uint256: Introduce package. #2787

davecgh · 2021-11-06T21:16:55Z

Profiling the CPU usage during an initial chain sync shows that roughly 65-70% of all time is spent in garbage collection operations. This is primarily the result of a large number of in-use allocations. Profiling the in-use allocations shows that around almost a quarter of all in-use allocations (~22%) are due to standard library big integers which require allocations. In other words, eliminating those allocations should lead to a speedup of around 5-10% to the initial chain sync. However, note that this series of commits only introduces the package and does not update all of the relevant code to make use of it as that will be done separately.

More specifically, the allocations in question are the result of several important calculations which could be done without allocations, and more efficiently in terms of execution time, via fixed precision unsigned 256-bit integers.

Thus, motivated by the previous discussion, this is part of a series of commits that implements highly optimized allocation free fixed precision unsigned 256-bit integer arithmetic that can ultimately be used in place of the standard library big integers.

For the time being, the package is introduced into the internal staging area for initial review.

The following is a brief overview of the main features and benefits:

Strong focus on performance and correctness
Every operation is faster than the stdlib big.Int equivalent and most operations, including the primary math operations, are significantly faster
Allocation free
- All non-formatting operations with the specialized type are allocation free
Supports boolean comparison, bitwise logic, and bitwise shift operations
All operations are performed modulo 2^256
Ergonomic API with unary-style arguments are well as some binary variants
Conversion-free support for interoperation with native uint64 integers
Direct conversion to and from little and big endian byte arrays
Full support for formatted output and common base conversions
- Formatted output uses fewer allocations than stdlib big.Int
100% test coverage
Comprehensive benchmarks
Fully documented in README.md

The following benchmark results demonstrate the performance of most operations as compared to standard library big.Ints. The benchmarks are from a Ryzen 7 1700 processor and are the result of feeding benchstat 10 iterations of each.

Arithmetic Methods

Name	`big.Int` Time/Op	`Uint256` Time/Op	Delta vs `big.Int`
Add	158ns ± 2%	2ns ± 1%	-98.67%
AddUint64	44.4ns ± 3%	3.4ns ± 2%	-92.27%
Sub	53.9ns ± 1%	2.1ns ± 1%	-96.12%
SubUint64	44.8ns ± 1%	3.4ns ± 2%	-92.37%
Mul	419ns ± 1%	10ns ± 2%	-97.64%
MulUint64	263ns ± 1%	4ns ± 1%	-98.30%
Square	418ns ± 0%	7ns ± 2%	-98.39%
Div/num_lt_den	75.4ns ± 1%	3.4ns ± 1%	-95.51%
Div/num_eq_den	253ns ± 2%	4ns ± 3%	-98.56%
Div/1_by_1_near	53.8ns ± 2%	4.5ns ± 2%	-91.63%
Div/1_by_1_far	31.4ns ± 2%	14.6ns ± 2%	-53.64%
Div/2_by_1_near	36.9ns ± 1%	10.1ns ± 2%	-72.63%
Div/2_by_1_far	49.1ns ± 1%	28.8ns ± 1%	-41.29%
Div/3_by_1_near	43.2ns ± 1%	13.7ns ± 3%	-68.24%
Div/3_by_1_far	57.0ns ± 1%	43.6ns ± 1%	-23.59%
Div/4_by_1_near	49.7ns ± 4%	18.0ns ± 1%	-63.87%
Div/4_by_1_far	65.2ns ± 4%	57.8ns ± 2%	-11.41%
Div/2_by_2_near	237ns ± 1%	22ns ± 3%	-90.81%
Div/2_by_2_far	237ns ± 1%	30ns ± 3%	-87.17%
Div/3_by_2_near	258ns ± 1%	29ns ± 1%	-88.60%
Div/3_by_2_far	257ns ± 1%	50ns ± 2%	-80.42%
Div/4_by_2_near	312ns ± 2%	40ns ± 3%	-87.27%
Div/4_by_2_far	310ns ± 1%	71ns ± 3%	-77.19%
Div/3_by_3_near	239ns ± 2%	21ns ± 2%	-91.39%
Div/3_by_3_far	242ns ± 4%	33ns ± 3%	-86.33%
Div/4_by_3_near	279ns ± 6%	31ns ± 1%	-89.01%
Div/4_by_3_far	271ns ± 1%	46ns ± 3%	-82.99%
Div/4_by_4_near	252ns ± 3%	20ns ± 3%	-91.99%
Div/4_by_4_far	249ns ± 2%	36ns ± 2%	-85.65%
DivRandom	202ns ± 1%	23ns ± 1%	-88.43%
DivUint64	129ns ± 1%	47ns ± 0%	-63.34%
Negate	47.3ns ± 2%	1.5ns ± 2%	-96.91%

Comparison Methods

Name	`big.Int` Time/Op	`Uint256` Time/Op	Delta vs `big.Int`
Eq	12.7ns ± 1%	2.1ns ± 1%	-83.72%
Lt	12.6ns ± 1%	3.0ns ± 1%	-75.96%
Gt	12.6ns ± 1%	3.0ns ± 1%	-75.91%
Cmp	12.6ns ± 1%	7.7ns ± 1%	-39.01%
CmpUint64	5.93ns ± 2%	3.70ns ± 1%	-37.60%

