metal-linalg

Eigensolver routing on Apple M5 Pro (20 GPU cores)

What every section and number below means: reading-reports.md.

Cost model scaled to this device from one probe point: block x0.14, cpu x0.94, whole-matrix x1.00 (1.00 is an M1).

Machine state: load 3.6/18 at the start, load 1.5/18 at the end; power mains.

Probe point after the sweep relative to before it: block x1.01, cpu x1.01, tg x1.01 (stable).

Generated by tuning/tune_eigh.py from 205 (N, batch) points, N in [2, 4, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096], batch in [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096], four backends, two or more passes, min-of-repeats.

Answer

Row for kTuned[] in src/eigh.mm:

// device, GPU cores,   simd_max_n, block_min_n, block_min_n_batched, block_min_batch,   gpu_max_n, gpu_min_batch_times_n, gpu_min_batch,   values_gpu_max_n, values_gpu_min_batch_times_n, values_gpu_min_batch,   tridiag_min_n, values_tridiag_min_n
{"Apple M5 Pro", 20,   0, 96, 0, 0,   1024, 512, 16,   256, 2048, 32,   1024, 0},

To try it without rebuilding:

EIGH_SIMD_MAX_N=0 EIGH_BLOCK_MIN_N=96 EIGH_BLOCK_MIN_N_BATCHED=0 EIGH_BLOCK_MIN_BATCH=0 EIGH_GPU_MAX_N=1024 EIGH_GPU_MIN_BATCH_TIMES_N=512 EIGH_GPU_MIN_BATCH=16 EIGH_TRIDIAG_MIN_N=1024 EIGH_VALUES_TRIDIAG_MIN_N=0 EIGH_VALUES_GPU_MAX_N=256 EIGH_VALUES_GPU_MIN_BATCH_TIMES_N=2048 EIGH_VALUES_GPU_MIN_BATCH=32

The policy in effect on this device came from tuned:Apple M5 Pro. It differs from the fitted one; see the warnings.

Against the best measured backend at every point the whole rule scores 1.0275 geometric-mean regret, worst 1.67x, 15 of 205 points losing more than 10%, and 1.319x the oracle’s total time. The decision is fitted in two stages, below, because the CPU routing would otherwise hide the GPU backend crossover.

Warnings

chosen rule loses more than 25% at N=768 batch=16 (block, 1.67x), N=2 batch=256 (tg, 1.60x), N=64 batch=4096 (tg, 1.55x), N=64 batch=1024 (tg, 1.55x), N=64 batch=2048 (tg, 1.51x), N=64 batch=512 (tg, 1.49x), N=4 batch=128 (tg, 1.46x), N=96 batch=16 (block, 1.38x) …
GPU split loses more than 25% against the best GPU backend at N=64 batch=4096 (tg, 1.55x), N=64 batch=1024 (tg, 1.55x), N=64 batch=2048 (tg, 1.51x), N=64 batch=512 (tg, 1.49x), N=96 batch=16 (block, 1.38x), N=96 batch=2 (block, 1.33x), N=96 batch=1 (block, 1.32x), N=96 batch=8 (block, 1.30x) …
chosen rule picks a backend that was not timed at 1 points; the cost model’s guess counts in the geomean and is kept out of the worst case: N=4096 batch=1 (cpu, est 2.80x)
the fitted policy differs from the one in effect (tuned:Apple M5 Pro): update this device’s row in kTuned[] in src/eigh.mm
eigenvalues alone: the chosen boundary loses more than 25% at N=64 batch=4096 (tg, 1.55x), N=64 batch=1024 (tg, 1.53x), N=64 batch=2048 (tg, 1.47x), N=12 batch=128 (cpu, 1.42x), N=64 batch=512 (tg, 1.40x), N=24 batch=64 (cpu, 1.29x)

Stage 1: which GPU backend

Scored against the best GPU backend at each of the 205 points, as if there were no CPU: this is the rule a forced-GPU call (EIGH_DEVICE=gpu) and the detail entry points follow, and it is what a GPU with more cores will lean on.

rule	geomean regret	worst	>10%	total time / oracle	est. picks
policy in effect (‘0’, ‘96’, ‘none’, ‘none’)	1.0180	1.55x	10	1.003	0
fitted (‘0’, ‘96’, ‘none’, ‘none’)	1.0180	1.55x	10	1.003	0

