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Russ Cox a812e5f3c3 math/big: update calibration tests and recalibrate 
Refactor calibration tests to use the same logic for all.

Choosing thresholds that are broadly appropriate for all systems is part science
but also part guesswork and judgement. We could instead set per-GOOS/GOARCH
thresholds, but that seems like too much work, and even then there would be
variation between different chips within a GOOS/GOARCH.
(For example see the three linux/amd64 systems benchmarked below.)

The thresholds chosen in this CL are:

	karatsubaThreshold = 40 // unchanged
	basicSqrThreshold = 12 // was 20
	karatsubaSqrThreshold = 80 // was 260
	divRecursiveThreshold = 40 // was 100

The new file calibrate.md explains the calibration process and links to graphs
justifying those values. (The graphs are hosted on swtch.com to avoid adding
a megabyte of extra data to the Go repo and Go distributions.)

A rendered copy of calibrate.md is at https://swtch.com/math/big/calibrate.html.

goos: linux
goarch: amd64
pkg: math/big
cpu: Intel(R) Xeon(R) Platinum 8481C CPU @ 2.70GHz
                         │     old      │                 new                 │
                         │    sec/op    │   sec/op     vs base                │
Div/20/10-88                13.13n ± 2%   13.14n ± 2%        ~ (p=0.494 n=15)
Div/40/20-88                13.13n ± 2%   13.14n ± 2%        ~ (p=0.137 n=15)
Div/100/50-88               25.50n ± 0%   25.51n ± 0%        ~ (p=0.038 n=15)
Div/200/100-88              113.1n ± 1%   116.0n ± 3%   +2.56% (p=0.000 n=15)
Div/400/200-88              135.3n ± 0%   137.1n ± 1%        ~ (p=0.004 n=15)
Div/1000/500-88             259.9n ± 1%   259.0n ± 2%        ~ (p=0.182 n=15)
Div/2000/1000-88            568.8n ± 1%   564.7n ± 3%        ~ (p=0.927 n=15)
Div/20000/10000-88          25.79µ ± 1%   22.11µ ± 2%  -14.26% (p=0.000 n=15)
Div/200000/100000-88        755.1µ ± 1%   737.6µ ± 1%   -2.32% (p=0.000 n=15)
Div/2000000/1000000-88      31.30m ± 0%   31.20m ± 1%        ~ (p=0.081 n=15)
Div/20000000/10000000-88     1.268 ± 0%    1.265 ± 0%        ~ (p=0.011 n=15)
NatMul/10-88                142.6n ± 0%   142.9n ± 7%        ~ (p=0.145 n=15)
NatMul/100-88               4.347µ ± 0%   4.350µ ± 3%        ~ (p=0.430 n=15)
NatMul/1000-88              187.6µ ± 0%   188.4µ ± 2%        ~ (p=0.004 n=15)
NatMul/10000-88             8.052m ± 0%   8.057m ± 1%        ~ (p=0.148 n=15)
NatMul/100000-88            260.6m ± 0%   260.7m ± 0%        ~ (p=0.512 n=15)
NatSqr/1-88                 26.58n ± 5%   27.96n ± 8%        ~ (p=0.574 n=15)
NatSqr/2-88                 42.35n ± 7%   44.87n ± 6%        ~ (p=0.690 n=15)
NatSqr/3-88                 53.28n ± 4%   55.62n ± 5%        ~ (p=0.151 n=15)
NatSqr/5-88                 76.26n ± 6%   81.43n ± 6%   +6.78% (p=0.000 n=15)
NatSqr/8-88                 110.8n ± 5%   116.4n ± 6%        ~ (p=0.040 n=15)
NatSqr/10-88                141.4n ± 4%   147.8n ± 4%        ~ (p=0.011 n=15)
NatSqr/20-88                325.8n ± 3%   341.7n ± 4%   +4.88% (p=0.000 n=15)
NatSqr/30-88                536.8n ± 3%   556.1n ± 4%        ~ (p=0.027 n=15)
NatSqr/50-88                1.168µ ± 3%   1.197µ ± 3%        ~ (p=0.442 n=15)
NatSqr/80-88                2.527µ ± 2%   2.480µ ± 2%   -1.86% (p=0.000 n=15)
NatSqr/100-88               3.771µ ± 2%   3.535µ ± 2%   -6.26% (p=0.000 n=15)
NatSqr/200-88               14.03µ ± 2%   10.57µ ± 3%  -24.68% (p=0.000 n=15)
NatSqr/300-88               24.06µ ± 2%   20.57µ ± 2%  -14.52% (p=0.000 n=15)
NatSqr/500-88               65.43µ ± 1%   45.45µ ± 1%  -30.55% (p=0.000 n=15)
NatSqr/800-88              126.41µ ± 1%   94.13µ ± 2%  -25.54% (p=0.000 n=15)
NatSqr/1000-88              196.4µ ± 1%   135.1µ ± 1%  -31.18% (p=0.000 n=15)
NatSqr/10000-88             6.404m ± 0%   5.326m ± 1%  -16.84% (p=0.000 n=15)
NatSqr/100000-88            267.2m ± 0%   198.7m ± 0%  -25.64% (p=0.000 n=15)
geomean                     7.318µ        6.948µ        -5.06%

