Optimize BigInteger.CompareTo()

[kzrnm]

I optimized CompareTo() as follows.

• Reduced number of comparison operation calls
• Removal of bound checks
• Shared implementation of BigInteger.CompareTo and BigIntegerCalculator.Compare

kzrnm/performance@b3d5819

BenchmarkDotNet v0.13.11-nightly.20231126.107, Windows 11 (10.0.22631.2861/23H2/2023Update/SunValley3)
13th Gen Intel Core i5-13500, 1 CPU, 20 logical and 14 physical cores
.NET SDK 9.0.100-alpha.1.24055.2
  [Host]     : .NET 9.0.0 (9.0.24.5410), X64 RyuJIT AVX2
  Job-TFLKKT : .NET 9.0.0 (42.42.42.42424), X64 RyuJIT AVX2
  Job-RQNTME : .NET 9.0.0 (42.42.42.42424), X64 RyuJIT AVX2

PowerPlanMode=00000000-0000-0000-0000-000000000000  IterationTime=250.0000 ms  MaxIterationCount=20  
MinIterationCount=15  WarmupCount=1  

Method	Job	Toolchain	arguments	Mean	Error	StdDev	Median	Min	Max	Ratio	RatioSD	Allocated	Alloc Ratio
Compare	Job-TFLKKT	\new\corerun.exe	259 bytes, DiffFirstByte	35.574 ns	0.1296 ns	0.1212 ns	35.565 ns	35.376 ns	35.776 ns	0.77	0.00	-	NA
Compare	Job-RQNTME	\old\corerun.exe	259 bytes, DiffFirstByte	46.289 ns	0.1244 ns	0.1102 ns	46.276 ns	46.154 ns	46.535 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	259 bytes, DiffLastByte	2.023 ns	0.0112 ns	0.0093 ns	2.022 ns	2.007 ns	2.044 ns	0.88	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	259 bytes, DiffLastByte	2.285 ns	0.0137 ns	0.0122 ns	2.285 ns	2.262 ns	2.303 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	259 bytes, DiffMiddleByte	14.943 ns	0.0859 ns	0.0761 ns	14.937 ns	14.853 ns	15.106 ns	0.69	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	259 bytes, DiffMiddleByte	21.642 ns	0.1474 ns	0.1307 ns	21.616 ns	21.410 ns	21.916 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	259 bytes, Same	30.253 ns	0.1889 ns	0.1577 ns	30.253 ns	29.968 ns	30.548 ns	0.83	0.02	-	NA
Compare	Job-RQNTME	\old\corerun.exe	259 bytes, Same	36.486 ns	0.6951 ns	0.6502 ns	36.725 ns	35.299 ns	37.722 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	67 bytes, DiffFirstByte	7.920 ns	0.0364 ns	0.0341 ns	7.919 ns	7.864 ns	7.978 ns	0.72	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	67 bytes, DiffFirstByte	11.046 ns	0.2108 ns	0.1972 ns	10.970 ns	10.824 ns	11.488 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	67 bytes, DiffLastByte	2.311 ns	0.0692 ns	0.0578 ns	2.297 ns	2.254 ns	2.455 ns	1.11	0.40	-	NA
Compare	Job-RQNTME	\old\corerun.exe	67 bytes, DiffLastByte	3.786 ns	1.8665 ns	2.1494 ns	2.934 ns	1.729 ns	6.698 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	67 bytes, DiffMiddleByte	5.747 ns	0.0471 ns	0.0418 ns	5.751 ns	5.682 ns	5.805 ns	0.87	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	67 bytes, DiffMiddleByte	6.631 ns	0.0667 ns	0.0624 ns	6.611 ns	6.564 ns	6.760 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	67 bytes, Same	6.220 ns	0.0496 ns	0.0464 ns	6.216 ns	6.169 ns	6.308 ns	0.75	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	67 bytes, Same	8.307 ns	0.0794 ns	0.0743 ns	8.284 ns	8.184 ns	8.418 ns	1.00	0.00	-	NA

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Issue Details

---

I optimized CompareTo() as follows.