2 of 128 (simd_max_n, block_min_n) pairs are within 0.5% of the best geomean: simd_max_n 0 .. 2, block_min_n 96 .. 96.

xychart-beta
    title "Regret by block_min_n"
    x-axis "block_min_n" [32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, none]
    y-axis "geometric-mean regret" 1.0 --> 2.53
    line [1.1934, 1.0992, 1.0359, 1.0180, 1.0425, 1.1121, 1.2376, 1.3783, 1.5490, 1.7218, 1.9334, 2.1172, 2.2551, 2.4010, 2.4591, 2.5187]

block_min_n	32	48	64	96	128	192	256	384	512	768	1024	1536	2048	3072	4096	none
geomean	1.1934	1.0992	1.0359	1.0180	1.0425	1.1121	1.2376	1.3783	1.5490	1.7218	1.9334	2.1172	2.2551	2.4010	2.4591	2.5187
worst	8.70x	4.49x	2.58x	1.55x	1.92x	2.24x	4.59x	5.66x	10.11x	15.91x	15.91x	15.91x	15.91x	15.91x	15.91x	15.91x

xychart-beta
    title "Regret by simd_max_n"
    x-axis "simd_max_n" [0, 2, 4, 8, 12, 16, 24, 32]
    y-axis "geometric-mean regret" 1.0 --> 1.20
    line [1.0180, 1.0200, 1.0255, 1.0345, 1.0491, 1.0726, 1.1149, 1.1824]

simd_max_n	0	2	4	8	12	16	24	32
geomean	1.0180	1.0200	1.0255	1.0345	1.0491	1.0726	1.1149	1.1824
worst	1.55x	1.55x	1.90x	2.42x	3.18x	3.66x	3.66x	4.98x

Held-out check of a batch-dependent crossover (block from a lower N once the batch is large enough). Fitted on 112 points, scored on the other 93; the verdict is a bootstrap over the test points.

rule	fitted on train	train geomean	test geomean	test worst	verdict
two constants	[0, 96, 1000000000, 1000000000]	1.0225	1.0127	1.55x	baseline
batch-dependent block crossover	{“block_lo”: 64, “batch_hi”: 128}	1.0020	1.0064	1.51x	rejected (better in 78% of resamples, median gain 0.6%)

Best GPU backend per point (s simd, t threadgroup, B block), then what the split picks:

  N \ batch     1     2     4     8    16    32    64   128   256   512  1024  2048  4096
          2     s     t     t     s     t     t     s     t     t     t     t     t     s
          4     s     t     t     t     t     t     s     t     t     s     s     s     t
          8     t     t     s     t     t     s     t     s     t     t     t     t     s
         12     t     t     t     t     t     t     t     t     t     t     t     s     t
         16     t     t     t     t     t     t     t     t     t     t     t     t     t
         24     t     t     t     t     t     t     t     t     t     t     t     t     t
         32     t     t     t     t     t     t     t     t     t     t     t     t     t
         48     t     t     t     t     t     t     t     t     t     t     t     t     t
         64     t     t     t     t     t     t     t     t     B     B     B     B     B
         96     t     t     t     t     t     B     B     B     B     B     B     B     B
        128     B     B     B     B     B     B     B     B     B     B     B     B     B
        192     B     B     B     B     B     B     B     B     B     B     B     B     B
        256     B     B     B     B     B     B     B     B     B     B     B     .     .
        384     B     B     B     B     B     B     B     B     B     B     .     .     .
        512     B     B     B     B     B     B     B     B     .     .     .     .     .
        768     B     B     B     B     B     B     B     .     .     .     .     .     .
       1024     B     B     B     B     B     .     .     .     .     .     .     .     .
       1536     B     B     B     .     .     .     .     .     .     .     .     .     .
       2048     B     B     B     .     .     .     .     .     .     .     .     .     .
       3072     B     .     .     .     .     .     .     .     .     .     .     .     .
       4096     B     .     .     .     .     .     .     .     .     .     .     .     .