goos: linux
goarch: amd64
pkg: math/big
cpu: Intel(R) Xeon(R) CPU @ 3.10GHz
                         │     old     │                 new                 │
                         │   sec/op    │   sec/op     vs base                │
Div/20/10-16               22.23n ± 0%   22.23n ± 0%        ~ (p=0.973 n=15)
Div/40/20-16               22.23n ± 0%   22.23n ± 0%        ~ (p=0.226 n=15)
Div/100/50-16              55.27n ± 1%   55.59n ± 0%        ~ (p=0.004 n=15)
Div/200/100-16             174.7n ± 3%   175.9n ± 2%        ~ (p=0.645 n=15)
Div/400/200-16             208.8n ± 1%   209.5n ± 2%        ~ (p=0.169 n=15)
Div/1000/500-16            378.7n ± 2%   380.5n ± 2%        ~ (p=0.091 n=15)
Div/2000/1000-16           778.4n ± 1%   781.1n ± 2%        ~ (p=0.104 n=15)
Div/20000/10000-16         25.16µ ± 1%   24.93µ ± 1%   -0.91% (p=0.000 n=15)
Div/200000/100000-16       926.4µ ± 0%   927.7µ ± 1%        ~ (p=0.436 n=15)
Div/2000000/1000000-16     35.58m ± 0%   35.53m ± 0%        ~ (p=0.267 n=15)
Div/20000000/10000000-16    1.333 ± 0%    1.330 ± 0%        ~ (p=0.126 n=15)
NatMul/10-16               172.6n ± 0%   165.4n ± 0%   -4.17% (p=0.000 n=15)
NatMul/100-16              5.706µ ± 0%   5.503µ ± 0%   -3.56% (p=0.000 n=15)
NatMul/1000-16             220.8µ ± 0%   219.1µ ± 0%   -0.76% (p=0.000 n=15)
NatMul/10000-16            8.688m ± 0%   8.621m ± 0%   -0.77% (p=0.000 n=15)
NatMul/100000-16           333.3m ± 0%   333.5m ± 0%        ~ (p=0.512 n=15)
NatSqr/1-16                28.66n ± 1%   28.42n ± 3%   -0.84% (p=0.000 n=15)
NatSqr/2-16                48.29n ± 2%   48.19n ± 2%        ~ (p=0.042 n=15)
NatSqr/3-16                59.93n ± 0%   59.64n ± 2%   -0.48% (p=0.000 n=15)
NatSqr/5-16                88.05n ± 0%   87.89n ± 3%        ~ (p=0.066 n=15)
NatSqr/8-16                127.7n ± 0%   126.9n ± 3%   -0.63% (p=0.000 n=15)
NatSqr/10-16               170.4n ± 0%   169.7n ± 3%        ~ (p=0.004 n=15)
NatSqr/20-16               388.8n ± 0%   392.9n ± 3%        ~ (p=0.123 n=15)
NatSqr/30-16               635.2n ± 0%   641.7n ± 3%        ~ (p=0.123 n=15)
NatSqr/50-16               1.304µ ± 1%   1.314µ ± 3%        ~ (p=0.927 n=15)
NatSqr/80-16               2.709µ ± 1%   2.899µ ± 4%   +7.01% (p=0.000 n=15)
NatSqr/100-16              3.885µ ± 0%   3.981µ ± 4%        ~ (p=0.123 n=15)
NatSqr/200-16              13.29µ ± 2%   12.14µ ± 4%   -8.67% (p=0.000 n=15)
NatSqr/300-16              23.39µ ± 0%   22.51µ ± 3%   -3.78% (p=0.000 n=15)
NatSqr/500-16              58.13µ ± 1%   50.56µ ± 2%  -13.02% (p=0.000 n=15)
NatSqr/800-16              118.4µ ± 1%   107.6µ ± 2%   -9.11% (p=0.000 n=15)
NatSqr/1000-16             172.7µ ± 1%   151.8µ ± 2%  -12.11% (p=0.000 n=15)
NatSqr/10000-16            6.065m ± 1%   5.757m ± 1%   -5.08% (p=0.000 n=15)
NatSqr/100000-16           240.9m ± 0%   228.1m ± 0%   -5.32% (p=0.000 n=15)
geomean                    8.601µ        8.453µ        -1.71%

