Port signed integer math to modern QDK

[sezna]

This PR ports the classic QDK's signed int math functionality to the modern QDK.

It is not intended to provide the perfect API -- it is just a port, that other libraries will build upon, primarily the fixed point library.

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Benchmark for 9bf065e

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Test	Base	PR	%
Array append evaluation	336.9±7.50µs	335.1±2.94µs	-0.53%
Array literal evaluation	186.2±0.81µs	186.3±1.07µs	+0.05%
Array update evaluation	414.6±6.11µs	413.6±1.25µs	-0.24%
Core + Standard library compilation	22.0±0.25ms	21.9±0.33ms	-0.45%
Deutsch-Jozsa evaluation	4.9±0.06ms	4.9±0.10ms	0.00%
Large file parity evaluation	34.5±0.26ms	34.5±0.27ms	0.00%
Large input file compilation	13.8±0.27ms	13.8±0.23ms	0.00%
Large input file compilation (interpreter)	51.5±1.69ms	51.4±1.50ms	-0.19%
Large nested iteration	33.0±0.30ms	32.8±0.31ms	-0.61%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1552.6±32.53µs	1551.9±33.59µs	-0.05%
Perform Runtime Capabilities Analysis (RCA) on large file sample	7.7±0.07ms	7.7±0.37ms	0.00%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1420.6±49.01µs	1417.9±40.44µs	-0.19%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	27.5±0.37ms	27.4±0.13ms	-0.36%
Teleport evaluation	92.9±3.57µs	94.0±3.42µs	+1.18%

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Benchmark for e9ecf1c

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Test	Base	PR	%
Array append evaluation	336.3±14.67µs	333.1±1.68µs	-0.95%
Array literal evaluation	208.1±1.96µs	224.3±1.14µs	+7.78%
Array update evaluation	415.4±1.52µs	412.1±2.79µs	-0.79%
Core + Standard library compilation	21.8±0.26ms	22.5±0.82ms	+3.21%
Deutsch-Jozsa evaluation	4.9±0.06ms	4.9±0.06ms	0.00%
Large file parity evaluation	34.5±0.27ms	34.6±0.48ms	+0.29%
Large input file compilation	13.7±0.22ms	13.7±0.50ms	0.00%
Large input file compilation (interpreter)	51.9±2.08ms	56.7±1.86ms	+9.25%
Large nested iteration	32.8±0.18ms	32.9±0.28ms	+0.30%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1563.2±32.61µs	1560.7±25.89µs	-0.16%
Perform Runtime Capabilities Analysis (RCA) on large file sample	7.8±0.12ms	7.8±0.13ms	0.00%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1423.3±37.19µs	1442.8±101.89µs	+1.37%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	27.6±0.34ms	27.8±0.71ms	+0.72%
Teleport evaluation	92.4±3.49µs	93.8±4.26µs	+1.52%

[github-actions]

Benchmark for 45e2c36

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Test	Base	PR	%
Array append evaluation	334.0±1.79µs	336.8±1.94µs	+0.84%
Array literal evaluation	192.4±1.14µs	197.4±5.17µs	+2.60%
Array update evaluation	412.6±2.00µs	416.3±2.18µs	+0.90%
Core + Standard library compilation	25.6±1.50ms	25.9±1.02ms	+1.17%
Deutsch-Jozsa evaluation	5.0±0.06ms	5.0±0.06ms	0.00%
Large file parity evaluation	35.0±0.27ms	34.9±0.34ms	-0.29%
Large input file compilation	15.4±0.49ms	15.3±0.48ms	-0.65%
Large input file compilation (interpreter)	59.8±2.55ms	59.2±2.23ms	-1.00%
Large nested iteration	32.7±0.18ms	33.1±0.21ms	+1.22%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1598.8±105.78µs	1606.2±119.65µs	+0.46%
Perform Runtime Capabilities Analysis (RCA) on large file sample	8.3±0.16ms	8.4±0.19ms	+1.20%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1457.8±103.24µs	1469.4±112.59µs	+0.80%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	28.4±0.27ms	28.6±0.23ms	+0.70%
Teleport evaluation	94.5±3.73µs	94.4±4.22µs	-0.11%

[github-actions]

Benchmark for 170b917

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Test	Base	PR	%
Array append evaluation	336.6±2.55µs	335.0±3.20µs	-0.48%
Array literal evaluation	178.3±4.53µs	192.4±2.34µs	+7.91%
Array update evaluation	417.1±3.25µs	412.9±1.55µs	-1.01%
Core + Standard library compilation	24.2±0.65ms	26.7±1.27ms	+10.33%
Deutsch-Jozsa evaluation	5.0±0.20ms	5.0±0.18ms	0.00%
Large file parity evaluation	34.9±0.51ms	34.8±0.49ms	-0.29%
Large input file compilation	14.4±0.40ms	14.0±0.42ms	-2.78%
Large input file compilation (interpreter)	56.7±1.86ms	59.8±2.99ms	+5.47%
Large nested iteration	33.1±0.33ms	32.9±0.43ms	-0.60%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1627.4±193.03µs	1572.4±56.68µs	-3.38%
Perform Runtime Capabilities Analysis (RCA) on large file sample	8.1±0.14ms	7.9±0.16ms	-2.47%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1452.3±83.16µs	1427.2±59.05µs	-1.73%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	28.4±1.48ms	28.0±0.46ms	-1.41%
Teleport evaluation	94.9±6.41µs	94.0±3.90µs	-0.95%

