BigInteger parsing optimization for large decimal string #51953

key-moon · 2021-04-27T20:13:58Z

Current BigNumer.NumberToBigInteger method is implemented using naive algorithm. It runs in Θ(N^2) time where N is number of digits. I implemented faster method known as divide-and-conquer algorithm. It runs Θ(N (log(N))^2). Since this algorithms running time has large constant factor, naive method is faster when N is small. So This method is only apply when N is large enough. (specifically, use divide-and-conquer method when N is more than 20000.)

I created branch from #47842 as it looks like #47842 will be merged shortly.

benchmark result

Previous method

BenchmarkDotNet=v0.12.1.1528-nightly, OS=Windows 10.0.19042.928 (20H2/October2020Update)
Intel Core i7-7500U CPU 2.70GHz (Kaby Lake), 1 CPU, 4 logical and 2 physical cores
.NET SDK=6.0.100-preview.3.21202.5
  [Host]     : .NET 6.0.0 (6.0.21.20104), X64 RyuJIT
  Job-CHCQPG : .NET 6.0.0 (42.42.42.42424), X64 RyuJIT

PowerPlanMode=00000000-0000-0000-0000-000000000000  Arguments=/p:DebugType=portable  Toolchain=CoreRun  
IterationTime=250.0000 ms  MaxIterationCount=20  MinIterationCount=15  
WarmupCount=1

Method	numberString	Mean	Error	StdDev	Median	Min	Max	Gen 0	Gen 1	Gen 2	Allocated
Parse	12345678901(...)01234567890 [20000]	2.611 ms	0.1786 ms	0.2057 ms	2.661 ms	2.208 ms	2.996 ms	26.7857	-	-	56 KB
Parse	12345678901(...)01234567890 [40000]	9.028 ms	0.7436 ms	0.8265 ms	8.816 ms	8.072 ms	10.909 ms	31.2500	-	-	96 KB
Parse	12345678901(...)01234567890 [60000]	18.521 ms	0.5179 ms	0.5756 ms	18.552 ms	17.349 ms	19.541 ms	71.4286	-	-	151 KB
Parse	12345678901(...)01234567890 [80000]	32.904 ms	1.1486 ms	1.2290 ms	32.761 ms	30.984 ms	34.686 ms	-	-	-	191 KB
Parse	12345678901(...)01234567890 [100000]	51.271 ms	1.7700 ms	2.0384 ms	51.186 ms	48.447 ms	54.856 ms	-	-	-	246 KB
Parse	12345678901(...)01234567890 [120000]	74.285 ms	3.6392 ms	3.8939 ms	73.489 ms	68.604 ms	82.719 ms	-	-	-	286 KB
Parse	12345678901(...)01234567890 [140000]	100.248 ms	5.2825 ms	5.8715 ms	98.712 ms	92.597 ms	113.046 ms	-	-	-	341 KB
Parse	12345678901(...)01234567890 [160000]	127.443 ms	4.8226 ms	5.5537 ms	125.749 ms	120.504 ms	138.583 ms	-	-	-	381 KB
Parse	12345678901(...)01234567890 [180000]	162.028 ms	4.9852 ms	5.7409 ms	162.142 ms	151.841 ms	171.640 ms	-	-	-	436 KB
Parse	12345678901(...)01234567890 [200000]	224.511 ms	16.7864 ms	19.3313 ms	224.392 ms	192.558 ms	255.098 ms	-	-	-	476 KB
Parse	12345678901(...)01234567890 [220000]	240.451 ms	10.9087 ms	12.1250 ms	234.971 ms	226.956 ms	265.072 ms	-	-	-	531 KB
Parse	12345678901(...)01234567890 [240000]	300.378 ms	25.1560 ms	27.9608 ms	296.348 ms	267.565 ms	357.131 ms	-	-	-	572 KB
Parse	12345678901(...)01234567890 [260000]	346.397 ms	26.8156 ms	29.8054 ms	335.024 ms	320.430 ms	412.120 ms	-	-	-	626 KB
Parse	12345678901(...)01234567890 [280000]	384.442 ms	12.8365 ms	14.2678 ms	381.489 ms	367.624 ms	420.767 ms	-	-	-	666 KB
Parse	12345678901(...)01234567890 [300000]	433.914 ms	9.1847 ms	10.5772 ms	433.046 ms	414.254 ms	452.394 ms	-	-	-	721 KB

