Optimize BigInteger.Parse

[kzrnm]

Optimize Multiplier

BigInteger.Parse treats $10^{9\times2^n}$ as a multiplier.
The leading $9\times2^n/32$ items of the array representation of $10^{9\times2^n}$ is zero, so the number of arrays for multiplication can be reduced.

For example, the array represention of $10^{9\times2^8} = 10^{2304}$ has 957 items, of which the leading 288 items are 0.

Parse powers of ten

BigInteger.Parse("1" + new string('0', n)) is too slow. It runs in $O(n^2)$.
This is because trailing zeros are always calculated naively.
I fixed the behavior.

Benchmark

using BenchmarkDotNet.Attributes; using BenchmarkDotNet.Running; using BenchmarkDotNet.Configs; using System.Numerics; using System.Runtime.InteropServices; BenchmarkSwitcher.FromAssembly(typeof(ParseTest).Assembly).Run(args); [DisassemblyDiagnoser] [GroupBenchmarksBy(BenchmarkLogicalGroupRule.ByMethod)] public class ParseTest { [Params(1000, 10000, 100000, 1000000)] public int N; string s1, s2, s3; [GlobalSetup] public void Setup() { s1 = "1" + new string('0', N); s2 = "1" + new string('0', N - 1) + "1"; s3 = new string('9', N); } [Benchmark] public BigInteger PowerOfTen() => BigInteger.Parse(s1); [Benchmark] public BigInteger PowerOfTenPlusOne() => BigInteger.Parse(s2); [Benchmark] public BigInteger PowerOfTenMinusOne() => BigInteger.Parse(s3); }

 BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.3527/23H2/2023Update/SunValley3) 13th Gen Intel Core i5-13500, 1 CPU, 20 logical and 14 physical cores .NET SDK 9.0.100-preview.3.24204.13 [Host] : .NET 9.0.0 (9.0.24.17209), X64 RyuJIT AVX2 Job-DWSMWG : .NET 9.0.0 (42.42.42.42424), X64 RyuJIT AVX2 Job-ECQBBV : .NET 9.0.0 (42.42.42.42424), X64 RyuJIT AVX2 