[github-actions]

Benchmark for 75a9a1b

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Test	Base	PR	%
Array append evaluation	333.3±3.34µs	336.0±5.99µs	+0.81%
Array literal evaluation	192.8±2.93µs	175.4±2.59µs	-9.02%
Array update evaluation	413.8±5.42µs	417.8±5.29µs	+0.97%
Core + Standard library compilation	23.1±0.60ms	23.1±0.71ms	0.00%
Deutsch-Jozsa evaluation	5.0±0.06ms	5.0±0.06ms	0.00%
Large file parity evaluation	34.8±0.27ms	34.8±0.37ms	0.00%
Large input file compilation	14.4±0.32ms	14.3±0.37ms	-0.69%
Large input file compilation (interpreter)	56.2±2.31ms	55.8±2.20ms	-0.71%
Large nested iteration	32.7±0.34ms	32.8±0.27ms	+0.31%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1586.5±138.96µs	1580.2±64.80µs	-0.40%
Perform Runtime Capabilities Analysis (RCA) on large file sample	8.0±0.13ms	8.0±0.12ms	0.00%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1441.6±63.84µs	1445.3±102.89µs	+0.26%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	27.9±0.28ms	28.0±0.29ms	+0.36%
Teleport evaluation	93.5±3.58µs	94.1±3.84µs	+0.64%

[github-actions]

Benchmark for 03a5d55

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Test	Base	PR	%
Array append evaluation	338.7±9.24µs	338.5±2.32µs	-0.06%
Array literal evaluation	168.9±2.19µs	186.2±0.84µs	+10.24%
Array update evaluation	417.5±7.21µs	415.8±2.93µs	-0.41%
Core + Standard library compilation	25.0±0.80ms	24.2±0.89ms	-3.20%
Deutsch-Jozsa evaluation	5.0±0.06ms	4.9±0.06ms	-2.00%
Large file parity evaluation	34.2±0.11ms	34.2±0.16ms	0.00%
Large input file compilation	15.0±0.59ms	14.7±0.51ms	-2.00%
Large input file compilation (interpreter)	56.2±1.83ms	56.6±2.08ms	+0.71%
Large nested iteration	33.3±1.72ms	32.8±0.36ms	-1.50%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1585.3±68.07µs	1594.2±105.62µs	+0.56%
Perform Runtime Capabilities Analysis (RCA) on large file sample	8.2±0.17ms	8.1±0.14ms	-1.22%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1452.4±82.27µs	1451.1±137.74µs	-0.09%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	28.3±0.25ms	28.2±0.45ms	-0.35%
Teleport evaluation	93.9±3.67µs	93.7±4.72µs	-0.21%

[github-actions]

Benchmark for 072b2fe

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Test	Base	PR	%
Array append evaluation	339.1±3.88µs	336.8±8.86µs	-0.68%
Array literal evaluation	169.8±6.47µs	185.6±0.73µs	+9.31%
Array update evaluation	419.4±21.64µs	413.7±3.18µs	-1.36%
Core + Standard library compilation	22.6±0.74ms	22.2±0.73ms	-1.77%
Deutsch-Jozsa evaluation	4.9±0.14ms	5.0±0.07ms	+2.04%
Large file parity evaluation	34.2±0.08ms	34.2±0.10ms	0.00%
Large input file compilation	14.2±0.67ms	13.7±0.23ms	-3.52%
Large input file compilation (interpreter)	51.5±1.52ms	53.5±1.94ms	+3.88%
Large nested iteration	32.7±0.33ms	32.7±0.39ms	0.00%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1558.8±35.97µs	1559.3±30.30µs	+0.03%
Perform Runtime Capabilities Analysis (RCA) on large file sample	7.8±0.09ms	7.9±0.11ms	+1.28%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1428.1±46.30µs	1443.3±139.48µs	+1.06%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	28.3±1.08ms	27.8±0.32ms	-1.77%
Teleport evaluation	93.6±3.49µs	93.4±5.91µs	-0.21%

[cesarzc]

Left a few minor comments.