goos: linux
goarch: amd64
pkg: math/big
cpu: AMD Ryzen 9 7950X 16-Core Processor
                         │     old      │                  new                  │
                         │    sec/op    │    sec/op      vs base                │
Div/20/10-32               11.11n ±  0%    11.11n ±  1%        ~ (p=0.532 n=15)
Div/40/20-32               11.08n ±  1%    11.11n ±  0%        ~ (p=0.815 n=15)
Div/100/50-32              16.81n ±  0%    16.84n ± 29%        ~ (p=0.020 n=15)
Div/200/100-32             73.91n ±  0%    76.85n ± 11%   +3.98% (p=0.000 n=15)
Div/400/200-32             87.35n ±  0%    88.91n ± 34%   +1.79% (p=0.000 n=15)
Div/1000/500-32            169.3n ±  1%    168.9n ±  1%        ~ (p=0.049 n=15)
Div/2000/1000-32           369.3n ±  0%    369.0n ±  0%        ~ (p=0.108 n=15)
Div/20000/10000-32         15.92µ ±  0%    13.55µ ±  2%  -14.91% (p=0.000 n=15)
Div/200000/100000-32       491.4µ ±  0%    482.4µ ±  1%   -1.84% (p=0.000 n=15)
Div/2000000/1000000-32     20.09m ±  0%    19.96m ±  0%   -0.69% (p=0.000 n=15)
Div/20000000/10000000-32   756.5m ±  0%    755.5m ±  0%        ~ (p=0.089 n=15)
NatMul/10-32               125.4n ±  5%    124.8n ±  1%        ~ (p=0.588 n=15)
NatMul/100-32              2.952µ ±  3%    2.969µ ±  0%        ~ (p=0.237 n=15)
NatMul/1000-32             120.7µ ±  0%    121.1µ ±  0%   +0.30% (p=0.000 n=15)
NatMul/10000-32            4.845m ±  0%    4.839m ±  1%        ~ (p=0.653 n=15)
NatMul/100000-32           173.3m ±  0%    173.3m ±  0%        ~ (p=0.838 n=15)
NatSqr/1-32                31.18n ± 23%    32.08n ±  2%        ~ (p=0.015 n=15)
NatSqr/2-32                57.22n ± 28%    58.88n ±  2%        ~ (p=0.054 n=15)
NatSqr/3-32                61.34n ± 18%    64.33n ±  2%        ~ (p=0.237 n=15)
NatSqr/5-32                72.47n ± 17%    79.81n ±  3%        ~ (p=0.067 n=15)
NatSqr/8-32                83.26n ± 26%   100.10n ±  3%        ~ (p=0.016 n=15)
NatSqr/10-32               87.31n ± 43%   125.50n ±  2%        ~ (p=0.003 n=15)
NatSqr/20-32               193.5n ± 25%    244.4n ± 13%        ~ (p=0.002 n=15)
NatSqr/30-32               323.9n ± 17%    380.9n ±  6%        ~ (p=0.003 n=15)
NatSqr/50-32               713.4n ±  9%    761.7n ±  8%        ~ (p=0.419 n=15)
NatSqr/80-32               1.486µ ±  7%    1.609µ ±  5%   +8.28% (p=0.000 n=15)
NatSqr/100-32              2.115µ ±  9%    2.253µ ±  1%        ~ (p=0.104 n=15)
NatSqr/200-32              7.201µ ±  4%    6.610µ ±  1%   -8.21% (p=0.000 n=15)
NatSqr/300-32              13.08µ ±  2%    12.37µ ±  1%   -5.41% (p=0.000 n=15)
NatSqr/500-32              32.56µ ±  2%    27.83µ ±  2%  -14.52% (p=0.000 n=15)
NatSqr/800-32              66.83µ ±  3%    59.59µ ±  1%  -10.83% (p=0.000 n=15)
NatSqr/1000-32             98.09µ ±  1%    83.59µ ±  1%  -14.78% (p=0.000 n=15)
NatSqr/10000-32            3.445m ±  1%    3.245m ±  0%   -5.81% (p=0.000 n=15)
NatSqr/100000-32           137.3m ±  0%    127.0m ±  0%   -7.54% (p=0.000 n=15)
geomean                    4.897µ          4.972µ         +1.52%