Bitwise Methods

Name	`big.Int` Time/Op	`Uint256` Time/Op	Delta vs `big.Int`
Lsh/bits_0	7.15ns ± 3%	2.58ns ± 1%	-63.94%
Lsh/bits_1	14.8ns ± 1%	4.2ns ± 1%	-71.40%
Lsh/bits_64	16.7ns ± 1%	2.7ns ± 1%	-84.00%
Lsh/bits_128	16.9ns ± 2%	2.7ns ± 0%	-84.21%
Lsh/bits_192	16.6ns ± 1%	2.6ns ± 1%	-84.19%
Lsh/bits_255	16.3ns ± 2%	2.8ns ± 2%	-83.11%
Lsh/bits_256	16.9ns ± 2%	2.6ns ± 2%	-84.77%
Rsh/bits_0	8.76ns ± 2%	2.57ns ± 1%	-70.63%
Rsh/bits_1	14.4ns ± 2%	4.3ns ± 2%	-70.28%
Rsh/bits_64	12.8ns ± 1%	2.9ns ± 2%	-77.31%
Rsh/bits_128	11.8ns ± 0%	2.9ns ± 2%	-75.51%
Rsh/bits_192	10.5ns ± 2%	2.6ns ± 1%	-75.17%
Rsh/bits_255	10.5ns ± 3%	2.8ns ± 2%	-73.89%
Rsh/bits_256	5.50ns ± 1%	2.58ns ± 2%	-53.15%
Not	25.4ns ± 2%	3.3ns ± 2%	-86.79%
Or	17.9ns ± 5%	3.4ns ± 6%	-80.94%
And	16.7ns ± 2%	3.4ns ± 0%	-79.93%
Xor	17.9ns ± 1%	3.4ns ± 2%	-80.91%
BitLen/bits_64	2.24ns ± 1%	1.94ns ± 3%	-13.04%
BitLen/bits_128	2.25ns ± 2%	1.96ns ± 2%	-13.17%
BitLen/bits_192	2.25ns ± 1%	1.60ns ± 1%	-28.65%
BitLen/bits_255	2.26ns ± 2%	1.61ns ± 1%	-29.04%

Conversion Methods

Name	`big.Int` Time/Op	`Uint256` Time/Op	Delta vs `big.Int`
SetBytes	9.09ns ±13%	3.05ns ± 1%	-66.43%
SetBytesLE	59.9ns ± 4%	3.1ns ± 2%	-94.76%
Bytes	61.3ns ± 1%	13.8ns ± 3%	-77.49%
BytesLE	83.5ns ± 2%	13.9ns ± 2%	-83.32%

Misc Convenience Methods

Name	`big.Int` Time/Op	`Uint256` Time/Op	Delta vs `big.Int`
Zero	2.99ns ± 2%	1.29ns ± 1%	-56.82%
IsZero	1.78ns ± 0%	1.63ns ± 2%	-8.23%
IsOdd	3.62ns ± 4%	1.64ns ± 1%	-54.65%

Output Formatting Methods

Name	`big.Int` Time/Op	`Uint256` Time/Op	Delta vs `big.Int`
Text/base_2	579ns ± 3%	496ns ± 2%	-14.37%
Text/base_8	266ns ± 1%	227ns ± 1%	-14.58%
Text/base_10	536ns ± 1%	458ns ± 2%	-14.58%
Text/base_16	205ns ± 2%	180ns ± 4%	-11.90%
Format/base_2	987ns ±15%	852ns ± 2%	-13.64%
Format/base_8	620ns ± 6%	544ns ± 3%	-12.31%
Format/base_10	888ns ± 1%	726ns ± 1%	-18.25%
Format/base_16	565ns ± 1%	449ns ± 1%	-20.41%

This is work towards #2786.

internal/staging/primitives/uint256/uint256.go

dnldd · 2021-11-12T17:17:26Z

Need to have another pass over the multiplication and division sections but looks good so far.

internal/staging/primitives/uint256/uint256.go

matheusd

Halfway through the commits

internal/staging/primitives/uint256/uint256_test.go

internal/staging/primitives/uint256/uint256.go

JoeGruffins · 2021-11-17T12:30:01Z

Pretty amazing work. Learning a lot looking over this.

In commit message of c8fc7bf
- Ergonomic API with unary-style arguments are well as some binary variants
should maybe be as well as

In commit message of dce5714
This adds the ability zero an existing uint256 and determine if it is
should maybe have ability to zero