Method	Job	Toolchain	N	Mean	Error	StdDev	Ratio	RatioSD	Code Size	Gen0	Allocated	Alloc Ratio
PowerOfTen	Job-DWSMWG	\main\corerun.exe	1000	5.022 μs	0.0594 μs	0.0496 μs	1.00	0.00	2,909 B	0.0305	440 B	1.00
PowerOfTen	Job-ECQBBV	\pr\corerun.exe	1000	5.020 μs	0.0969 μs	0.0859 μs	1.00	0.01	2,909 B	0.0305	440 B	1.00
PowerOfTen	Job-DWSMWG	\main\corerun.exe	10000	404.471 μs	7.6946 μs	7.1975 μs	1.00	0.00	2,902 B	-	4187 B	1.00
PowerOfTen	Job-ECQBBV	\pr\corerun.exe	10000	68.792 μs	1.3603 μs	1.3970 μs	0.17	0.00	2,877 B	0.2441	4185 B	1.00
PowerOfTen	Job-DWSMWG	\main\corerun.exe	100000	39,121.600 μs	246.3455 μs	205.7096 μs	1.00	0.00	2,901 B	-	41612 B	1.00
PowerOfTen	Job-ECQBBV	\pr\corerun.exe	100000	2,638.464 μs	14.9664 μs	13.2673 μs	0.07	0.00	2,877 B	-	41579 B	1.00
PowerOfTen	Job-DWSMWG	\main\corerun.exe	1000000	4,009,495.647 μs	17,321.2555 μs	16,202.3132 μs	1.00	0.00	94 B	-	439056 B	1.00
PowerOfTen	Job-ECQBBV	\pr\corerun.exe	1000000	97,940.946 μs	487.5769 μs	432.2242 μs	0.02	0.00	2,869 B	-	416352 B	0.95
PowerOfTenPlusOne	Job-DWSMWG	\main\corerun.exe	1000	5.881 μs	0.0758 μs	0.0592 μs	1.00	0.00	2,909 B	0.0305	440 B	1.00
PowerOfTenPlusOne	Job-ECQBBV	\pr\corerun.exe	1000	5.841 μs	0.0784 μs	0.0733 μs	0.99	0.01	2,877 B	0.0305	440 B	1.00
PowerOfTenPlusOne	Job-DWSMWG	\main\corerun.exe	10000	278.657 μs	1.8829 μs	1.5723 μs	1.00	0.00	2,877 B	0.4883	8659 B	1.00
PowerOfTenPlusOne	Job-ECQBBV	\pr\corerun.exe	10000	80.380 μs	1.5721 μs	1.4705 μs	0.29	0.00	2,880 B	0.2441	4184 B	0.48
PowerOfTenPlusOne	Job-DWSMWG	\main\corerun.exe	100000	9,978.399 μs	84.3427 μs	78.8943 μs	1.00	0.00	2,872 B	-	86136 B	1.00
PowerOfTenPlusOne	Job-ECQBBV	\pr\corerun.exe	100000	3,041.650 μs	13.5062 μs	11.2783 μs	0.30	0.00	2,870 B	-	41579 B	0.48
PowerOfTenPlusOne	Job-DWSMWG	\main\corerun.exe	1000000	370,703.885 μs	3,617.1873 μs	3,020.5152 μs	1.00	0.00	94 B	-	866608 B	1.00
PowerOfTenPlusOne	Job-ECQBBV	\pr\corerun.exe	1000000	112,643.729 μs	870.3710 μs	814.1455 μs	0.30	0.00	2,872 B	-	416568 B	0.48
PowerOfTenMinusOne	Job-DWSMWG	\main\corerun.exe	1000	5.978 μs	0.0465 μs	0.0412 μs	1.00	0.00	2,909 B	0.0305	440 B	1.00
PowerOfTenMinusOne	Job-ECQBBV	\pr\corerun.exe	1000	6.055 μs	0.1183 μs	0.1265 μs	1.01	0.03	2,877 B	0.0305	440 B	1.00
PowerOfTenMinusOne	Job-DWSMWG	\main\corerun.exe	10000	279.346 μs	2.8043 μs	2.3417 μs	1.00	0.00	2,877 B	0.4883	8659 B	1.00
PowerOfTenMinusOne	Job-ECQBBV	\pr\corerun.exe	10000	208.960 μs	1.3014 μs	1.2173 μs	0.75	0.01	2,877 B	0.2441	4186 B	0.48
PowerOfTenMinusOne	Job-DWSMWG	\main\corerun.exe	100000	10,202.449 μs	58.1694 μs	54.4117 μs	1.00	0.00	2,872 B	-	86042 B	1.00
PowerOfTenMinusOne	Job-ECQBBV	\pr\corerun.exe	100000	7,508.013 μs	72.8591 μs	64.5877 μs	0.74	0.01	2,870 B	-	41613 B	0.48
PowerOfTenMinusOne	Job-DWSMWG	\main\corerun.exe	1000000	367,924.436 μs	2,814.6511 μs	2,495.1149 μs	1.00	0.00	94 B	-	866560 B	1.00
PowerOfTenMinusOne	Job-ECQBBV	\pr\corerun.exe	1000000	260,532.370 μs	4,869.6777 μs	4,555.0995 μs	0.71	0.01	94 B	-	415736 B	0.48

[ghost]

Tagging subscribers to this area: @dotnet/area-system-numerics
See info in area-owners.md if you want to be subscribed.

Issue Details

---

BigInteger.Parse("1" + new string('0', n)) is too slow. It runs in $O(n^2)$.
This is because trailing zeros are always calculated naively.
I fixed the behavior.

Benchmark

using BenchmarkDotNet.Attributes; using BenchmarkDotNet.Running; using System.Numerics; using System.Runtime.InteropServices; BenchmarkSwitcher.FromAssembly(typeof(Tests).Assembly).Run(args); [DisassemblyDiagnoser] public class Tests { [Params(1000, 10000, 100000, 1000000)] public int N; string s1, s2, s3; [GlobalSetup] public void Setup() { s1 = "1" + new string('0', N); s2 = "1" + new string('0', N - 1) + "1"; s3 = new string('9', N - 1); } [Benchmark] public BigInteger PowerOfTen() => BigInteger.Parse(s1); [Benchmark(Baseline = true)] public BigInteger PowerOfTenPlusOne() => BigInteger.Parse(s2); [Benchmark] public BigInteger PowerOfTenMinusOne() => BigInteger.Parse(s3); }

 BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.3085/23H2/2023Update/SunValley3) 13th Gen Intel Core i5-13500, 1 CPU, 20 logical and 14 physical cores .NET SDK 9.0.100-alpha.1.23615.4 [Host] : .NET 9.0.0 (9.0.23.61410), X64 RyuJIT AVX2 Job-KEBJOQ : .NET 9.0.0 (42.42.42.42424), X64 RyuJIT AVX2 Job-VLAEBK : .NET 9.0.0 (42.42.42.42424), X64 RyuJIT AVX2 