Implemented method

BenchmarkDotNet=v0.12.1.1528-nightly, OS=Windows 10.0.19042.928 (20H2/October2020Update)
Intel Core i7-7500U CPU 2.70GHz (Kaby Lake), 1 CPU, 4 logical and 2 physical cores
.NET SDK=6.0.100-preview.3.21202.5
  [Host]     : .NET 6.0.0 (6.0.21.20104), X64 RyuJIT
  Job-YASIZJ : .NET 6.0.0 (42.42.42.42424), X64 RyuJIT

PowerPlanMode=00000000-0000-0000-0000-000000000000  Arguments=/p:DebugType=portable  Toolchain=CoreRun  
IterationTime=250.0000 ms  MaxIterationCount=20  MinIterationCount=15  
WarmupCount=1

Method	numberString	Mean	Error	StdDev	Median	Min	Max	Gen 0	Gen 1	Gen 2	Allocated
Parse	12345678901(...)01234567890 [20000]	2.017 ms	0.0559 ms	0.0643 ms	2.024 ms	1.921 ms	2.127 ms	140.6250	-	-	288 KB
Parse	12345678901(...)01234567890 [40000]	6.237 ms	0.1116 ms	0.0932 ms	6.218 ms	6.127 ms	6.434 ms	437.5000	83.3333	-	994 KB
Parse	12345678901(...)01234567890 [60000]	15.522 ms	1.3853 ms	1.5953 ms	15.153 ms	13.686 ms	18.949 ms	1062.5000	218.7500	-	2,831 KB
Parse	12345678901(...)01234567890 [80000]	20.554 ms	0.4685 ms	0.5208 ms	20.429 ms	19.880 ms	21.552 ms	1181.8182	181.8182	-	3,572 KB
Parse	12345678901(...)01234567890 [100000]	39.146 ms	1.8050 ms	1.8536 ms	38.681 ms	36.992 ms	44.189 ms	3000.0000	333.3333	-	7,680 KB
Parse	12345678901(...)01234567890 [120000]	47.999 ms	1.5866 ms	1.8271 ms	47.429 ms	46.147 ms	51.705 ms	3750.0000	250.0000	-	10,447 KB
Parse	12345678901(...)01234567890 [140000]	41.915 ms	1.3341 ms	1.3700 ms	41.657 ms	40.299 ms	44.621 ms	2166.6667	500.0000	-	6,532 KB
Parse	12345678901(...)01234567890 [160000]	67.668 ms	1.4404 ms	1.6010 ms	67.296 ms	65.587 ms	70.763 ms	4750.0000	250.0000	-	12,897 KB
Parse	12345678901(...)01234567890 [180000]	103.943 ms	2.4616 ms	2.8347 ms	103.285 ms	100.249 ms	109.843 ms	6500.0000	500.0000	-	18,962 KB
Parse	12345678901(...)01234567890 [200000]	136.343 ms	3.9093 ms	4.0146 ms	135.607 ms	131.575 ms	148.198 ms	9500.0000	500.0000	-	28,922 KB
Parse	12345678901(...)01234567890 [220000]	154.695 ms	3.6123 ms	3.7096 ms	154.182 ms	149.801 ms	163.375 ms	17500.0000	500.0000	-	40,999 KB
Parse	12345678901(...)01234567890 [240000]	184.792 ms	20.8938 ms	24.0613 ms	173.449 ms	163.513 ms	234.269 ms	16000.0000	1000.0000	-	39,244 KB
Parse	12345678901(...)01234567890 [260000]	160.434 ms	3.0439 ms	3.5053 ms	160.026 ms	155.602 ms	167.424 ms	12500.0000	500.0000	-	33,322 KB
Parse	12345678901(...)01234567890 [280000]	134.838 ms	2.4207 ms	2.2644 ms	134.531 ms	132.314 ms	139.587 ms	9500.0000	500.0000	-	22,696 KB
Parse	12345678901(...)01234567890 [300000]	140.690 ms	2.4686 ms	2.4245 ms	141.285 ms	134.758 ms	144.021 ms	7500.0000	1500.0000	1000.0000	24,318 KB

ghost · 2021-04-27T20:14:06Z

Tagging subscribers to this area: @tannergooding, @pgovind
See info in area-owners.md if you want to be subscribed.

Issue Details

Current BigNumer.NumberToBigInteger method is implemented using naive algorithm. It runs in Θ(N^2) time where N is number of digits. I implemented faster method known as divide-and-conquer algorithm. It runs Θ(N (log(N))^2). Since this algorithms running time has large constant factor, naive method is faster when N is small. So This method is only apply when N is large enough. (specifically, use divide-and-conquer method when N is more than 20000.)