benchmarks

goos: linux
goarch: amd64
pkg: github.com/decred/dcrd/internal/staging/primitives/uint256
cpu: AMD Ryzen 9 3900XT 12-Core Processor           
BenchmarkUint256SetBytes-24      	626857800	         1.801 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSetBytes-24       	192123936	         6.213 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256SetBytesLE-24    	579135675	         1.862 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSetBytesLE-24     	18501447	        67.09 ns/op	      32 B/op	       1 allocs/op
BenchmarkUint256Bytes-24         	124904251	         9.149 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBytes-24          	16091646	        79.41 ns/op	      32 B/op	       1 allocs/op
BenchmarkUint256BytesLE-24       	135137600	         8.951 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBytesLE-24        	13922724	        97.98 ns/op	      32 B/op	       1 allocs/op
BenchmarkUint256Zero-24          	1000000000	         0.7060 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntZero-24           	494819776	         2.159 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256IsZero-24        	806305870	         1.370 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntIsZero-24         	749324908	         1.521 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256IsOdd-24         	1000000000	         1.144 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntIsOdd-24          	477044432	         2.322 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Eq-24            	786457744	         1.518 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntEq-24             	182344155	         6.708 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lt-24            	541656760	         1.980 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLt-24             	186473148	         6.458 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Gt-24            	532842606	         1.977 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntGt-24             	178758286	         6.379 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Cmp-24           	437226667	         2.637 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntCmp-24            	185312695	         6.041 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256CmpUint64-24     	635997724	         1.622 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntCmpUint64-24      	297241944	         4.004 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Add-24           	702670026	         1.439 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntAdd-24            	 9621193	       120.7 ns/op	       3 B/op	       0 allocs/op
BenchmarkUint256AddUint64-24     	487079854	         2.141 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntAddUint64-24      	42218737	        27.30 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Sub-24           	703910578	         1.525 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSub-24            	33799041	        35.51 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256SubUint64-24     	573150536	         2.141 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSubUint64-24      	41408493	        28.95 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Mul-24           	205485963	         5.674 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntMul-24            	 2451584	       469.9 ns/op	      64 B/op	       1 allocs/op
BenchmarkUint256MulUint64-24     	378212292	         2.993 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntMulUint64-24      	 4817528	       226.4 ns/op	       8 B/op	       1 allocs/op
BenchmarkUint256Square-24        	273366194	         4.085 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSquare-24         	 2502544	       493.0 ns/op	      64 B/op	       1 allocs/op
BenchmarkUint256Div/dividend_lt_divisor-24         	447356533	         2.375 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/dividend_eq_divisor-24         	440418166	         2.556 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/1_by_1_near-24                 	357880683	         3.321 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/1_by_1_far-24                  	100000000	        10.99 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/2_by_1_near-24                 	165720555	         7.381 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/2_by_1_far-24                  	57083955	        21.11 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_1_near-24                 	113972001	         9.993 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_1_far-24                  	38814946	        32.29 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_1_near-24                 	90064765	        13.06 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_1_far-24                  	28466821	        41.80 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/2_by_2_near-24                 	74131861	        15.55 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/2_by_2_far-24                  	53563335	        23.12 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_2_near-24                 	56249758	        21.93 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_2_far-24                  	32042884	        35.83 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_2_near-24                 	42563181	        27.74 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_2_far-24                  	24508135	        49.32 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_3_near-24                 	81699478	        14.12 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_3_far-24                  	48410469	        24.48 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_3_near-24                 	53083888	        21.94 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_3_far-24                  	36933514	        32.68 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_4_near-24                 	78725864	        15.36 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_4_far-24                  	44327823	        27.38 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256DivRandom-24                       	79271268	        15.27 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/dividend_lt_divisor-24          	16322353	        74.75 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/dividend_eq_divisor-24          	 4489509	       279.3 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/1_by_1_near-24                  	18364558	        62.23 ns/op	       8 B/op	       1 allocs/op
BenchmarkBigIntDiv/1_by_1_far-24                   	54461589	        21.26 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/2_by_1_near-24                  	37645087	        27.15 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/2_by_1_far-24                   	34748634	        34.90 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/3_by_1_near-24                  	36574906	        32.15 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/3_by_1_far-24                   	28280524	        40.10 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/4_by_1_near-24                  	32926687	        37.17 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/4_by_1_far-24                   	26827346	        47.72 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/2_by_2_near-24                  	 4243052	       276.4 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/2_by_2_far-24                   	 4456932	       276.9 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/3_by_2_near-24                  	 3941820	       307.3 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/3_by_2_far-24                   	 3893846	       300.3 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_2_near-24                  	 3383415	       342.9 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_2_far-24                   	 3577161	       338.8 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/3_by_3_near-24                  	 4432884	       279.9 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/3_by_3_far-24                   	 4402246	       284.7 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_3_near-24                  	 3721740	       312.4 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_3_far-24                   	 3741186	       315.3 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_4_near-24                  	 4409409	       265.8 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_4_far-24                   	 4451058	       264.0 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDivRandom-24                        	 5221705	       241.6 ns/op	      72 B/op	       1 allocs/op
BenchmarkUint256DivUint64-24                       	33089503	        34.19 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDivUint64-24                        	10080028	       133.8 ns/op	       8 B/op	       1 allocs/op
BenchmarkUint256Negate-24                          	992767736	         1.014 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntNegate-24                           	37861459	        30.20 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_0-24                      	729918438	         1.718 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_1-24                      	387857133	         3.003 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_64-24                     	520758091	         2.146 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_128-24                    	568290314	         1.904 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_192-24                    	739967994	         1.633 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_255-24                    	547926159	         1.918 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_256-24                    	733664517	         1.697 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_0-24                       	223699926	         5.348 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_1-24                       	116737645	        10.05 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_64-24                      	105860778	        11.51 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_128-24                     	106117347	        10.90 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_192-24                     	109361703	        11.41 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_255-24                     	105343557	        11.10 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_256-24                     	103054900	        11.43 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_0-24                      	550372821	         1.939 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_1-24                      	392731686	         3.109 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_64-24                     	569238034	         1.968 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_128-24                    	637000917	         1.690 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_192-24                    	806247422	         1.432 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_255-24                    	602076444	         1.939 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_256-24                    	598181062	         1.718 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_0-24                       	195011600	         6.259 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_1-24                       	100000000	        10.35 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_64-24                      	126069898	         9.517 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_128-24                     	134734641	         8.795 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_192-24                     	155518081	         7.415 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_255-24                     	155382307	         7.437 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_256-24                     	288011690	         4.045 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Not-24                             	520997385	         2.051 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntNot-24                              	78752209	        15.59 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Or-24                              	484275884	         2.383 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntOr-24                               	98529921	        12.25 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256And-24                             	477428367	         2.260 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntAnd-24                              	100000000	        11.53 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Xor-24                             	475271222	         2.326 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntXor-24                              	96482734	        12.73 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256BitLen/bits_64-24                  	769874131	         1.512 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256BitLen/bits_128-24                 	816861885	         1.430 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256BitLen/bits_192-24                 	1000000000	         1.156 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256BitLen/bits_255-24                 	841902804	         1.231 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBitLen/bits_64-24                   	628294862	         1.665 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBitLen/bits_128-24                  	623833395	         1.628 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBitLen/bits_192-24                  	641823882	         1.665 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBitLen/bits_255-24                  	660455758	         1.620 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Text/base_2-24                     	 2203741	       544.0 ns/op	     512 B/op	       2 allocs/op
BenchmarkUint256Text/base_8-24                     	 4886019	       245.4 ns/op	     192 B/op	       2 allocs/op
BenchmarkUint256Text/base_10-24                    	 2212734	       565.5 ns/op	     160 B/op	       2 allocs/op
BenchmarkUint256Text/base_16-24                    	 6908899	       180.1 ns/op	     128 B/op	       2 allocs/op
BenchmarkBigIntText/base_2-24                      	 1998284	       608.5 ns/op	     528 B/op	       2 allocs/op
BenchmarkBigIntText/base_8-24                      	 4385248	       271.5 ns/op	     192 B/op	       2 allocs/op
BenchmarkBigIntText/base_10-24                     	 1914667	       629.6 ns/op	     224 B/op	       3 allocs/op
BenchmarkBigIntText/base_16-24                     	 5653011	       213.0 ns/op	     136 B/op	       2 allocs/op
BenchmarkUint256Format/base_2-24                   	 1252276	       958.6 ns/op	     768 B/op	       3 allocs/op
BenchmarkUint256Format/base_8-24                   	 1961947	       609.3 ns/op	     288 B/op	       3 allocs/op
BenchmarkUint256Format/base_10-24                  	 1313508	       932.1 ns/op	     240 B/op	       3 allocs/op
BenchmarkUint256Format/base_16-24                  	 2193850	       545.1 ns/op	     192 B/op	       3 allocs/op
BenchmarkBigIntFormat/base_2-24                    	 1000000	      1049 ns/op	     552 B/op	       5 allocs/op
BenchmarkBigIntFormat/base_8-24                    	 1708375	       698.7 ns/op	     216 B/op	       5 allocs/op
BenchmarkBigIntFormat/base_10-24                   	 1000000	      1038 ns/op	     248 B/op	       6 allocs/op
BenchmarkBigIntFormat/base_16-24                   	 1843668	       663.4 ns/op	     160 B/op	       5 allocs/op
BenchmarkUint256PutBig-24                          	54292158	        21.95 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256SetBig-24                          	44077651	        27.90 ns/op	       0 B/op	       0 allocs/op
PASS
ok  	github.com/decred/dcrd/internal/staging/primitives/uint256	236.892s