• Reduced number of comparison operation calls
• Removal of bound checks
• Shared implementation of BigInteger.CompareTo and BigIntegerCalculator.Compare

BenchmarkDotNet v0.13.11-nightly.20231126.107, Windows 11 (10.0.22631.2861/23H2/2023Update/SunValley3)
13th Gen Intel Core i5-13500, 1 CPU, 20 logical and 14 physical cores
.NET SDK 9.0.100-alpha.1.24055.2
  [Host]     : .NET 9.0.0 (9.0.24.5410), X64 RyuJIT AVX2
  Job-TFLKKT : .NET 9.0.0 (42.42.42.42424), X64 RyuJIT AVX2
  Job-RQNTME : .NET 9.0.0 (42.42.42.42424), X64 RyuJIT AVX2

PowerPlanMode=00000000-0000-0000-0000-000000000000  IterationTime=250.0000 ms  MaxIterationCount=20  
MinIterationCount=15  WarmupCount=1  

Method	Job	Toolchain	arguments	Mean	Error	StdDev	Median	Min	Max	Ratio	RatioSD	Allocated	Alloc Ratio
Compare	Job-TFLKKT	\new\corerun.exe	259 bytes, DiffFirstByte	35.574 ns	0.1296 ns	0.1212 ns	35.565 ns	35.376 ns	35.776 ns	0.77	0.00	-	NA
Compare	Job-RQNTME	\old\corerun.exe	259 bytes, DiffFirstByte	46.289 ns	0.1244 ns	0.1102 ns	46.276 ns	46.154 ns	46.535 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	259 bytes, DiffLastByte	2.023 ns	0.0112 ns	0.0093 ns	2.022 ns	2.007 ns	2.044 ns	0.88	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	259 bytes, DiffLastByte	2.285 ns	0.0137 ns	0.0122 ns	2.285 ns	2.262 ns	2.303 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	259 bytes, DiffMiddleByte	14.943 ns	0.0859 ns	0.0761 ns	14.937 ns	14.853 ns	15.106 ns	0.69	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	259 bytes, DiffMiddleByte	21.642 ns	0.1474 ns	0.1307 ns	21.616 ns	21.410 ns	21.916 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	259 bytes, Same	30.253 ns	0.1889 ns	0.1577 ns	30.253 ns	29.968 ns	30.548 ns	0.83	0.02	-	NA
Compare	Job-RQNTME	\old\corerun.exe	259 bytes, Same	36.486 ns	0.6951 ns	0.6502 ns	36.725 ns	35.299 ns	37.722 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	67 bytes, DiffFirstByte	7.920 ns	0.0364 ns	0.0341 ns	7.919 ns	7.864 ns	7.978 ns	0.72	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	67 bytes, DiffFirstByte	11.046 ns	0.2108 ns	0.1972 ns	10.970 ns	10.824 ns	11.488 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	67 bytes, DiffLastByte	2.311 ns	0.0692 ns	0.0578 ns	2.297 ns	2.254 ns	2.455 ns	1.11	0.40	-	NA
Compare	Job-RQNTME	\old\corerun.exe	67 bytes, DiffLastByte	3.786 ns	1.8665 ns	2.1494 ns	2.934 ns	1.729 ns	6.698 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	67 bytes, DiffMiddleByte	5.747 ns	0.0471 ns	0.0418 ns	5.751 ns	5.682 ns	5.805 ns	0.87	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	67 bytes, DiffMiddleByte	6.631 ns	0.0667 ns	0.0624 ns	6.611 ns	6.564 ns	6.760 ns	1.00	0.00	-	NA
Compare	Job-TFLKKT	\new\corerun.exe	67 bytes, Same	6.220 ns	0.0496 ns	0.0464 ns	6.216 ns	6.169 ns	6.308 ns	0.75	0.01	-	NA
Compare	Job-RQNTME	\old\corerun.exe	67 bytes, Same	8.307 ns	0.0794 ns	0.0743 ns	8.284 ns	8.184 ns	8.418 ns	1.00	0.00	-	NA

Author:	kzrnm
Assignees:	-
Labels:	area-System.Numerics
Milestone:	-