  N \ batch     1     2     4     8    16    32    64   128   256   512  1024  2048  4096
          2     t     t     t     t     t     t     t     t     t     t     t     t     t
          4     t     t     t     t     t     t     t     t     t     t     t     t     t
          8     t     t     t     t     t     t     t     t     t     t     t     t     t
         12     t     t     t     t     t     t     t     t     t     t     t     t     t
         16     t     t     t     t     t     t     t     t     t     t     t     t     t
         24     t     t     t     t     t     t     t     t     t     t     t     t     t
         32     t     t     t     t     t     t     t     t     t     t     t     t     t
         48     t     t     t     t     t     t     t     t     t     t     t     t     t
         64     t     t     t     t     t     t     t     t     t     t     t     t     t
         96     B     B     B     B     B     B     B     B     B     B     B     B     B
        128     B     B     B     B     B     B     B     B     B     B     B     B     B
        192     B     B     B     B     B     B     B     B     B     B     B     B     B
        256     B     B     B     B     B     B     B     B     B     B     B     .     .
        384     B     B     B     B     B     B     B     B     B     B     .     .     .
        512     B     B     B     B     B     B     B     B     .     .     .     .     .
        768     B     B     B     B     B     B     B     .     .     .     .     .     .
       1024     B     B     B     B     B     .     .     .     .     .     .     .     .
       1536     B     B     B     .     .     .     .     .     .     .     .     .     .
       2048     B     B     B     .     .     .     .     .     .     .     .     .     .
       3072     B     .     .     .     .     .     .     .     .     .     .     .     .
       4096     B     .     .     .     .     .     .     .     .     .     .     .     .

Stage 2: GPU or CPU

Given the split above, GPU iff N <= gpu_max_n, batch * N >= gpu_min_batch_times_n and batch >= gpu_min_batch, scored against the best of all four backends. worst is over the points where the chosen backend was timed; a pick the cost model had to guess is listed in the warnings instead.

rule	geomean regret	worst	>10%	total time / oracle	est. picks
oracle (best per point)	1.0000	1.00x	0	1.000	0
policy in effect (‘1024’, ‘512’, ‘16’)	1.0275	1.67x	15	1.319	1
fitted (‘1024’, ‘512’, ‘16’)	1.0275	1.67x	15	1.319	1

6 of 1188 combinations are within 0.5% of the best geomean: gpu_max_n 1024 .. none, gpu_min_batch_times_n 512 .. 512, gpu_min_batch 16 .. 16.

xychart-beta
    title "Regret by gpu_min_batch_times_n"
    x-axis "gpu_min_batch_times_n" [0, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, none]
    y-axis "geometric-mean regret" 1.0 --> 1.97
    line [1.1217, 1.1053, 1.0800, 1.0483, 1.0275, 1.0333, 1.0648, 1.1267, 1.2227, 1.3501, 1.9557]

gpu_min_batch_times_n	0	64	128	256	512	1024	2048	4096	8192	16384	none
geomean	1.1217	1.1053	1.0800	1.0483	1.0275	1.0333	1.0648	1.1267	1.2227	1.3501	1.9557
worst	20.66x	11.52x	6.68x	3.35x	1.67x	2.18x	3.49x	5.26x	7.03x	9.75x	16.90x

xychart-beta
    title "Regret by gpu_min_batch"
    x-axis "gpu_min_batch" [1, 2, 4, 8, 16, 32]
    y-axis "geometric-mean regret" 1.0 --> 1.11
    line [1.0929, 1.0753, 1.0557, 1.0376, 1.0275, 1.0446]

gpu_min_batch	1	2	4	8	16	32
geomean	1.0929	1.0753	1.0557	1.0376	1.0275	1.0446
worst	3.32x	3.00x	3.00x	2.11x	1.67x	1.76x

xychart-beta
    title "Regret by gpu_max_n"
    x-axis "gpu_max_n" [16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, none]
    y-axis "geometric-mean regret" 1.0 --> 1.57
    line [1.5578, 1.4512, 1.3574, 1.2796, 1.2197, 1.1678, 1.1222, 1.0838, 1.0600, 1.0461, 1.0410, 1.0330, 1.0275, 1.0275, 1.0275, 1.0275, 1.0275, 1.0275]

gpu_max_n	16	24	32	48	64	96	128	192	256	384	512	768	1024	1536	2048	3072	4096	none
geomean	1.5578	1.4512	1.3574	1.2796	1.2197	1.1678	1.1222	1.0838	1.0600	1.0461	1.0410	1.0330	1.0275	1.0275	1.0275	1.0275	1.0275	1.0275
worst	10.64x	8.09x	5.68x	5.68x	3.80x	3.00x	2.34x	2.00x	1.60x	1.60x	1.60x	1.67x	1.67x	1.67x	1.67x	1.67x	1.67x	1.67x