internal/staging/primitives/uint256/uint256.go

internal/staging/primitives/uint256/README.md

matheusd

🎉 🎉 🎉

Excellent work as always! Only caught few more documentational issues.

internal/staging/primitives/uint256/uint256.go

davecgh · 2021-11-17T18:37:54Z

Updated the commit messages per the @JoeGruffins review as well.

matheusd

Great work as always!

Benchmarks

goos: linux
goarch: amd64
pkg: github.com/decred/dcrd/internal/staging/primitives/uint256
cpu: AMD Ryzen 3 2200G with Radeon Vega Graphics    
BenchmarkUint256SetBytes-4     	476069810	         2.482 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSetBytes-4      	160615147	         7.908 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256SetBytesLE-4   	430822285	         2.687 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSetBytesLE-4    	19294600	        60.83 ns/op	      32 B/op	       1 allocs/op
BenchmarkUint256Bytes-4        	88200577	        12.33 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBytes-4         	18895275	        55.32 ns/op	      32 B/op	       1 allocs/op
BenchmarkUint256BytesLE-4      	100000000	        12.18 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBytesLE-4       	15329814	        68.77 ns/op	      32 B/op	       1 allocs/op
BenchmarkUint256Zero-4         	1000000000	         1.120 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntZero-4          	451413762	         2.716 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256IsZero-4       	681048356	         1.635 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntIsZero-4        	613439154	         1.849 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256IsOdd-4        	797677572	         1.669 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntIsOdd-4         	302746519	         3.462 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Eq-4           	654700365	         1.949 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntEq-4            	112233123	        10.35 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lt-4           	480044094	         2.420 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLt-4            	100000000	        10.72 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Gt-4           	428775073	         2.633 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntGt-4            	112796678	        12.01 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Cmp-4          	162790765	         6.916 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntCmp-4           	117192634	        10.42 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256CmpUint64-4    	375092656	         3.216 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntCmpUint64-4     	241991760	         6.247 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Add-4          	575967142	         1.912 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntAdd-4           	 8228707	       138.5 ns/op	       4 B/op	       0 allocs/op
BenchmarkUint256AddUint64-4    	462350301	         2.604 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntAddUint64-4     	26791534	        45.15 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Sub-4          	651187911	         1.755 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSub-4           	22559347	        55.86 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256SubUint64-4    	448262576	         2.629 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSubUint64-4     	25150804	        40.20 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Mul-4          	135067701	         8.883 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntMul-4           	 2939754	       388.9 ns/op	      64 B/op	       1 allocs/op
BenchmarkUint256MulUint64-4    	321874484	         3.923 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntMulUint64-4     	 5118799	       247.4 ns/op	       8 B/op	       1 allocs/op
BenchmarkUint256Square-4       	194034268	         7.041 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntSquare-4        	 2914981	       393.1 ns/op	      64 B/op	       1 allocs/op
BenchmarkUint256Div/dividend_lt_divisor-4         	398487291	         2.945 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/dividend_eq_divisor-4         	364279308	         3.101 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/1_by_1_near-4                 	302580482	         3.855 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/1_by_1_far-4                  	96309692	        13.61 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/2_by_1_near-4                 	129636962	         8.936 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/2_by_1_far-4                  	46576605	        25.07 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_1_near-4                 	100000000	        11.71 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_1_far-4                  	32242239	        37.36 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_1_near-4                 	63737451	        15.75 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_1_far-4                  	20309397	        49.48 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/2_by_2_near-4                 	53796532	        20.07 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/2_by_2_far-4                  	42929392	        30.03 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_2_near-4                 	38020507	        26.79 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_2_far-4                  	25221169	        47.17 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_2_near-4                 	33020859	        35.22 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_2_far-4                  	16499960	        61.37 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_3_near-4                 	68166744	        17.98 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/3_by_3_far-4                  	42235713	        29.73 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_3_near-4                 	35219878	        32.05 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_3_far-4                  	28236904	        41.50 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_4_near-4                 	70831348	        17.26 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Div/4_by_4_far-4                  	38107536	        31.37 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256DivRandom-4                       	60160770	        20.02 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/dividend_lt_divisor-4          	15166644	        71.20 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/dividend_eq_divisor-4          	 5455660	       261.5 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/1_by_1_near-4                  	20247571	        58.81 ns/op	       8 B/op	       1 allocs/op
BenchmarkBigIntDiv/1_by_1_far-4                   	42041121	        28.51 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/2_by_1_near-4                  	36022141	        32.12 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/2_by_1_far-4                   	28347584	        42.89 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/3_by_1_near-4                  	30974647	        38.03 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/3_by_1_far-4                   	20732623	        49.20 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/4_by_1_near-4                  	28156827	        44.69 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/4_by_1_far-4                   	17195563	        63.88 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDiv/2_by_2_near-4                  	 5086784	       216.1 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/2_by_2_far-4                   	 5746678	       212.5 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/3_by_2_near-4                  	 5075608	       253.1 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/3_by_2_far-4                   	 4244466	       257.3 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_2_near-4                  	 4156348	       295.6 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_2_far-4                   	 4208538	       295.9 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/3_by_3_near-4                  	 4301845	       269.1 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/3_by_3_far-4                   	 5341867	       221.1 ns/op	      64 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_3_near-4                  	 4738832	       247.4 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_3_far-4                   	 4631062	       250.4 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_4_near-4                  	 5088583	       234.5 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDiv/4_by_4_far-4                   	 5235777	       229.4 ns/op	      80 B/op	       1 allocs/op