goos: linux
goarch: arm64
pkg: math/big
                         │     old     │                 new                 │
                         │   sec/op    │   sec/op     vs base                │
Div/20/10-16               15.26n ± 2%   15.14n ± 1%        ~ (p=0.212 n=15)
Div/40/20-16               15.22n ± 1%   15.16n ± 0%        ~ (p=0.190 n=15)
Div/100/50-16              26.53n ± 2%   26.42n ± 0%   -0.41% (p=0.000 n=15)
Div/200/100-16             124.3n ± 0%   124.0n ± 0%        ~ (p=0.704 n=15)
Div/400/200-16             142.4n ± 0%   141.8n ± 0%        ~ (p=0.074 n=15)
Div/1000/500-16            262.0n ± 1%   261.3n ± 1%        ~ (p=0.046 n=15)
Div/2000/1000-16           532.6n ± 0%   532.5n ± 1%        ~ (p=0.798 n=15)
Div/20000/10000-16         22.27µ ± 0%   22.88µ ± 0%   +2.73% (p=0.000 n=15)
Div/200000/100000-16       890.4µ ± 0%   902.8µ ± 0%   +1.39% (p=0.000 n=15)
Div/2000000/1000000-16     35.03m ± 0%   35.10m ± 0%        ~ (p=0.305 n=15)
Div/20000000/10000000-16    1.380 ± 0%    1.385 ± 0%        ~ (p=0.019 n=15)
NatMul/10-16               177.6n ± 1%   175.6n ± 3%        ~ (p=0.480 n=15)
NatMul/100-16              5.675µ ± 0%   5.669µ ± 1%        ~ (p=0.705 n=15)
NatMul/1000-16             224.3µ ± 0%   224.6µ ± 0%        ~ (p=0.653 n=15)
NatMul/10000-16            8.735m ± 0%   8.739m ± 0%        ~ (p=0.567 n=15)
NatMul/100000-16           331.6m ± 0%   331.6m ± 1%        ~ (p=0.412 n=15)
NatSqr/1-16                43.69n ± 2%   42.77n ± 6%        ~ (p=0.383 n=15)
NatSqr/2-16                65.26n ± 2%   63.91n ± 5%        ~ (p=0.285 n=15)
NatSqr/3-16                73.95n ± 1%   72.25n ± 6%        ~ (p=0.198 n=15)
NatSqr/5-16                95.06n ± 1%   94.21n ± 3%        ~ (p=0.721 n=15)
NatSqr/8-16                155.5n ± 1%   153.4n ± 4%        ~ (p=0.170 n=15)
NatSqr/10-16               175.4n ± 1%   174.0n ± 2%        ~ (p=0.271 n=15)
NatSqr/20-16               360.8n ± 0%   358.5n ± 2%        ~ (p=0.170 n=15)
NatSqr/30-16               584.7n ± 0%   582.9n ± 1%        ~ (p=0.170 n=15)
NatSqr/50-16               1.323µ ± 0%   1.322µ ± 0%        ~ (p=0.627 n=15)
NatSqr/80-16               2.916µ ± 0%   2.674µ ± 0%   -8.30% (p=0.000 n=15)
NatSqr/100-16              4.365µ ± 0%   3.802µ ± 0%  -12.90% (p=0.000 n=15)
NatSqr/200-16              16.42µ ± 0%   11.29µ ± 0%  -31.26% (p=0.000 n=15)
NatSqr/300-16              28.07µ ± 0%   22.83µ ± 0%  -18.68% (p=0.000 n=15)
NatSqr/500-16              76.30µ ± 0%   50.06µ ± 0%  -34.39% (p=0.000 n=15)
NatSqr/800-16              147.5µ ± 0%   101.2µ ± 1%  -31.41% (p=0.000 n=15)
NatSqr/1000-16             228.6µ ± 0%   149.5µ ± 0%  -34.61% (p=0.000 n=15)
NatSqr/10000-16            7.417m ± 0%   6.025m ± 0%  -18.76% (p=0.000 n=15)
NatSqr/100000-16           309.2m ± 0%   214.9m ± 0%  -30.50% (p=0.000 n=15)
geomean                    8.559µ        7.906µ        -7.63%

