zkp: HAL cleanups and perf bump

[flaub]

• Parallelize a top 10 hotspot in the prover. TODO: consider moving this hotspot to a HAL function that stays on-device.
• Rename EvalCheck to CircuitHal to be more appropriate for what it is now and in the future. The plan is to add more circuit-specific HALs to CircuitHal.
• Drop unused CircuitStepHandler::calc_prefix_products.

[github-actions]

Benchmark for Linux-cuda

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Benchmark for Linux-default

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Benchmark for macOS-default 3250cf9

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Test	Base	PR	%
fib/100/execute	2.8±0.09ms	2.7±0.08ms	-3.57%
fib/100/prove	3.7±0.05s	3.6±0.07s	-2.70%
fib/100/total	3.7±0.05s	3.6±0.09s	-2.70%
fib/1000/execute	3.1±0.07ms	3.0±0.10ms	-3.23%
fib/1000/prove	3.7±0.05s	3.6±0.07s	-2.70%
fib/1000/total	3.7±0.06s	3.7±0.03s	0.00%
fib/10000/execute	5.9±0.08ms	5.6±0.12ms	-5.08%
fib/10000/prove	15.2±0.17s	15.0±0.13s	-1.32%
fib/10000/total	15.2±0.11s	15.1±0.09s	-0.66%

Benchmark for macOS-metal 3250cf9

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Test	Base	PR	%
fib/100/execute	2.8±0.11ms	2.6±0.09ms	-7.14%
fib/100/prove	849.9±2.51ms	795.5±4.43ms	-6.40%
fib/100/total	874.3±5.96ms	817.2±5.35ms	-6.53%
fib/1000/execute	3.0±0.04ms	3.0±0.05ms	0.00%
fib/1000/prove	869.1±2.18ms	817.0±4.03ms	-5.99%
fib/1000/total	892.8±5.68ms	837.1±5.37ms	-6.24%
fib/10000/execute	5.8±0.04ms	5.8±0.10ms	0.00%
fib/10000/prove	3.3±0.01s	3.1±0.01s	-6.06%
fib/10000/total	3.3±0.01s	3.1±0.01s	-6.06%

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Benchmark for Linux-cuda 01e999b

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Test	Base	PR	%
fib/100/execute	5.0±0.09ms	5.0±0.09ms	0.00%
fib/100/prove	772.9±4.34ms	726.2±3.55ms	-6.04%
fib/100/total	778.6±4.67ms	743.3±2.19ms	-4.53%
fib/1000/execute	5.7±0.11ms	5.5±0.10ms	-3.51%
fib/1000/prove	801.8±4.66ms	749.4±3.30ms	-6.54%
fib/1000/total	812.8±2.92ms	768.4±3.39ms	-5.46%
fib/10000/execute	11.9±0.11ms	11.2±0.08ms	-5.88%
fib/10000/prove	3.2±0.02s	2.5±0.01s	-21.88%
fib/10000/total	3.2±0.01s	2.5±0.01s	-21.88%

Benchmark for Linux-default 01e999b

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Test	Base	PR	%
fib/100/execute	4.9±0.48ms	4.7±0.19ms	-4.08%
fib/100/prove	2.4±1.33s	2.3±0.31s	-4.17%
fib/100/total	2.5±0.55s	2.1±0.24s	-16.00%
fib/1000/execute	6.4±1.31ms	5.3±0.10ms	-17.19%
fib/1000/prove	3.2±0.72s	2.3±0.51s	-28.13%
fib/1000/total	2.2±0.23s	2.1±0.17s	-4.55%
fib/10000/execute	10.6±0.85ms	9.9±0.09ms	-6.60%
fib/10000/prove	7.4±0.39s	7.3±0.38s	-1.35%
fib/10000/total	7.5±0.63s	7.2±0.45s	-4.00%

Benchmark for macOS-default 01e999b

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Test	Base	PR	%
fib/100/execute	2.8±0.10ms	2.7±0.15ms	-3.57%
fib/100/prove	3.7±0.06s	3.6±0.08s	-2.70%
fib/100/total	3.7±0.06s	3.7±0.06s	0.00%
fib/1000/execute	3.0±0.08ms	3.0±0.06ms	0.00%
fib/1000/prove	3.7±0.06s	3.7±0.05s	0.00%
fib/1000/total	3.7±0.04s	3.7±0.06s	0.00%
fib/10000/execute	5.9±0.09ms	5.8±0.10ms	-1.69%
fib/10000/prove	15.2±0.07s	15.0±0.08s	-1.32%
fib/10000/total	15.3±0.10s	15.0±0.16s	-1.96%

Benchmark for macOS-metal 01e999b

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Test	Base	PR	%
fib/100/execute	2.8±0.12ms	2.7±0.09ms	-3.57%
fib/100/prove	851.7±4.60ms	796.1±5.67ms	-6.53%
fib/100/total	878.5±5.01ms	818.9±4.80ms	-6.78%
fib/1000/execute	3.0±0.04ms	3.0±0.05ms	0.00%
fib/1000/prove	867.8±3.62ms	814.2±3.67ms	-6.18%
fib/1000/total	896.6±6.05ms	840.0±6.76ms	-6.31%
fib/10000/execute	5.8±0.16ms	5.8±0.10ms	0.00%
fib/10000/prove	3.2±0.01s	3.1±0.01s	-3.13%
fib/10000/total	3.2±0.01s	3.1±0.02s	-3.13%