Held-out check of a per-N boundary (a lookup table of the smallest batch at which the GPU wins, per N) against the product rule. Fitted on 112 points, scored on the other 93.

rule	fitted on train	train geomean	test geomean	test worst	verdict
product rule	[1024, 512, 16]	1.0394	1.0134	1.55x	baseline
per-N table	{“min_batch_by_n”: {“2”: 1024, “4”: 256, “8”: 128, “12”: 64, “16”: 32, “24”: 64, “32”: 64, “48”: 32, “64”: 32, “96”: 32, “128”: 16, “192”: 16, “256”: 8, “384”: 8, “512”: 16, “768”: null, “1024”: 16, “1536”: null, “2048”: null, “3072”: null, “4096”: 1}}	1.0147	1.0707	2.52x	rejected (better in 0% of resamples, median gain -5.2%)

Best backend per point (c CPU, s simd, t threadgroup, B block, . not measured), what the whole rule picks, and the speedup of the best GPU backend over the CPU:

  N \ batch     1     2     4     8    16    32    64   128   256   512  1024  2048  4096
          2     c     c     c     c     c     c     c     c     c     t     t     t     s
          4     c     c     c     c     c     c     c     c     t     s     s     s     t
          8     c     c     c     c     c     c     c     s     t     t     t     t     s
         12     c     c     c     c     c     c     t     t     t     t     t     s     t
         16     c     c     c     c     c     t     t     t     t     t     t     t     t
         24     c     c     c     c     t     t     t     t     t     t     t     t     t
         32     c     c     c     c     t     t     t     t     t     t     t     t     t
         48     c     c     c     c     t     t     t     t     t     t     t     t     t
         64     c     c     c     c     t     t     t     t     B     B     B     B     B
         96     c     c     c     c     t     B     B     B     B     B     B     B     B
        128     c     c     c     c     B     B     B     B     B     B     B     B     B
        192     c     c     c     c     B     B     B     B     B     B     B     B     B
        256     c     c     c     B     B     B     B     B     B     B     B     .     .
        384     c     c     c     B     B     B     B     B     B     B     .     .     .
        512     c     c     c     B     B     c     c     B     .     .     .     .     .
        768     c     c     c     c     c     B     B     .     .     .     .     .     .
       1024     c     c     c     c     B     .     .     .     .     .     .     .     .
       1536     c     c     c     .     .     .     .     .     .     .     .     .     .
       2048     c     c     c     .     .     .     .     .     .     .     .     .     .
       3072     c     .     .     .     .     .     .     .     .     .     .     .     .
       4096     B     .     .     .     .     .     .     .     .     .     .     .     .

  N \ batch     1     2     4     8    16    32    64   128   256   512  1024  2048  4096
          2     c     c     c     c     c     c     c     c     t     t     t     t     t
          4     c     c     c     c     c     c     c     t     t     t     t     t     t
          8     c     c     c     c     c     c     t     t     t     t     t     t     t
         12     c     c     c     c     c     c     t     t     t     t     t     t     t
         16     c     c     c     c     c     t     t     t     t     t     t     t     t
         24     c     c     c     c     c     t     t     t     t     t     t     t     t
         32     c     c     c     c     t     t     t     t     t     t     t     t     t
         48     c     c     c     c     t     t     t     t     t     t     t     t     t
         64     c     c     c     c     t     t     t     t     t     t     t     t     t
         96     c     c     c     c     B     B     B     B     B     B     B     B     B
        128     c     c     c     c     B     B     B     B     B     B     B     B     B
        192     c     c     c     c     B     B     B     B     B     B     B     B     B
        256     c     c     c     c     B     B     B     B     B     B     B     .     .
        384     c     c     c     c     B     B     B     B     B     B     .     .     .
        512     c     c     c     c     B     B     B     B     .     .     .     .     .
        768     c     c     c     c     B     B     B     .     .     .     .     .     .
       1024     c     c     c     c     B     .     .     .     .     .     .     .     .
       1536     c     c     c     .     .     .     .     .     .     .     .     .     .
       2048     c     c     c     .     .     .     .     .     .     .     .     .     .
       3072     c     .     .     .     .     .     .     .     .     .     .     .     .
       4096     c     .     .     .     .     .     .     .     .     .     .     .     .