Method	Job	Toolchain	N	Mean	Error	StdDev	Ratio	RatioSD	Code Size	Gen0	Allocated	Alloc Ratio
PowerOfTen	Job-KEBJOQ	\main\corerun.exe	1000	5.464 μs	0.0769 μs	0.0720 μs	0.88	0.01	3,216 B	0.0305	440 B	1.00
PowerOfTenPlusOne	Job-KEBJOQ	\main\corerun.exe	1000	6.200 μs	0.0829 μs	0.0775 μs	1.00	0.00	3,216 B	0.0305	440 B	1.00
PowerOfTenMinusOne	Job-KEBJOQ	\main\corerun.exe	1000	5.965 μs	0.0475 μs	0.0444 μs	0.96	0.01	3,216 B	0.0305	440 B	1.00
PowerOfTen	Job-VLAEBK	\pr\corerun.exe	1000	5.728 μs	0.0488 μs	0.0456 μs	0.92	0.01	3,309 B	0.0763	976 B	2.22
PowerOfTenPlusOne	Job-VLAEBK	\pr\corerun.exe	1000	6.172 μs	0.0492 μs	0.0460 μs	1.00	0.01	3,309 B	0.0763	976 B	2.22
PowerOfTenMinusOne	Job-VLAEBK	\pr\corerun.exe	1000	5.778 μs	0.0388 μs	0.0344 μs	0.93	0.01	3,309 B	0.0763	976 B	2.22
PowerOfTen	Job-KEBJOQ	\main\corerun.exe	10000	425.126 μs	6.6050 μs	6.1783 μs	0.98	0.02	3,216 B	-	4184 B	1.00
PowerOfTenPlusOne	Job-KEBJOQ	\main\corerun.exe	10000	433.456 μs	6.0261 μs	5.6369 μs	1.00	0.00	3,216 B	-	4184 B	1.00
PowerOfTenMinusOne	Job-KEBJOQ	\main\corerun.exe	10000	432.347 μs	3.8901 μs	3.6388 μs	1.00	0.02	3,216 B	-	4177 B	1.00
PowerOfTen	Job-VLAEBK	\pr\corerun.exe	10000	424.032 μs	6.4220 μs	6.0071 μs	0.98	0.02	3,309 B	0.9766	12400 B	2.96
PowerOfTenPlusOne	Job-VLAEBK	\pr\corerun.exe	10000	434.967 μs	5.7997 μs	5.4250 μs	1.00	0.02	3,309 B	0.9766	12400 B	2.96
PowerOfTenMinusOne	Job-VLAEBK	\pr\corerun.exe	10000	429.771 μs	5.5313 μs	5.1740 μs	0.99	0.02	3,305 B	0.9766	12392 B	2.96
PowerOfTen	Job-KEBJOQ	\main\corerun.exe	100000	41,307.777 μs	380.6849 μs	356.0929 μs	3.67	0.08	3,216 B	-	41583 B	0.48
PowerOfTenPlusOne	Job-KEBJOQ	\main\corerun.exe	100000	11,274.413 μs	215.6506 μs	211.7977 μs	1.00	0.00	2,954 B	-	86046 B	1.00
PowerOfTenMinusOne	Job-KEBJOQ	\main\corerun.exe	100000	11,382.852 μs	214.8872 μs	201.0056 μs	1.01	0.03	2,954 B	-	86041 B	1.00
PowerOfTen	Job-VLAEBK	\pr\corerun.exe	100000	4,972.020 μs	73.2368 μs	68.5057 μs	0.44	0.01	3,047 B	7.8125	107118 B	1.24
PowerOfTenPlusOne	Job-VLAEBK	\pr\corerun.exe	100000	5,093.083 μs	56.5632 μs	52.9092 μs	0.45	0.01	3,047 B	-	41556 B	0.48
PowerOfTenMinusOne	Job-VLAEBK	\pr\corerun.exe	100000	10,432.147 μs	116.1019 μs	108.6018 μs	0.93	0.02	3,047 B	-	41564 B	0.48
PowerOfTen	Job-KEBJOQ	\main\corerun.exe	1000000	4,151,269.093 μs	43,494.0408 μs	40,684.3528 μs	10.46	0.14	94 B	-	415720 B	0.48
PowerOfTenPlusOne	Job-KEBJOQ	\main\corerun.exe	1000000	396,808.680 μs	6,230.0066 μs	5,827.5520 μs	1.00	0.00	94 B	-	860144 B	1.00
PowerOfTenMinusOne	Job-KEBJOQ	\main\corerun.exe	1000000	395,750.933 μs	7,009.0187 μs	6,556.2404 μs	1.00	0.02	94 B	-	860864 B	1.00
PowerOfTen	Job-VLAEBK	\pr\corerun.exe	1000000	199,223.140 μs	2,441.7662 μs	2,284.0296 μs	0.50	0.01	3,047 B	-	939717 B	1.09
PowerOfTenPlusOne	Job-VLAEBK	\pr\corerun.exe	1000000	196,380.902 μs	2,521.1383 μs	2,358.2743 μs	0.50	0.01	3,047 B	-	415517 B	0.48
PowerOfTenMinusOne	Job-VLAEBK	\pr\corerun.exe	1000000	376,507.469 μs	3,501.7144 μs	2,924.0902 μs	0.95	0.01	94 B	-	416008 B	0.48