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Benchmark for Linux-cuda 17b2c2c

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Test	Base	PR	%
fib/100/execute	5.1±0.08ms	5.1±0.11ms	0.00%
fib/100/prove	936.0±4.32ms	768.4±6.22ms	-17.91%
fib/100/total	945.1±3.95ms	765.9±4.32ms	-18.96%
fib/1000/execute	5.8±0.10ms	5.7±0.13ms	-1.72%
fib/1000/prove	960.6±4.85ms	800.1±3.88ms	-16.71%
fib/1000/total	963.6±4.50ms	801.2±5.52ms	-16.85%
fib/10000/execute	12.0±0.12ms	11.3±0.12ms	-5.83%
fib/10000/prove	3.2±0.02s	2.5±0.01s	-21.88%
fib/10000/total	3.2±0.02s	2.5±0.01s	-21.88%

Benchmark for Linux-default 17b2c2c

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Test	Base	PR	%
fib/100/execute	6.9±0.89ms	6.7±0.45ms	-2.90%
fib/100/prove	5.1±0.03s	5.1±0.08s	0.00%
fib/100/total	5.1±0.02s	5.0±0.02s	-1.96%
fib/1000/execute	8.7±1.36ms	7.8±0.60ms	-10.34%
fib/1000/prove	5.2±0.03s	5.1±0.03s	-1.92%
fib/1000/total	5.2±0.02s	5.1±0.02s	-1.92%
fib/10000/execute	14.9±1.45ms	14.0±0.51ms	-6.04%
fib/10000/prove	21.2±0.07s	21.0±0.10s	-0.94%
fib/10000/total	21.2±0.11s	20.9±0.08s	-1.42%

Benchmark for macOS-default 17b2c2c

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Test	Base	PR	%
fib/100/execute	2.7±0.05ms	2.7±0.11ms	0.00%
fib/100/prove	3.7±0.08s	3.6±0.05s	-2.70%
fib/100/total	3.7±0.04s	3.6±0.06s	-2.70%
fib/1000/execute	3.0±0.10ms	2.9±0.17ms	-3.33%
fib/1000/prove	3.7±0.08s	3.7±0.05s	0.00%
fib/1000/total	3.7±0.05s	3.7±0.05s	0.00%
fib/10000/execute	5.9±0.06ms	5.6±0.14ms	-5.08%
fib/10000/prove	15.2±0.07s	15.1±0.11s	-0.66%
fib/10000/total	15.3±0.15s	15.1±0.13s	-1.31%

Benchmark for macOS-metal 17b2c2c

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Test	Base	PR	%
fib/100/execute	2.8±0.12ms	2.7±0.09ms	-3.57%
fib/100/prove	846.8±4.40ms	797.2±4.66ms	-5.86%
fib/100/total	876.8±6.33ms	822.2±3.45ms	-6.23%
fib/1000/execute	3.0±0.07ms	3.0±0.08ms	0.00%
fib/1000/prove	869.2±7.09ms	816.9±4.71ms	-6.02%
fib/1000/total	896.1±4.45ms	842.2±2.53ms	-6.01%
fib/10000/execute	5.8±0.18ms	5.7±0.07ms	-1.72%
fib/10000/prove	3.3±0.01s	3.1±0.01s	-6.06%
fib/10000/total	3.3±0.01s	3.1±0.01s	-6.06%

[SchmErik]

I don't have a lot of knowledge on the specific prover change but everything else looks good to me. I'll approve but maybe @jbruestle or @shkoo could take a look at that portion?

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Benchmark for Linux-cuda

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Benchmark for Linux-default

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Benchmark for macOS-default 62f5b09

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Test	Base	PR	%
fib/100/execute	2.8±0.17ms	2.8±0.13ms	0.00%
fib/100/prove	3.7±0.08s	3.6±0.04s	-2.70%
fib/100/total	3.7±0.08s	3.7±0.04s	0.00%
fib/1000/execute	3.1±0.06ms	2.9±0.04ms	-6.45%
fib/1000/prove	3.7±0.07s	3.6±0.08s	-2.70%
fib/1000/total	3.7±0.09s	3.7±0.06s	0.00%
fib/10000/execute	6.0±0.08ms	5.8±0.14ms	-3.33%
fib/10000/prove	15.2±0.22s	15.0±0.13s	-1.32%
fib/10000/total	15.3±0.08s	15.0±0.10s	-1.96%

Benchmark for macOS-metal 62f5b09

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Test	Base	PR	%
fib/100/execute	2.8±0.04ms	2.6±0.06ms	-7.14%
fib/100/prove	848.2±4.31ms	806.2±6.24ms	-4.95%
fib/100/total	877.1±6.45ms	825.2±7.30ms	-5.92%
fib/1000/execute	3.0±0.06ms	2.9±0.08ms	-3.33%
fib/1000/prove	867.4±2.48ms	825.1±5.70ms	-4.88%
fib/1000/total	893.2±6.87ms	840.5±10.05ms	-5.90%
fib/10000/execute	5.8±0.04ms	5.7±0.16ms	-1.72%
fib/10000/prove	3.3±0.01s	3.1±0.02s	-6.06%
fib/10000/total	3.3±0.01s	3.1±0.01s	-6.06%