  N \ batch     1     2     4     8    16    32    64   128   256   512  1024  2048  4096
          2  0.01  0.01  0.02  0.02  0.05  0.09  0.15  0.30  0.63  1.18  1.92  3.77  7.03
          4  0.01  0.02  0.03  0.05  0.10  0.16  0.31  0.69  1.14  2.32  4.35  7.30 11.17
          8  0.02  0.04  0.06  0.12  0.23  0.38  0.81  1.63  3.16  5.06  8.61 12.72 16.90
         12  0.03  0.06  0.10  0.19  0.39  0.72  1.44  2.77  4.59  7.03  9.75 11.65 14.03
         16  0.04  0.09  0.15  0.29  0.62  1.15  2.30  4.01  5.91  8.67  9.84 12.70 14.57
         24  0.08  0.17  0.30  0.57  1.13  2.18  3.49  5.26  6.33  8.26  9.19 10.06 10.64
         32  0.11  0.19  0.37  0.74  1.44  2.52  3.64  4.23  5.29  6.70  7.35  7.53  8.09
         48  0.10  0.22  0.43  0.83  1.76  2.53  3.07  3.96  4.69  5.03  5.14  5.41  5.08
         64  0.12  0.23  0.44  0.89  1.72  2.38  2.63  3.28  4.28  5.13  5.42  5.44  5.68
         96  0.08  0.16  0.31  0.62  1.23  1.65  2.36  3.09  3.68  3.66  3.70  3.69  3.80
        128  0.09  0.17  0.33  0.64  1.13  1.91  2.51  3.00  2.99  2.92  2.86  2.94  2.93
        192  0.13  0.26  0.49  0.91  1.59  1.98  2.34  2.28  2.12  2.10  2.13   gpu   gpu
        256  0.19  0.37  0.69  1.20  1.70  2.00  1.87  1.75  1.76  1.76   gpu     .     .
        384  0.23  0.41  0.70  1.13  1.32  1.19  1.17  1.07   gpu   gpu     .     .     .
        512  0.30  0.50  0.81  1.11  1.04  0.97  0.93   gpu     .     .     .     .     .
        768  0.31  0.50  0.70  0.63  0.60   gpu   gpu     .     .     .     .     .     .
       1024  0.39  0.60  0.64  0.59   gpu     .     .     .     .     .     .     .     .
       1536  0.40  0.44  0.40     .     .     .     .     .     .     .     .     .     .
       2048  0.39  0.39  0.39     .     .     .     .     .     .     .     .     .     .
       3072  0.33     .     .     .     .     .     .     .     .     .     .     .     .
       4096   gpu     .     .     .     .     .     .     .     .     .     .     .     .

Stage 3: GPU or CPU, eigenvalues alone

The same rule for eigvalsh, with its own thresholds (values_gpu_max_n, values_gpu_min_batch_times_n, values_gpu_min_batch), fitted on the _vals timings of 195 points given the split above. The CPU computes eigenvalues alone by LAPACK’s two-stage reduction from N = 128, so the boundary need not be eigh’s.

rule	geomean regret	worst	>10%	total time / oracle
policy in effect	1.0148	1.55x	10	1.013
eigh’s fitted boundary	1.0680	3.95x	29	1.096
fitted (‘256’, ‘2048’, ‘32’)	1.0148	1.55x	10	1.013

7 combinations are within 0.5% of the best geomean: values_gpu_max_n 192 .. 384, values_gpu_min_batch_times_n 1024 .. 2048, values_gpu_min_batch 16 .. 32.

Held out: fitted on 106 points (‘256’, ‘2048’, ‘32’), scored on the other 89: geomean 1.0204x, worst 1.53x, against 1.0566x, worst 2.19x for eigh’s boundary on the same points.