Author:	kzrnm
Assignees:	-
Labels:	area-System.Numerics, community-contribution
Milestone:	-

[kzrnm]

I updated the benchmark target to the latest commit.

[tannergooding]

I updated the benchmark target to the latest commit.

Thanks! Slowly getting through stuff here and just want to ensure no conflicts/accurate numbers/etc as they go through.

[tannergooding]

Looks like there are some related CI failures that need to get resolved.

[kzrnm]

Tests fail when parseTest and ToStringTest are run in parallel. I think RunWithFakeThreshold is the cause of failure.
I set DisableParallelization so that RunWithFakeThreshold is not executed in parallel.

[kzrnm]

I was able to reproduce the error with the following code.

Number.s_naiveThreshold = 0; BigInteger.Parse("99000000000");

[tannergooding]

@huoyaoyuan, if you have some time I'd appreciate if you could give this a once over as well, given you've also been touching/updating the parsing logic.

I'd ideally like to get #95402 done first and I know there's another PR out, but you recently changed that one back to draft

[huoyaoyuan]

I'd ideally like to get #95402 done first and I know there's another PR out, but you recently changed that one back to draft

I've done the code update and measuring the performance. I'd expect to make it ready this weekend.

[tannergooding]

@kzrnm, sorry for the delay on this. Could you share updated numbers, just so we can confirm nothing has regressed given all the other work that's been done?

After that, I think we can get this merged.

[kzrnm]

@tannergooding I ran benchmarks on the latest branch.

 BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.3810/23H2/2023Update/SunValley3) 13th Gen Intel Core i5-13500, 1 CPU, 20 logical and 14 physical cores .NET SDK 9.0.100-preview.5.24307.3 [Host] : .NET 9.0.0 (9.0.24.30607), X64 RyuJIT AVX2 ShortRun : .NET 9.0.0 (42.42.42.42424), X64 RyuJIT AVX2 Job=ShortRun IterationCount=3 LaunchCount=1 WarmupCount=3 