BenchmarkBigIntDivRandom-4                        	 5518939	       221.6 ns/op	      72 B/op	       1 allocs/op
BenchmarkUint256DivUint64-4                       	22925576	        44.61 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntDivUint64-4                        	10211529	       124.1 ns/op	       8 B/op	       1 allocs/op
BenchmarkUint256Negate-4                          	850187539	         1.238 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntNegate-4                           	24669282	        51.68 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_0-4                      	507476983	         2.201 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_1-4                      	316203012	         3.606 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_64-4                     	459433334	         2.491 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_128-4                    	484224193	         2.384 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_192-4                    	462848384	         2.296 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_255-4                    	480112038	         2.348 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Lsh/bits_256-4                    	448478752	         2.463 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_0-4                       	172591105	         6.000 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_1-4                       	93923139	        12.78 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_64-4                      	81818536	        14.59 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_128-4                     	79875747	        14.30 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_192-4                     	83981918	        14.12 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_255-4                     	87148645	        13.77 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntLsh/bits_256-4                     	84002761	        14.29 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_0-4                      	475755678	         2.233 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_1-4                      	313881753	         3.717 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_64-4                     	448903030	         2.456 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_128-4                    	522788181	         2.415 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_192-4                    	501043711	         2.303 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_255-4                    	493278232	         2.352 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Rsh/bits_256-4                    	524338425	         2.198 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_0-4                       	163935820	         7.280 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_1-4                       	79080118	        13.90 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_64-4                      	107008660	        10.92 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_128-4                     	121404361	         9.779 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_192-4                     	136675233	         8.820 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_255-4                     	135231632	         9.048 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntRsh/bits_256-4                     	179642262	         6.345 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Not-4                             	455189844	         2.649 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntNot-4                              	56325128	        21.92 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Or-4                              	425439813	         2.828 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntOr-4                               	76605534	        15.22 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256And-4                             	385027156	         3.201 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntAnd-4                              	79475395	        15.53 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Xor-4                             	415490449	         3.001 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntXor-4                              	63178353	        15.93 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256BitLen/bits_64-4                  	688524416	         1.729 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256BitLen/bits_128-4                 	681189094	         1.707 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256BitLen/bits_192-4                 	872857674	         1.380 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256BitLen/bits_255-4                 	865733118	         1.431 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBitLen/bits_64-4                   	540039884	         2.160 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBitLen/bits_128-4                  	600470946	         1.953 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBitLen/bits_192-4                  	575591056	         1.964 ns/op	       0 B/op	       0 allocs/op
BenchmarkBigIntBitLen/bits_255-4                  	570677790	         2.301 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256Text/base_2-4                     	 2326405	       532.3 ns/op	     512 B/op	       2 allocs/op
BenchmarkUint256Text/base_8-4                     	 5222268	       214.1 ns/op	     192 B/op	       2 allocs/op
BenchmarkUint256Text/base_10-4                    	 2746434	       466.3 ns/op	     160 B/op	       2 allocs/op
BenchmarkUint256Text/base_16-4                    	 7155501	       195.4 ns/op	     128 B/op	       2 allocs/op
BenchmarkBigIntText/base_2-4                      	 2267157	       523.1 ns/op	     528 B/op	       2 allocs/op
BenchmarkBigIntText/base_8-4                      	 4910493	       246.6 ns/op	     192 B/op	       2 allocs/op
BenchmarkBigIntText/base_10-4                     	 2231427	       529.7 ns/op	     224 B/op	       3 allocs/op
BenchmarkBigIntText/base_16-4                     	 6620342	       184.6 ns/op	     135 B/op	       2 allocs/op
BenchmarkUint256Format/base_2-4                   	 1265379	       966.8 ns/op	     768 B/op	       3 allocs/op
BenchmarkUint256Format/base_8-4                   	 2023450	       523.9 ns/op	     288 B/op	       3 allocs/op
BenchmarkUint256Format/base_10-4                  	 1683890	       712.5 ns/op	     240 B/op	       3 allocs/op
BenchmarkUint256Format/base_16-4                  	 2705778	       450.0 ns/op	     192 B/op	       3 allocs/op
BenchmarkBigIntFormat/base_2-4                    	 1315701	       919.3 ns/op	     552 B/op	       5 allocs/op
BenchmarkBigIntFormat/base_8-4                    	 2011153	       584.3 ns/op	     216 B/op	       5 allocs/op
BenchmarkBigIntFormat/base_10-4                   	 1255659	       889.5 ns/op	     248 B/op	       6 allocs/op
BenchmarkBigIntFormat/base_16-4                   	 2304246	       522.1 ns/op	     160 B/op	       5 allocs/op
BenchmarkUint256PutBig-4                          	46232820	        23.74 ns/op	       0 B/op	       0 allocs/op
BenchmarkUint256SetBig-4                          	26237026	        43.49 ns/op	       0 B/op	       0 allocs/op
PASS
ok  	github.com/decred/dcrd/internal/staging/primitives/uint256	230.729s