Stage 4: the tridiag backend instead of the CPU

Where the rule above chooses the CPU, the tridiag backend from a threshold N on (0: never), fitted over the measured N against the best of all backends, tridiag included, on the points where tridiag was timed (N >= 128, within the cost cap): the region the threshold decides.

	threshold	geomean regret	worst	without tridiag: geomean	worst	held out (fitted on half)
with eigenvectors	1024	1.0393	2.09x	1.1750	2.73x	from 1024: 1.0691 vs 1.1136
eigenvalues alone	never	1.0021	1.13x	1.0021	1.13x	from never: 1.0000 vs 1.0000

tridiag over the CPU (with eigenvectors), N x batch: 128x1 0.21x, 128x2 0.21x, 128x4 0.21x, 128x8 0.21x, 128x16 0.20x, 128x32 0.21x, 128x64 0.21x, 128x128 0.21x, 128x256 0.21x, 128x512 0.21x, 192x1 0.31x, 192x2 0.31x, 192x4 0.29x, 192x8 0.30x, 192x16 0.30x, 192x32 0.31x, 192x64 0.30x, 192x128 0.30x, 192x256 0.30x, 256x1 0.42x, 256x2 0.42x, 256x4 0.41x, 256x8 0.42x, 256x16 0.42x, 256x32 0.41x, 256x64 0.42x, 256x128 0.41x, 256x256 0.42x, 384x1 0.51x, 384x2 0.50x, 384x4 0.48x, 384x8 0.50x, 384x16 0.50x, 384x32 0.50x, 384x64 0.50x, 384x128 0.49x, 512x1 0.69x, 512x2 0.67x, 512x4 0.67x, 512x8 0.67x, 512x16 0.66x, 512x32 0.67x, 512x64 0.67x, 768x1 0.81x, 768x2 0.80x, 768x4 0.80x, 768x8 0.79x, 768x16 0.80x, 1024x1 1.13x, 1024x2 1.13x, 1024x4 1.13x, 1024x8 1.13x, 1536x1 1.47x, 1536x2 1.43x, 1536x4 1.44x, 2048x1 1.93x, 2048x2 1.95x, 2048x4 1.93x, 3072x1 2.73x

tridiag over the CPU (eigenvalues alone), N x batch: 128x1 0.14x, 128x2 0.14x, 128x4 0.13x, 128x8 0.13x, 128x16 0.13x, 128x32 0.13x, 128x64 0.13x, 128x128 0.13x, 128x256 0.13x, 128x512 0.13x, 192x1 0.19x, 192x2 0.19x, 192x4 0.18x, 192x8 0.19x, 192x16 0.19x, 192x32 0.18x, 192x64 0.19x, 192x128 0.19x, 192x256 0.19x, 256x1 0.24x, 256x2 0.24x, 256x4 0.23x, 256x8 0.24x, 256x16 0.23x, 256x32 0.23x, 256x64 0.24x, 256x128 0.24x, 256x256 0.24x, 384x1 0.33x, 384x2 0.33x, 384x4 0.32x, 384x8 0.33x, 384x16 0.32x, 384x32 0.33x, 384x64 0.32x, 384x128 0.33x, 512x1 0.40x, 512x2 0.40x, 512x4 0.40x, 512x8 0.39x, 512x16 0.40x, 512x32 0.40x, 512x64 0.40x, 768x1 0.54x, 768x2 0.55x, 768x4 0.54x, 768x8 0.53x, 768x16 0.54x, 1024x1 0.68x, 1024x2 0.67x, 1024x4 0.68x, 1024x8 0.67x, 1536x1 0.85x, 1536x2 0.85x, 1536x4 0.84x, 2048x1 0.93x, 2048x2 0.94x, 2048x4 0.94x, 3072x1 1.13x

Noise floor

Pass-to-pass ratio (max/min of the same measurement across passes), 1284 measurements: median 1.013, p90 1.091, max 2.98. The held-out verdicts use a bootstrap rather than this figure, since a mean over many points is far less noisy than one measurement.

runtime	n	median	p90	max
<1 ms	465	1.034	1.298	2.98
1-3 ms	119	1.008	1.031	1.16
3-10 ms	187	1.008	1.032	1.11
10-30 ms	123	1.008	1.035	1.09
30-100 ms	141	1.012	1.066	1.13
>100 ms	249	1.010	1.050	1.14

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