Method	Toolchain	N	Mean	Error	StdDev	Ratio	RatioSD	Gen0	Code Size	Allocated	Alloc Ratio
PowerOfTen	\main\corerun.exe	1000	4.723 μs	0.7022 μs	0.0385 μs	1.00	0.00	0.0305	3,051 B	440 B	1.00
PowerOfTen	\pr\corerun.exe	1000	4.727 μs	0.2059 μs	0.0113 μs	1.00	0.01	0.0305	3,051 B	440 B	1.00
PowerOfTen	\main\corerun.exe	10000	417.409 μs	85.4963 μs	4.6863 μs	1.00	0.00	-	3,049 B	4185 B	1.00
PowerOfTen	\pr\corerun.exe	10000	65.805 μs	2.0472 μs	0.1122 μs	0.16	0.00	0.2441	3,019 B	4184 B	1.00
PowerOfTen	\main\corerun.exe	100000	39,509.697 μs	7,036.3549 μs	385.6864 μs	1.00	0.00	-	3,048 B	41634 B	1.00
PowerOfTen	\pr\corerun.exe	100000	2,621.521 μs	445.6280 μs	24.4264 μs	0.07	0.00	-	3,016 B	41556 B	1.00
PowerOfTen	\main\corerun.exe	1000000	5,547,848.100 μs	44,683.6720 μs	2,449.2628 μs	1.00	0.00	-	94 B	416344 B	1.00
PowerOfTen	\pr\corerun.exe	1000000	106,203.493 μs	35,159.8003 μs	1,927.2273 μs	0.02	0.00	-	94 B	415486 B	1.00
PowerOfTenPlusOne	\main\corerun.exe	1000	5.631 μs	0.2055 μs	0.0113 μs	1.00	0.00	0.0305	3,049 B	440 B	1.00
PowerOfTenPlusOne	\pr\corerun.exe	1000	5.309 μs	0.1675 μs	0.0092 μs	0.94	0.00	0.0305	3,019 B	440 B	1.00
PowerOfTenPlusOne	\main\corerun.exe	10000	287.339 μs	16.9327 μs	0.9281 μs	1.00	0.00	0.4883	3,017 B	8657 B	1.00
PowerOfTenPlusOne	\pr\corerun.exe	10000	76.457 μs	8.4699 μs	0.4643 μs	0.27	0.00	0.2441	3,017 B	4184 B	0.48
PowerOfTenPlusOne	\main\corerun.exe	100000	10,017.519 μs	2,451.2130 μs	134.3593 μs	1.00	0.00	-	3,016 B	86046 B	1.00
PowerOfTenPlusOne	\pr\corerun.exe	100000	3,088.058 μs	581.6661 μs	31.8831 μs	0.31	0.00	-	3,017 B	41556 B	0.48
PowerOfTenPlusOne	\main\corerun.exe	1000000	371,023.767 μs	47,955.9585 μs	2,628.6279 μs	1.00	0.00	-	94 B	860864 B	1.00
PowerOfTenPlusOne	\pr\corerun.exe	1000000	117,715.373 μs	38,234.2942 μs	2,095.7507 μs	0.32	0.00	-	94 B	415429 B	0.48
PowerOfTenMinusOne	\main\corerun.exe	1000	5.784 μs	0.7608 μs	0.0417 μs	1.00	0.00	0.0305	3,051 B	440 B	1.00
PowerOfTenMinusOne	\pr\corerun.exe	1000	5.551 μs	0.5350 μs	0.0293 μs	0.96	0.01	0.0305	3,018 B	440 B	1.00
PowerOfTenMinusOne	\main\corerun.exe	10000	296.562 μs	88.8331 μs	4.8692 μs	1.00	0.00	0.4883	3,017 B	8657 B	1.00
PowerOfTenMinusOne	\pr\corerun.exe	10000	208.304 μs	79.8736 μs	4.3781 μs	0.70	0.02	0.2441	3,019 B	4184 B	0.48
PowerOfTenMinusOne	\main\corerun.exe	100000	10,168.222 μs	1,159.4629 μs	63.5541 μs	1.00	0.00	-	3,016 B	86046 B	1.00
PowerOfTenMinusOne	\pr\corerun.exe	100000	7,655.886 μs	1,894.1289 μs	103.8236 μs	0.75	0.01	-	3,017 B	41560 B	0.48
PowerOfTenMinusOne	\main\corerun.exe	1000000	366,404.433 μs	47,445.9123 μs	2,600.6706 μs	1.00	0.00	-	94 B	860864 B	1.00
PowerOfTenMinusOne	\pr\corerun.exe	1000000	263,400.400 μs	50,544.4774 μs	2,770.5134 μs	0.72	0.01	-	94 B	415808 B	0.48

[LoopedBard3]

@tannergooding Regressions:
Linux x64: dotnet/perf-autofiling-issues#37866, dotnet/perf-autofiling-issues#37802
Windows x64: dotnet/perf-autofiling-issues#37852 (BigInteger regressions), dotnet/perf-autofiling-issues#37817 (BigInteger regressions)
Linux arm64: dotnet/perf-autofiling-issues#38039

Mono related regressions:

• [Perf] Linux/arm64: 2 Regressions on 7/3/2024 6:29:56 PM perf-autofiling-issues#37939
• [Perf] Linux/x64: 3 Regressions on 7/3/2024 8:41:35 PM perf-autofiling-issues#37879
  Mono related improvements:
• [Perf] Linux/arm64: 2 Improvements on 7/3/2024 6:29:56 PM perf-autofiling-issues#37943
• [Perf] Linux/x64: 3 Improvements on 7/3/2024 8:41:35 PM perf-autofiling-issues#37884

[tannergooding]

Just noting on the regressions above that many of them are for very small inputs, like 123. I've raised that these aren't "representative" of the cases we care about here since if users care about perf for numbers that are less than or equal to 128-bits, then we have existing dedicated types they can use.

Rather, we want to ensure that BigInteger really shines for values above this cutoff. -- There is notably some consideration that we also don't want to overly regress the perf of BigInteger values with 128 or less bits, just that its not as important. For a case like Parse we could likely have a fast path that does something like if (stringLength < 40) { ParseAsInt128 } else { ParseAsBigInt }, since any string with this few digits must fit into Int128 (and a corresponding cutoff for hex numbers, etc). This would likely fix the regression without hurting the improved cases.