goos: darwin
goarch: arm64
pkg: math/big
cpu: Apple M3 Pro
                         │     old      │                 new                 │
                         │    sec/op    │   sec/op     vs base                │
Div/20/10-12                9.577n ± 6%   9.473n ± 5%        ~ (p=0.384 n=15)
Div/40/20-12                9.480n ± 1%   9.430n ± 1%        ~ (p=0.019 n=15)
Div/100/50-12               14.82n ± 0%   14.82n ± 0%        ~ (p=0.845 n=15)
Div/200/100-12              83.94n ± 1%   84.35n ± 4%        ~ (p=0.512 n=15)
Div/400/200-12              102.7n ± 1%   102.9n ± 0%        ~ (p=0.845 n=15)
Div/1000/500-12             185.3n ± 1%   181.9n ± 1%   -1.83% (p=0.000 n=15)
Div/2000/1000-12            397.0n ± 1%   396.7n ± 0%        ~ (p=0.959 n=15)
Div/20000/10000-12          14.05µ ± 0%   13.70µ ± 1%        ~ (p=0.002 n=15)
Div/200000/100000-12        529.4µ ± 3%   526.7µ ± 2%        ~ (p=0.967 n=15)
Div/2000000/1000000-12      20.05m ± 0%   20.05m ± 0%        ~ (p=0.653 n=15)
Div/20000000/10000000-12    788.2m ± 1%   789.0m ± 1%        ~ (p=0.412 n=15)
NatMul/10-12                79.95n ± 1%   80.87n ± 1%   +1.15% (p=0.000 n=15)
NatMul/100-12               2.973µ ± 0%   2.986µ ± 2%        ~ (p=0.051 n=15)
NatMul/1000-12              122.6µ ± 5%   123.0µ ± 1%        ~ (p=0.783 n=15)
NatMul/10000-12             4.990m ± 1%   5.000m ± 1%        ~ (p=0.653 n=15)
NatMul/100000-12            185.3m ± 3%   190.3m ± 1%        ~ (p=0.089 n=15)
NatSqr/1-12                 11.84n ± 1%   11.88n ± 1%        ~ (p=0.735 n=15)
NatSqr/2-12                 21.01n ± 1%   21.44n ± 6%        ~ (p=0.039 n=15)
NatSqr/3-12                 25.59n ± 0%   26.74n ± 9%   +4.49% (p=0.000 n=15)
NatSqr/5-12                 36.78n ± 0%   37.04n ± 1%   +0.71% (p=0.000 n=15)
NatSqr/8-12                 63.09n ± 3%   63.22n ± 1%        ~ (p=0.846 n=15)
NatSqr/10-12                79.98n ± 0%   79.78n ± 0%        ~ (p=0.100 n=15)
NatSqr/20-12                174.0n ± 0%   175.5n ± 1%        ~ (p=0.361 n=15)
NatSqr/30-12                290.0n ± 0%   291.4n ± 0%        ~ (p=0.002 n=15)
NatSqr/50-12                655.2n ± 4%   658.1n ± 0%        ~ (p=0.060 n=15)
NatSqr/80-12                1.506µ ± 0%   1.397µ ± 5%   -7.24% (p=0.000 n=15)
NatSqr/100-12               2.273µ ± 0%   2.005µ ± 5%  -11.79% (p=0.000 n=15)
NatSqr/200-12               8.833µ ± 6%   6.109µ ± 0%  -30.84% (p=0.000 n=15)
NatSqr/300-12               15.15µ ± 4%   12.37µ ± 0%  -18.34% (p=0.000 n=15)
NatSqr/500-12               41.89µ ± 0%   27.70µ ± 1%  -33.88% (p=0.000 n=15)
NatSqr/800-12               80.72µ ± 0%   56.40µ ± 0%  -30.12% (p=0.000 n=15)
NatSqr/1000-12             127.06µ ± 1%   84.06µ ± 1%  -33.84% (p=0.000 n=15)
NatSqr/10000-12             4.130m ± 0%   3.390m ± 0%  -17.91% (p=0.000 n=15)
NatSqr/100000-12            173.2m ± 0%   131.2m ± 6%  -24.25% (p=0.000 n=15)
geomean                     4.489µ        4.189µ        -6.68%