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Benchmark for 36e7798

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Test	Base	PR	%
Array append evaluation	339.8±4.61µs	338.2±2.55µs	-0.47%
Array literal evaluation	168.9±1.17µs	170.0±8.99µs	+0.65%
Array update evaluation	417.7±5.07µs	415.2±1.68µs	-0.60%
Core + Standard library compilation	21.7±0.10ms	21.7±0.41ms	0.00%
Deutsch-Jozsa evaluation	4.9±0.07ms	4.9±0.06ms	0.00%
Large file parity evaluation	34.2±0.09ms	34.2±0.10ms	0.00%
Large input file compilation	13.5±0.12ms	13.6±0.24ms	+0.74%
Large input file compilation (interpreter)	50.6±1.53ms	50.7±0.94ms	+0.20%
Large nested iteration	34.1±2.30ms	32.8±0.77ms	-3.81%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1555.0±27.65µs	1554.2±27.03µs	-0.05%
Perform Runtime Capabilities Analysis (RCA) on large file sample	7.8±0.15ms	7.8±0.09ms	0.00%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1420.5±34.77µs	1419.6±41.41µs	-0.06%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	27.7±0.60ms	27.6±0.28ms	-0.36%
Teleport evaluation	93.2±3.36µs	93.0±4.35µs	-0.21%

[github-actions]

Benchmark for b38992a

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Test	Base	PR	%
Array append evaluation	338.2±4.01µs	339.4±2.80µs	+0.35%
Array literal evaluation	186.3±1.06µs	186.7±4.26µs	+0.21%
Array update evaluation	415.1±3.93µs	416.8±5.90µs	+0.41%
Core + Standard library compilation	25.0±1.02ms	24.7±0.73ms	-1.20%
Deutsch-Jozsa evaluation	5.0±0.06ms	5.0±0.06ms	0.00%
Large file parity evaluation	34.5±0.64ms	34.4±0.61ms	-0.29%
Large input file compilation	14.8±0.34ms	15.0±0.61ms	+1.35%
Large input file compilation (interpreter)	57.3±1.94ms	57.8±2.48ms	+0.87%
Large nested iteration	32.9±0.84ms	32.8±0.15ms	-0.30%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1608.4±114.85µs	1603.2±93.14µs	-0.32%
Perform Runtime Capabilities Analysis (RCA) on large file sample	8.1±0.16ms	8.2±0.16ms	+1.23%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1473.4±137.92µs	1470.6±121.52µs	-0.19%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	28.5±0.38ms	28.3±0.26ms	-0.70%
Teleport evaluation	94.4±3.70µs	94.1±3.75µs	-0.32%

[DmitryVasilevsky]

@sezna , Feel free to postpone all my comments for later time if you need. We can always improve code :)

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Benchmark for 5bbb91a

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Test	Base	PR	%
Array append evaluation	337.8±6.12µs	339.0±1.75µs	+0.36%
Array literal evaluation	186.5±0.83µs	169.1±1.25µs	-9.33%
Array update evaluation	415.7±2.67µs	415.6±2.63µs	-0.02%
Core + Standard library compilation	22.5±0.49ms	22.6±0.59ms	+0.44%
Deutsch-Jozsa evaluation	5.0±0.06ms	4.9±0.06ms	-2.00%
Large file parity evaluation	34.4±0.92ms	34.2±0.11ms	-0.58%
Large input file compilation	14.1±0.27ms	14.2±0.56ms	+0.71%
Large input file compilation (interpreter)	53.6±1.89ms	54.0±1.93ms	+0.75%
Large nested iteration	32.6±0.11ms	33.7±1.22ms	+3.37%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1566.3±36.82µs	1566.5±39.48µs	+0.01%
Perform Runtime Capabilities Analysis (RCA) on large file sample	7.9±0.11ms	8.0±0.14ms	+1.27%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1428.8±38.35µs	1438.2±83.07µs	+0.66%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	27.8±0.18ms	27.8±0.22ms	0.00%
Teleport evaluation	93.6±3.63µs	92.9±3.76µs	-0.75%

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Benchmark for 91aeb81

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Test	Base	PR	%
Array append evaluation	338.9±3.41µs	343.1±10.11µs	+1.24%
Array literal evaluation	168.6±1.50µs	169.6±6.15µs	+0.59%
Array update evaluation	415.7±2.27µs	415.7±1.97µs	0.00%
Core + Standard library compilation	25.8±1.55ms	22.8±0.86ms	-11.63%
Deutsch-Jozsa evaluation	5.0±0.06ms	5.0±0.08ms	0.00%
Large file parity evaluation	34.3±0.11ms	34.3±0.47ms	0.00%
Large input file compilation	14.3±0.51ms	14.5±0.70ms	+1.40%
Large input file compilation (interpreter)	57.1±2.36ms	54.9±2.80ms	-3.85%
Large nested iteration	32.8±0.32ms	32.7±0.60ms	-0.30%
Perform Runtime Capabilities Analysis (RCA) on Deutsch-Jozsa sample	1580.9±43.76µs	1609.9±188.18µs	+1.83%
Perform Runtime Capabilities Analysis (RCA) on large file sample	8.1±0.19ms	8.2±0.23ms	+1.23%
Perform Runtime Capabilities Analysis (RCA) on teleport sample	1443.3±82.96µs	1440.2±67.44µs	-0.21%
Perform Runtime Capabilities Analysis (RCA) on the core and std libraries	28.1±0.45ms	28.1±0.41ms	0.00%
Teleport evaluation	93.7±3.44µs	94.3±7.97µs	+0.64%