I created branch from #47842 because #47872 looks like merged soon. sorry for inconvenience.

benchmark result

Previous method

BenchmarkDotNet=v0.12.1.1528-nightly, OS=Windows 10.0.19042.928 (20H2/October2020Update)
Intel Core i7-7500U CPU 2.70GHz (Kaby Lake), 1 CPU, 4 logical and 2 physical cores
.NET SDK=6.0.100-preview.3.21202.5
  [Host]     : .NET 6.0.0 (6.0.21.20104), X64 RyuJIT
  Job-CHCQPG : .NET 6.0.0 (42.42.42.42424), X64 RyuJIT

PowerPlanMode=00000000-0000-0000-0000-000000000000  Arguments=/p:DebugType=portable  Toolchain=CoreRun  
IterationTime=250.0000 ms  MaxIterationCount=20  MinIterationCount=15  
WarmupCount=1

Method	numberString	Mean	Error	StdDev	Median	Min	Max	Gen 0	Gen 1	Gen 2	Allocated
Parse	12345678901(...)01234567890 [20000]	2.611 ms	0.1786 ms	0.2057 ms	2.661 ms	2.208 ms	2.996 ms	26.7857	-	-	56 KB
Parse	12345678901(...)01234567890 [40000]	9.028 ms	0.7436 ms	0.8265 ms	8.816 ms	8.072 ms	10.909 ms	31.2500	-	-	96 KB
Parse	12345678901(...)01234567890 [60000]	18.521 ms	0.5179 ms	0.5756 ms	18.552 ms	17.349 ms	19.541 ms	71.4286	-	-	151 KB
Parse	12345678901(...)01234567890 [80000]	32.904 ms	1.1486 ms	1.2290 ms	32.761 ms	30.984 ms	34.686 ms	-	-	-	191 KB
Parse	12345678901(...)01234567890 [100000]	51.271 ms	1.7700 ms	2.0384 ms	51.186 ms	48.447 ms	54.856 ms	-	-	-	246 KB
Parse	12345678901(...)01234567890 [120000]	74.285 ms	3.6392 ms	3.8939 ms	73.489 ms	68.604 ms	82.719 ms	-	-	-	286 KB
Parse	12345678901(...)01234567890 [140000]	100.248 ms	5.2825 ms	5.8715 ms	98.712 ms	92.597 ms	113.046 ms	-	-	-	341 KB
Parse	12345678901(...)01234567890 [160000]	127.443 ms	4.8226 ms	5.5537 ms	125.749 ms	120.504 ms	138.583 ms	-	-	-	381 KB
Parse	12345678901(...)01234567890 [180000]	162.028 ms	4.9852 ms	5.7409 ms	162.142 ms	151.841 ms	171.640 ms	-	-	-	436 KB
Parse	12345678901(...)01234567890 [200000]	224.511 ms	16.7864 ms	19.3313 ms	224.392 ms	192.558 ms	255.098 ms	-	-	-	476 KB
Parse	12345678901(...)01234567890 [220000]	240.451 ms	10.9087 ms	12.1250 ms	234.971 ms	226.956 ms	265.072 ms	-	-	-	531 KB
Parse	12345678901(...)01234567890 [240000]	300.378 ms	25.1560 ms	27.9608 ms	296.348 ms	267.565 ms	357.131 ms	-	-	-	572 KB
Parse	12345678901(...)01234567890 [260000]	346.397 ms	26.8156 ms	29.8054 ms	335.024 ms	320.430 ms	412.120 ms	-	-	-	626 KB
Parse	12345678901(...)01234567890 [280000]	384.442 ms	12.8365 ms	14.2678 ms	381.489 ms	367.624 ms	420.767 ms	-	-	-	666 KB
Parse	12345678901(...)01234567890 [300000]	433.914 ms	9.1847 ms	10.5772 ms	433.046 ms	414.254 ms	452.394 ms	-	-	-	721 KB

Implemented method

BenchmarkDotNet=v0.12.1.1528-nightly, OS=Windows 10.0.19042.928 (20H2/October2020Update)
Intel Core i7-7500U CPU 2.70GHz (Kaby Lake), 1 CPU, 4 logical and 2 physical cores
.NET SDK=6.0.100-preview.3.21202.5
  [Host]     : .NET 6.0.0 (6.0.21.20104), X64 RyuJIT
  Job-YASIZJ : .NET 6.0.0 (42.42.42.42424), X64 RyuJIT