Change-Id: Iaf65fd85457b003ebf07a787c875cda321b40cc9
Reviewed-on: https://go-review.googlesource.com/c/go/+/652058
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Robert Griesemer <gri@google.com>
Reviewed-by: Alan Donovan <adonovan@google.com>
Auto-Submit: Russ Cox <rsc@golang.org>
2025-03-12 05:41:50 -07:00
.github .github: update language change proposal template 2024-08-08 19:02:29 +00:00
api go/types: add Var.Kind() VarKind method 2025-03-05 10:21:15 -08:00
doc cmd/go: allow symlinks of non-directory files in embed 2025-03-11 07:51:38 -07:00
lib lib/time: build with Ubuntu backward compatibility options 2025-02-06 17:10:15 -08:00
misc misc/wasm: move wasm runtime files to lib/wasm 2024-08-30 19:15:21 +00:00
src math/big: update calibration tests and recalibrate 2025-03-12 05:41:50 -07:00
test cmd/compile: compute bits.OnesCount's limits from argument's limits 2025-03-11 20:17:36 -07:00
.gitattributes all: treat all files as binary, but check in .bat with CRLF 2020-06-08 15:31:43 +00:00
.gitignore runtime,internal: move runtime/internal/sys to internal/runtime/sys 2024-07-23 19:05:35 +00:00
codereview.cfg codereview.cfg: add codereview.cfg for master branch 2021-02-19 18:44:53 +00:00
CONTRIBUTING.md doc: normalize proposal-process links 2023-03-29 22:00:27 +00:00
go.env cmd/go: additional doc-inspired tests and bug fixes 2023-06-06 19:18:46 +00:00
LICENSE LICENSE: update per Google Legal 2024-08-09 14:54:31 +00:00
PATENTS LICENSE: separate, change PATENTS text 2010-12-06 16:31:59 -05:00
README.md README: fix CC BY license name 2024-07-22 17:45:27 +00:00
SECURITY.md SECURITY.md: update the Reporting a Vulnerability link 2023-09-22 21:17:24 +00:00

README.md

The Go Programming Language

Go is an open source programming language that makes it easy to build simple, reliable, and efficient software.

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Our canonical Git repository is located at https://go.googlesource.com/go. There is a mirror of the repository at https://github.com/golang/go.

Unless otherwise noted, the Go source files are distributed under the BSD-style license found in the LICENSE file.

Download and Install

Binary Distributions

Official binary distributions are available at https://go.dev/dl/.

After downloading a binary release, visit https://go.dev/doc/install for installation instructions.

Install From Source

If a binary distribution is not available for your combination of operating system and architecture, visit https://go.dev/doc/install/source for source installation instructions.

Contributing

Go is the work of thousands of contributors. We appreciate your help!

To contribute, please read the contribution guidelines at https://go.dev/doc/contribute.

Note that the Go project uses the issue tracker for bug reports and proposals only. See https://go.dev/wiki/Questions for a list of places to ask questions about the Go language.