rstaudt2

This looks great. The documentation is excellent, making the logic easy to follow. I just had a few very minor comments inline.

internal/staging/primitives/uint256/README.md

internal/staging/primitives/uint256/uint256.go

internal/staging/primitives/uint256/uint256_test.go

Profiling the CPU usage during an initial chain sync shows that roughly 65-70% of all time is spent in garbage collection operations. This is primarily the result of a large number of in-use allocations. Profiling the in-use allocations shows that around almost a quarter of all in-use allocations (~22%) are due to standard library big integers which require allocations. In other words, eliminating those allocations should lead to a speedup of around 10% to the initial chain sync. More specifically, the allocations in question are the result of several important calculations which could be done without allocations, and more efficiently in terms of execution time, via fixed precision unsigned 256-bit integers. Thus, motivated by the previous discussion, this is part of a series of commits that implements highly optimized allocation free fixed precision unsigned 256-bit integer arithmetic that can ultimately be used in place of the standard library big integers. For the time being, the package is introduced into the internal staging area for initial review. The following is a brief overview of the main features and benefits: - Strong focus on performance and correctness - Every operation is faster than the stdlib big.Int equivalent and most operations, including the primary math operations, are significantly faster - Allocation free - All non-formatting operations with the specialized type are allocation free - Supports boolean comparison, bitwise logic, and bitwise shift operations - All operations are performed modulo 2^256 - Ergonomic API with unary-style arguments as well as some binary variants - Conversion-free support for interoperation with native uint64 integers - Direct conversion to and from little and big endian byte arrays - Full support for formatted output and common base conversions - Formatted output uses fewer allocations than stdlib big.Int - 100% test coverage - Comprehensive benchmarks In order to help ease the review process, the full implementation will be done across many commits. This commit only contains the basic type definition and ability to set it to a uint64 or another uint256 along with tests, so it is not very useful on its own. Future commits will implement support for interpreting and producing big and little endian bytes, the primary arithmetic operations (addition, subtraction, multiplication, squaring, division, negation), bitwise operations (lsh, rsh, not, or, and, xor), comparison operations (equals, less, greater, cmp), and other convenience methods such as determining the minimum number of bits required to represent the current value, whether or not the value can be represented as a uint64 without loss of precision, and text formatting with base conversion.

This adds the ability for the uint256 to be set by interpreting arrays and slices as a 256-bit big-endian integer and associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta ------------------------------------------------------------------ SetBytes 9.09ns ±13% 3.05ns ± 1% -66.43% (p=0.000 n=10+10) name old allocs/op new allocs/op delta ---------------------------------------------------------- SetBytes 0.00 0.00 ~ (all equal) This is part of a series of commits to fully implement the uint256 package.

This adds the ability to determine if a uint256 is odd along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta ------------------------------------------------------------------ IsOdd 3.62ns ± 4% 1.64ns ± 1% -54.65% (p=0.000 n=10+10) name old allocs/op new allocs/op delta --------------------------------------------------------- IsOdd 0.00 0.00 ~ (all equal) This is part of a series of commits to fully implement the uint256 package.

This adds support for uint256 bitwise left shifting along with associated tests to ensure proper functionality. It includes left shifting an existing uint256 (a << b) and assigning the result of left shifting a uint256 to a second one (a <<= b). This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta ------------------------------------------------------------------------- Lsh/bits_0 7.1ns ± 3% 2.58ns ± 1% -63.94% (p=0.000 n=10+10) Lsh/bits_1 14.8ns ± 1% 4.2ns ± 1% -71.40% (p=0.000 n=10+10) Lsh/bits_64 16.7ns ± 1% 2.7ns ± 1% -84.00% (p=0.000 n=10+10) Lsh/bits_128 16.9ns ± 2% 2.7ns ± 0% -84.21% (p=0.000 n=10+10) Lsh/bits_192 16.6ns ± 1% 2.6ns ± 1% -84.19% (p=0.000 n=10+10) Lsh/bits_255 16.3ns ± 2% 2.8ns ± 2% -83.11% (p=0.000 n=10+10) Lsh/bits_256 16.9ns ± 2% 2.6ns ± 2% -84.77% (p=0.000 n=10+10) name old allocs/op new allocs/op delta ---------------------------------------------------------------- Lsh/bits_0 0.00 0.00 ~ (all equal) Lsh/bits_1 0.00 0.00 ~ (all equal) Lsh/bits_64 0.00 0.00 ~ (all equal) Lsh/bits_128 0.00 0.00 ~ (all equal) Lsh/bits_192 0.00 0.00 ~ (all equal) Lsh/bits_255 0.00 0.00 ~ (all equal) Lsh/bits_256 0.00 0.00 ~ (all equal) This is part of a series of commits to fully implement the uint256 package.

