Store memory image as a btree of pages

[shkoo]

This significantly improves execute performance, both in memory usage and runtime.

[github-actions]

Benchmark for Linux-cuda c096be1

Click to hide benchmark

Test	Base	PR	%
fib/100/execute	317.9±2.67ms	20.9±0.14ms	-93.43%
fib/100/prove	2.9±0.01s	1146.1±6.03ms	-60.48%
fib/100/total	3.2±0.01s	1179.8±4.88ms	-63.13%
fib/1000/execute	329.7±0.29ms	40.4±0.09ms	-87.75%
fib/1000/prove	3.0±0.00s	1174.2±5.81ms	-60.86%
fib/1000/total	3.3±0.01s	1235.7±3.92ms	-62.55%
fib/10000/execute	449.4±0.78ms	233.2±0.35ms	-48.11%
fib/10000/prove	10.6±0.03s	4.8±0.05s	+-54.72%
fib/10000/total	11.1±0.04s	4.9±0.04s	+-55.86%

Benchmark for Linux-default c096be1

Click to hide benchmark

Test	Base	PR	%
fib/100/execute	1409.6±3.67ms	55.2±0.19ms	-96.08%
fib/100/prove	5.9±0.12s	5.1±0.02s	-13.56%
fib/100/total	7.2±0.05s	5.1±0.02s	-29.17%
fib/1000/execute	1419.4±2.19ms	77.1±0.94ms	-94.57%
fib/1000/prove	5.9±0.06s	5.1±0.02s	-13.56%
fib/1000/total	7.4±0.08s	5.2±0.01s	-29.73%
fib/10000/execute	1554.5±21.47ms	281.8±1.55ms	-81.87%
fib/10000/prove	22.2±0.15s	21.1±0.10s	-4.95%
fib/10000/total	23.7±0.15s	21.4±0.11s	-9.70%

Benchmark for macOS-default c096be1

Click to hide benchmark

Test	Base	PR	%
fib/100/execute	694.6±9.48ms	28.2±0.03ms	-95.94%
fib/100/prove	3.8±0.07s	3.7±0.04s	-2.63%
fib/100/total	4.5±0.04s	3.7±0.06s	-17.78%
fib/1000/execute	691.2±1.40ms	37.9±0.14ms	-94.52%
fib/1000/prove	3.8±0.05s	3.7±0.04s	-2.63%
fib/1000/total	4.5±0.07s	3.8±0.07s	-15.56%
fib/10000/execute	747.9±1.18ms	131.4±0.28ms	-82.43%
fib/10000/prove	15.3±0.12s	15.3±0.06s	0.00%
fib/10000/total	16.0±0.13s	15.4±0.15s	-3.75%

Benchmark for macOS-metal c096be1

Click to hide benchmark

Test	Base	PR	%
fib/100/execute	685.4±0.85ms	28.2±0.09ms	-95.89%
fib/100/prove	901.3±4.24ms	844.3±3.88ms	-6.32%
fib/100/total	1614.3±4.71ms	898.3±10.25ms	-44.35%
fib/1000/execute	690.4±1.50ms	37.6±0.09ms	-94.55%
fib/1000/prove	914.8±4.40ms	862.2±4.34ms	-5.75%
fib/1000/total	1634.8±8.08ms	925.0±6.53ms	-43.42%
fib/10000/execute	746.8±1.24ms	132.2±0.13ms	-82.30%
fib/10000/prove	3.4±0.01s	3.3±0.01s	-2.94%
fib/10000/total	4.1±0.01s	3.5±0.01s	-14.63%

[flaub]

Perf looks amazing!!

[github-actions]

Benchmark for Linux-cuda e062357

Click to hide benchmark

Test	Base	PR	%
fib/100/execute	322.8±0.30ms	21.5±0.13ms	-93.34%
fib/100/prove	2.5±0.01s	1111.4±6.66ms	-55.54%
fib/100/total	3.0±0.01s	1139.3±5.68ms	-62.02%
fib/1000/execute	338.6±8.48ms	41.3±0.18ms	-87.80%
fib/1000/prove	2.6±0.01s	1148.4±3.91ms	-55.83%
fib/1000/total	3.1±0.01s	1190.9±3.98ms	-61.58%
fib/10000/execute	461.4±7.87ms	240.2±1.86ms	-47.94%
fib/10000/prove	6.9±0.05s	4.2±0.02s	-39.13%
fib/10000/total	7.8±0.06s	4.5±0.04s	-42.31%

Benchmark for Linux-default e062357

Click to hide benchmark

Test	Base	PR	%
fib/100/execute	1435.9±4.76ms	56.2±1.27ms	-96.09%
fib/100/prove	5.8±0.03s	5.1±0.03s	-12.07%
fib/100/total	7.2±0.05s	5.1±0.02s	-29.17%
fib/1000/execute	1444.9±18.97ms	76.3±0.31ms	-94.72%
fib/1000/prove	5.8±0.05s	5.1±0.01s	-12.07%
fib/1000/total	7.3±0.07s	5.2±0.04s	-28.77%
fib/10000/execute	1566.9±2.72ms	284.8±0.88ms	-81.82%
fib/10000/prove	22.1±0.18s	21.3±0.14s	-3.62%
fib/10000/total	23.8±0.17s	21.5±0.07s	-9.66%

Benchmark for macOS-default e062357

Click to hide benchmark

Test	Base	PR	%
fib/100/execute	685.8±1.68ms	28.4±0.03ms	-95.86%
fib/100/prove	3.7±0.06s	3.7±0.07s	0.00%
fib/100/total	4.5±0.06s	3.8±0.04s	-15.56%
fib/1000/execute	690.9±1.30ms	37.5±0.07ms	-94.57%
fib/1000/prove	3.7±0.08s	3.7±0.07s	0.00%
fib/1000/total	4.5±0.03s	3.8±0.05s	-15.56%
fib/10000/execute	748.1±1.27ms	129.9±0.30ms	-82.64%
fib/10000/prove	15.3±0.11s	15.2±0.10s	-0.65%
fib/10000/total	16.1±0.07s	15.4±0.07s	-4.35%

Benchmark for macOS-metal e062357

Click to hide benchmark

Test	Base	PR	%
fib/100/execute	685.1±1.16ms	28.2±0.04ms	-95.88%
fib/100/prove	906.7±3.41ms	850.7±4.37ms	-6.18%
fib/100/total	1625.9±5.61ms	906.1±9.11ms	-44.27%
fib/1000/execute	690.3±1.08ms	37.6±0.08ms	-94.55%
fib/1000/prove	924.0±4.54ms	867.0±4.98ms	-6.17%
fib/1000/total	1651.7±9.39ms	934.9±4.08ms	-43.40%
fib/10000/execute	746.2±1.50ms	131.6±0.30ms	-82.36%
fib/10000/prove	3.4±0.01s	3.3±0.01s	-2.94%
fib/10000/total	4.1±0.01s	3.5±0.01s	-14.63%