PowerPlanMode=00000000-0000-0000-0000-000000000000  Arguments=/p:DebugType=portable  Toolchain=CoreRun  
IterationTime=250.0000 ms  MaxIterationCount=20  MinIterationCount=15  
WarmupCount=1

Method	numberString	Mean	Error	StdDev	Median	Min	Max	Gen 0	Gen 1	Gen 2	Allocated
Parse	12345678901(...)01234567890 [20000]	2.017 ms	0.0559 ms	0.0643 ms	2.024 ms	1.921 ms	2.127 ms	140.6250	-	-	288 KB
Parse	12345678901(...)01234567890 [40000]	6.237 ms	0.1116 ms	0.0932 ms	6.218 ms	6.127 ms	6.434 ms	437.5000	83.3333	-	994 KB
Parse	12345678901(...)01234567890 [60000]	15.522 ms	1.3853 ms	1.5953 ms	15.153 ms	13.686 ms	18.949 ms	1062.5000	218.7500	-	2,831 KB
Parse	12345678901(...)01234567890 [80000]	20.554 ms	0.4685 ms	0.5208 ms	20.429 ms	19.880 ms	21.552 ms	1181.8182	181.8182	-	3,572 KB
Parse	12345678901(...)01234567890 [100000]	39.146 ms	1.8050 ms	1.8536 ms	38.681 ms	36.992 ms	44.189 ms	3000.0000	333.3333	-	7,680 KB
Parse	12345678901(...)01234567890 [120000]	47.999 ms	1.5866 ms	1.8271 ms	47.429 ms	46.147 ms	51.705 ms	3750.0000	250.0000	-	10,447 KB
Parse	12345678901(...)01234567890 [140000]	41.915 ms	1.3341 ms	1.3700 ms	41.657 ms	40.299 ms	44.621 ms	2166.6667	500.0000	-	6,532 KB
Parse	12345678901(...)01234567890 [160000]	67.668 ms	1.4404 ms	1.6010 ms	67.296 ms	65.587 ms	70.763 ms	4750.0000	250.0000	-	12,897 KB
Parse	12345678901(...)01234567890 [180000]	103.943 ms	2.4616 ms	2.8347 ms	103.285 ms	100.249 ms	109.843 ms	6500.0000	500.0000	-	18,962 KB
Parse	12345678901(...)01234567890 [200000]	136.343 ms	3.9093 ms	4.0146 ms	135.607 ms	131.575 ms	148.198 ms	9500.0000	500.0000	-	28,922 KB
Parse	12345678901(...)01234567890 [220000]	154.695 ms	3.6123 ms	3.7096 ms	154.182 ms	149.801 ms	163.375 ms	17500.0000	500.0000	-	40,999 KB
Parse	12345678901(...)01234567890 [240000]	184.792 ms	20.8938 ms	24.0613 ms	173.449 ms	163.513 ms	234.269 ms	16000.0000	1000.0000	-	39,244 KB
Parse	12345678901(...)01234567890 [260000]	160.434 ms	3.0439 ms	3.5053 ms	160.026 ms	155.602 ms	167.424 ms	12500.0000	500.0000	-	33,322 KB
Parse	12345678901(...)01234567890 [280000]	134.838 ms	2.4207 ms	2.2644 ms	134.531 ms	132.314 ms	139.587 ms	9500.0000	500.0000	-	22,696 KB
Parse	12345678901(...)01234567890 [300000]	140.690 ms	2.4686 ms	2.4245 ms	141.285 ms	134.758 ms	144.021 ms	7500.0000	1500.0000	1000.0000	24,318 KB

Author:	key-moon
Assignees:	-
Labels:	`area-System.Numerics`
Milestone:	-

dnfadmin · 2021-04-27T20:14:13Z

All CLA requirements met.

jeffhandley · 2021-05-11T22:50:22Z

@pgovind Could you review this when you get a chance please?

pgovind · 2021-05-19T07:11:21Z

Would you mind rebasing this PR on the latest main? I spent a little bit of time looking at the PR today and the changes from #47842 making it hard to discern this PR's changes.

key-moon · 2021-05-19T10:01:06Z

Thanks for reviewing. I rebased onto current main branch. Since it requires history modification, I force-pushed the change. Sorry for inconvenience.

pgovind · 2021-05-25T18:08:19Z

src/libraries/System.Runtime.Numerics/src/System/Numerics/BigNumber.cs

+                }
+                else
+                {
+                    if (numberScale < 0)