This adds support for uint256 bitwise right shifting along with associated tests to ensure proper functionality. It includes right shifting an existing uint256 (a >> b) and assigning the result of right shifting a uint256 to a second one (a >>= b). This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta ------------------------------------------------------------------------- Rsh/bits_0 8.76ns ± 2% 2.57ns ± 1% -70.63% (p=0.000 n=10+10) Rsh/bits_1 14.4ns ± 2% 4.3ns ± 2% -70.28% (p=0.000 n=10+10) Rsh/bits_64 12.8ns ± 1% 2.9ns ± 2% -77.31% (p=0.000 n=10+10) Rsh/bits_128 11.8ns ± 0% 2.9ns ± 2% -75.51% (p=0.000 n=10+10) Rsh/bits_192 10.5ns ± 2% 2.6ns ± 1% -75.17% (p=0.000 n=10+10) Rsh/bits_255 10.5ns ± 3% 2.8ns ± 2% -73.89% (p=0.000 n=10+10) Rsh/bits_256 5.50ns ± 1% 2.58ns ± 2% -53.15% (p=0.000 n=10+10) name old allocs/op new allocs/op delta ---------------------------------------------------------------- Rsh/bits_0 0.00 0.00 ~ (all equal) Rsh/bits_1 0.00 0.00 ~ (all equal) Rsh/bits_64 0.00 0.00 ~ (all equal) Rsh/bits_128 0.00 0.00 ~ (all equal) Rsh/bits_192 0.00 0.00 ~ (all equal) Rsh/bits_255 0.00 0.00 ~ (all equal) Rsh/bits_256 0.00 0.00 ~ (all equal) This is part of a series of commits to fully implement the uint256 package.

This adds support to compute the bitwise not of a uint256 along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta ----------------------------------------------------------------- Not 25.4ns ± 2% 3.3ns ± 2% -86.79% (p=0.000 n=10+10) name old allocs/op new allocs/op delta -------------------------------------------------------- Not 0.00 0.00 ~ (all equal) This is part of a series of commits to fully implement the uint256 package.

This adds support to compute the bitwise or of two uint256s along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta ----------------------------------------------------------------- Or 17.9ns ± 5% 3.4ns ± 6% -80.94% (p=0.000 n=10+10) name old allocs/op new allocs/op delta -------------------------------------------------------- Or 0.00 0.00 ~ (all equal) This is part of a series of commits to fully implement the uint256 package.

This adds support to compute the bitwise and of two uint256s along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta ----------------------------------------------------------------- And 16.7ns ± 5% 3.4ns ± 6% -79.93% (p=0.000 n=10+10) name old allocs/op new allocs/op delta -------------------------------------------------------- And 0.00 0.00 ~ (all equal) This is part of a series of commits to fully implement the uint256 package.

This adds support to compute the bitwise xor of two uint256s along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta ----------------------------------------------------------------- Xor 17.9ns ± 5% 3.4ns ± 6% -80.91% (p=0.000 n=10+10) name old allocs/op new allocs/op delta -------------------------------------------------------- Xor 0.00 0.00 ~ (all equal) This is part of a series of commits to fully implement the uint256 package.

This adds support for determining the minimum number of bits required to represent the current value of a uint256 along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta --------------------------------------------------------------------- bits_64 2.24ns ± 1% 1.94ns ± 3% -13.04% (p=0.000 n=10+10) bits_128 2.25ns ± 2% 1.96ns ± 2% -13.17% (p=0.000 n=10+10) bits_192 2.25ns ± 1% 1.60ns ± 1% -28.65% (p=0.000 n=10+10) bits_255 2.26ns ± 2% 1.61ns ± 1% -29.04% (p=0.000 n=10+10) name old allocs/op new allocs/op delta ------------------------------------------------------------ bits_64 0.00 0.00 ~ (all equal) bits_128 0.00 0.00 ~ (all equal) bits_192 0.00 0.00 ~ (all equal) bits_255 0.00 0.00 ~ (all equal) This is part of a series of commits to fully implement the uint256 package.

This adds full support for formatting a uint256 along with associated tests to ensure proper functionality. It includes a fmt.Formatter that supports the full suite of the fmt package format flags for integral types, a fmt.Stringer, and a separate Text method that accepts an output base directly and produces the relevant output with fewer allocations than using the standard fmt methods. This is part of a series of commits to fully implement the uint256 package.

