg.Linalg.time_op('svd', 'int64')
-        6.52±1ms          899±2μs     0.14  bench_linalg.Linalg.time_op('svd', 'int16')
-       799±300μs          109±2μs     0.14  bench_linalg.Eindot.time_dot_trans_atc_a
-       502±100μs       65.0±0.2μs     0.13  bench_linalg.Eindot.time_dot_trans_a_atc
-       542±300μs      64.2±0.05μs     0.12  bench_linalg.Eindot.time_matmul_trans_a_atc
-       458±300μs      41.6±0.09μs     0.09  bench_linalg.Linalg.time_op('det', 'int32')
-       471±100μs      41.9±0.03μs     0.09  bench_linalg.Linalg.time_op('det', 'float32')
-       510±100μs      43.6±0.06μs     0.09  bench_linalg.Linalg.time_op('det', 'int16')
-       478±200μs      39.6±0.05μs     0.08  bench_linalg.Linalg.time_op('det', 'longfloat')
-       599±200μs      39.6±0.09μs     0.07  bench_linalg.Linalg.time_op('det', 'float64')
-       758±300μs       41.6±0.1μs     0.05  bench_linalg.Linalg.time_op('det', 'int64')

emscripten doesn't use external BLAS / LAPACK.  It uses a f2c version that's embedded in NumPy.  They happen to declare some LAPACK APIs as returning int instead of void, because that's the way that f2c worked for subroutines.

Also remove some debug prints from umath_linalg

Removing the prints and providing an option that removes the dispatching for Accelerate.

[skip circle]

[skip circle]

[skip ci]