Just adding a note to myself: This is the real change in the PR. The block above is just refactoring inside an if. I'll review this PR this week. It's taking some time since I need to go through the algorithm first and then review the implementation here.

stephentoub · 2021-05-26T13:42:48Z

src/libraries/System.Runtime.Numerics/src/System/Numerics/BigNumber.cs

@@ -494,35 +494,242 @@ private static bool HexNumberToBigInteger(ref BigNumberBuffer number, out BigInt
            }
        }

+        private static int s_naiveThreshold = 20000;


Nit:

private const int NaiveThreshold = 20_000;

Also, it'd be helpful to add a comment about how this value was selected.

src/libraries/System.Runtime.Numerics/src/System/Numerics/BigNumber.cs

Co-authored-by: Stephen Toub <stoub@microsoft.com>

jeffhandley · 2021-07-03T06:45:08Z

@key-moon and @dotnet/area-system-numerics, I just realized that this PR was still open, but the originating branch has been deleted. I'm going to close the PR, but if you want to proceed with it, we could still carry forward starting with the last commit.

key-moon · 2021-07-03T08:41:16Z

I accidentally deleted a forked repository yesterday. I want to continue from the last commit. What do I need to do? I apologize for the inconvenience caused.

jeffhandley · 2021-07-03T08:46:36Z

No problem; I'm sorry we let the PR sit as long as we did.

I tried to see if I could recover the commit, but I'm not sure if that will work. I think the best bet here is to create a new branch and reapply the changes that are still shown in this PRs files changed tab. Since the changes look pretty well-contained, I think that'll be easier than trying to pull off some GitHub/git magic to recover the actual previous commits. From there, you can create a new PR and link to this one in the new PR description.

dotnet-issue-labeler bot added the area-System.Numerics label Apr 27, 2021

jeffhandley assigned pgovind May 11, 2021

pgovind requested review from tannergooding and pgovind May 11, 2021 23:02

key-moon added 2 commits May 19, 2021 18:46

implement divide-and-conquer method for parsing digits

e93dde5

fix argument order in Assert when x equals to 0

2fdbe45

pgovind reviewed May 25, 2021

View reviewed changes

stephentoub reviewed May 26, 2021

View reviewed changes

src/libraries/System.Runtime.Numerics/src/System/Numerics/BigNumber.cs Show resolved Hide resolved

stephentoub reviewed May 26, 2021

View reviewed changes

src/libraries/System.Runtime.Numerics/src/System/Numerics/BigNumber.cs Outdated Show resolved Hide resolved

Apply format fix

7d89c46

Co-authored-by: Stephen Toub <stoub@microsoft.com>

jeffhandley closed this Jul 3, 2021

key-moon mentioned this pull request Jul 3, 2021

[resubmit] BigInteger parsing optimization for large decimal string #55121

Merged

karelz mentioned this pull request Jul 28, 2021

System.Net.Security test run killed on Mono Linux #56478

Closed

ghost locked as resolved and limited conversation to collaborators Aug 2, 2021

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

BigInteger parsing optimization for large decimal string #51953

BigInteger parsing optimization for large decimal string #51953

key-moon commented Apr 27, 2021 •

edited

Loading

ghost commented Apr 27, 2021

benchmark result

dnfadmin commented Apr 27, 2021 •

edited

Loading

jeffhandley commented May 11, 2021

pgovind commented May 19, 2021

key-moon commented May 19, 2021

pgovind May 25, 2021

stephentoub May 26, 2021

stephentoub May 26, 2021

jeffhandley commented Jul 3, 2021

key-moon commented Jul 3, 2021

jeffhandley commented Jul 3, 2021

BigInteger parsing optimization for large decimal string #51953

BigInteger parsing optimization for large decimal string #51953

Conversation

key-moon commented Apr 27, 2021 • edited Loading

benchmark result

ghost commented Apr 27, 2021

benchmark result

dnfadmin commented Apr 27, 2021 • edited Loading

jeffhandley commented May 11, 2021

pgovind commented May 19, 2021

key-moon commented May 19, 2021

pgovind May 25, 2021

Choose a reason for hiding this comment

stephentoub May 26, 2021

Choose a reason for hiding this comment

stephentoub May 26, 2021

Choose a reason for hiding this comment

jeffhandley commented Jul 3, 2021

key-moon commented Jul 3, 2021

jeffhandley commented Jul 3, 2021

key-moon commented Apr 27, 2021 •

edited

Loading

dnfadmin commented Apr 27, 2021 •

edited

Loading