The following is a comparison between stdlib big integers (old) and the specialized type (new) averaging 10 runs each: name old time/op new time/op delta --------------------------------------------------------------------------- Text/base_2 579ns ± 3% 496ns ± 2% -14.37% (p=0.000 n=10+10) Text/base_8 266ns ± 1% 227ns ± 1% -14.58% (p=0.000 n=10+10) Text/base_10 536ns ± 1% 458ns ± 2% -14.58% (p=0.000 n=10+10) Text/base_16 205ns ± 2% 180ns ± 4% -11.90% (p=0.000 n=10+10) Format/base_2 987ns ±15% 852ns ± 2% -13.64% (p=0.000 n=10+10) Format/base_8 620ns ± 6% 544ns ± 3% -12.31% (p=0.000 n=10+10) Format/base_10 888ns ± 1% 726ns ± 1% -18.25% (p=0.000 n=10+10) Format/base_16 565ns ± 1% 449ns ± 1% -20.41% (p=0.000 n=10+10) name old allocs/op new allocs/op delta -------------------------------------------------------------------------- Text/base_2 2.00 ± 0% 2.00 ± 0% ~ (all equal) Text/base_8 2.00 ± 0% 2.00 ± 0% ~ (all equal) Text/base_10 3.00 ± 0% 2.00 ± 0% -33.33% (p=0.000 n=10+10) Text/base_16 2.00 ± 0% 2.00 ± 0% ~ (all equal) Format/base_2 5.00 ± 0% 3.00 ± 0% -40.00% (p=0.000 n=10+10) Format/base_8 5.00 ± 0% 3.00 ± 0% -40.00% (p=0.000 n=10+10) Format/base_10 6.00 ± 0% 3.00 ± 0% -50.00% (p=0.000 n=10+10) Format/base_16 5.00 ± 0% 3.00 ± 0% -40.00% (p=0.000 n=10+10) This is part of a series of commits to fully implement the uint256 package.

internal/staging/primitives/uint256/uint256_test.go

This adds convenience methods for converting a uint256 to a standard library big integer along with associated tests to ensure proper functionality. It includes a method that allows an existing big integer to be reused thereby potentially saving allocations as well as a method that returns a new big integer. The latter is often more convenient to use, but is also virtually guaranteed to cause an allocation. This is part of a series of commits to fully implement the uint256 package.

The following shows the typical performance of converting a uint256 to a standard library big integer using one that already exists: Uint256PutBig 43651442 27.29 ns/op 0 B/op 0 allocs/op This is part of a series of commits to fully implement the uint256 package.

This adds a convenience method for converting a standard library big integer to a uint256 (modulo 2^256) along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

The following shows the typical performance of converting a standard library big integer that has already been reduced modulo 2^256 to a uint256: Uint256SetBig 26944130 44.45 ns/op 0 B/op 0 allocs/op This is part of a series of commits to fully implement the uint256 package.

This adds an example of calculating the result of dividing a max unsigned 256-bit integer by a max unsigned 128-bit integer and outputting that result in hex with leading zeros. This is part of a series of commits to fully implement the uint256 package.

davecgh added the optimization label Nov 6, 2021

davecgh mentioned this pull request Nov 6, 2021

Primitives Module Planning and Outline #2786

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davecgh changed the title ~~uint256: Introduce package infrastructure.~~ uint256: Introduce package. Nov 6, 2021

davecgh force-pushed the primitives_uint256 branch from e3f55fb to 8850e5c Compare November 7, 2021 06:55

davecgh mentioned this pull request Nov 7, 2021

primitives: Add initial proof-of-work funcs. #2788

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davecgh force-pushed the primitives_uint256 branch from 8850e5c to 41c2fa8 Compare November 8, 2021 07:31

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davecgh force-pushed the primitives_uint256 branch from 41c2fa8 to a876369 Compare November 8, 2021 22:15

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davecgh force-pushed the primitives_uint256 branch 2 times, most recently from 82ec71c to 090a6a9 Compare November 12, 2021 02:20

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davecgh force-pushed the primitives_uint256 branch from 08c130a to 40400a4 Compare November 16, 2021 20:56

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davecgh force-pushed the primitives_uint256 branch from 40400a4 to 08c8728 Compare November 17, 2021 18:36

davecgh force-pushed the primitives_uint256 branch from 08c8728 to 2fc2e67 Compare November 17, 2021 19:03

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davecgh force-pushed the primitives_uint256 branch 2 times, most recently from e097b4f to 15b8ddc Compare November 19, 2021 22:23

davecgh added 3 commits November 19, 2021 16:41

uint256: Add set from big endian bytes.

6beb1b3

This adds the ability for the uint256 to be set by interpreting arrays and slices as a 256-bit big-endian integer and associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

davecgh added 18 commits November 19, 2021 17:04

uint256: Add is odd support.

944a888

This adds the ability to determine if a uint256 is odd along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

uint256: Add bitwise not support.

a42b8c8

This adds support to compute the bitwise not of a uint256 along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

uint256: Add bitwise or support.

269eee2

This adds support to compute the bitwise or of two uint256s along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

uint256: Add bitwise and support.

97bdac8

This adds support to compute the bitwise and of two uint256s along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

uint256: Add bitwise xor support.

d176920

This adds support to compute the bitwise xor of two uint256s along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

uint256: Add bit length support.

c0854f6

This adds support for determining the minimum number of bits required to represent the current value of a uint256 along with associated tests to ensure proper functionality. This is part of a series of commits to fully implement the uint256 package.

davecgh force-pushed the primitives_uint256 branch from f9dc32d to e6218ce Compare November 19, 2021 23:04

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davecgh added 6 commits November 19, 2021 17:31

uint256: Add README.md.

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davecgh force-pushed the primitives_uint256 branch from e6218ce to 8f3fd5a Compare November 19, 2021 23:32

davecgh merged commit 8f3fd5a into decred:master Nov 20, 2021

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uint256: Introduce package. #2787

uint256: Introduce package. #2787

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uint256: Introduce package. #2787

uint256: Introduce package. #2787

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Arithmetic Methods

Comparison Methods

Bitwise Methods

Conversion Methods

Misc Convenience Methods

Output Formatting Methods

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