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Russ Cox 872496da2b math/big: replace nat pool with Word stack 
In the early days of math/big, algorithms that needed more space
grew the result larger than it needed to be and then used the
high words as extra space. This made results their own temporary
space caches, at the cost that saving a result in a data structure
might hold significantly more memory than necessary.
Specifically, new(big.Int).Mul(x, y) returned a big.Int with a
backing slice 3X as big as it strictly needed to be.
If you are storing many multiplication results, or even a single
large result, the 3X overhead can add up.

This approach to storage for temporaries also requires being able
to analyze the algorithms to predict the exact amount they need,
which can be difficult.

For both these reasons, the implementation of recursive long division,
which came later, introduced a “nat pool” where temporaries could be
stored and reused, or reclaimed by the GC when no longer used.
This avoids the storage and bookkeeping overheads but introduces a
per-temporary sync.Pool overhead. divRecursiveStep takes an array
of cached temporaries to remove some of that overhead.
The nat pool was better but is still not quite right.

This CL introduces something even better than the nat pool
(still probably not quite right, but the best I can see for now):
a sync.Pool holding stacks for allocating temporaries.
Now an operation can get one stack out of the pool and then
allocate as many temporaries as it needs during the operation,
eventually returning the stack back to the pool. The sync.Pool
operations are now per-exported-operation (like big.Int.Mul),
not per-temporary.

This CL converts both the pre-allocation in nat.mul and the
uses of the nat pool to use stack pools instead. This simplifies
some code and sets us up better for more complex algorithms
(such as Toom-Cook or FFT-based multiplication) that need
more temporaries. It is also a little bit faster.

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               23.68n ± 0%   22.21n ± 0%   -6.21% (p=0.000 n=15)
Div/40/20-16               23.68n ± 0%   22.21n ± 0%   -6.21% (p=0.000 n=15)
Div/100/50-16              56.65n ± 0%   55.53n ± 0%   -1.98% (p=0.000 n=15)
Div/200/100-16             194.6n ± 1%   172.8n ± 0%  -11.20% (p=0.000 n=15)
Div/400/200-16             232.1n ± 0%   206.7n ± 0%  -10.94% (p=0.000 n=15)
Div/1000/500-16            405.3n ± 1%   383.8n ± 0%   -5.30% (p=0.000 n=15)
Div/2000/1000-16           810.4n ± 1%   795.2n ± 0%   -1.88% (p=0.000 n=15)
Div/20000/10000-16         25.88µ ± 0%   25.39µ ± 0%   -1.89% (p=0.000 n=15)
Div/200000/100000-16       931.5µ ± 0%   924.3µ ± 0%   -0.77% (p=0.000 n=15)
Div/2000000/1000000-16     37.77m ± 0%   37.75m ± 0%        ~ (p=0.098 n=15)
Div/20000000/10000000-16    1.367 ± 0%    1.377 ± 0%   +0.72% (p=0.003 n=15)
NatMul/10-16               168.5n ± 3%   164.0n ± 4%        ~ (p=0.751 n=15)
NatMul/100-16              6.086µ ± 3%   5.380µ ± 3%  -11.60% (p=0.000 n=15)
NatMul/1000-16             238.1µ ± 3%   228.3µ ± 1%   -4.12% (p=0.000 n=15)
NatMul/10000-16            8.721m ± 2%   8.518m ± 1%   -2.33% (p=0.000 n=15)
NatMul/100000-16           369.6m ± 0%   371.1m ± 0%   +0.42% (p=0.000 n=15)
geomean                    19.57µ        18.74µ        -4.21%

                 │     old      │                  new                   │
                 │     B/op     │     B/op      vs base                  │
NatMul/10-16         192.0 ± 0%     192.0 ± 0%        ~ (p=1.000 n=15) ¹
NatMul/100-16      4.750Ki ± 0%   1.751Ki ± 0%  -63.14% (p=0.000 n=15)
NatMul/1000-16     48.16Ki ± 0%   16.02Ki ± 0%  -66.73% (p=0.000 n=15)
NatMul/10000-16    482.9Ki ± 1%   165.4Ki ± 3%  -65.75% (p=0.000 n=15)
NatMul/100000-16   5.747Mi ± 7%   4.197Mi ± 0%  -26.97% (p=0.000 n=15)
geomean            41.42Ki        20.63Ki       -50.18%
¹ all samples are equal

                 │     old     │                 new                  │
                 │  allocs/op  │  allocs/op   vs base                 │
NatMul/10-16       1.000 ±  0%   1.000 ±  0%       ~ (p=1.000 n=15) ¹
NatMul/100-16      1.000 ±  0%   1.000 ±  0%       ~ (p=1.000 n=15) ¹
NatMul/1000-16     1.000 ±  0%   1.000 ±  0%       ~ (p=1.000 n=15) ¹
NatMul/10000-16    1.000 ±  0%   1.000 ±  0%       ~ (p=1.000 n=15) ¹
NatMul/100000-16   7.000 ± 14%   7.000 ± 14%       ~ (p=0.668 n=15)
geomean            1.476         1.476        +0.00%
¹ all samples are equal

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               15.84n ± 1%   13.12n ± 0%  -17.17% (p=0.000 n=15)
Div/40/20-88               15.88n ± 1%   13.12n ± 0%  -17.38% (p=0.000 n=15)
Div/100/50-88              26.42n ± 0%   25.47n ± 0%   -3.60% (p=0.000 n=15)
Div/200/100-88             132.4n ± 0%   114.9n ± 0%  -13.22% (p=0.000 n=15)
Div/400/200-88             150.1n ± 0%   135.6n ± 0%   -9.66% (p=0.000 n=15)
Div/1000/500-88            275.5n ± 0%   264.1n ± 0%   -4.14% (p=0.000 n=15)
Div/2000/1000-88           586.5n ± 0%   581.1n ± 0%   -0.92% (p=0.000 n=15)
Div/20000/10000-88         25.87µ ± 0%   25.72µ ± 0%   -0.59% (p=0.000 n=15)
Div/200000/100000-88       772.2µ ± 0%   779.0µ ± 0%   +0.88% (p=0.000 n=15)
Div/2000000/1000000-88     33.36m ± 0%   33.63m ± 0%   +0.80% (p=0.000 n=15)
Div/20000000/10000000-88    1.307 ± 0%    1.320 ± 0%   +1.03% (p=0.000 n=15)
NatMul/10-88               140.4n ± 0%   148.8n ± 4%   +5.98% (p=0.000 n=15)
NatMul/100-88              4.663µ ± 1%   4.388µ ± 1%   -5.90% (p=0.000 n=15)
NatMul/1000-88             207.7µ ± 0%   205.8µ ± 0%   -0.89% (p=0.000 n=15)
NatMul/10000-88            8.456m ± 0%   8.468m ± 0%   +0.14% (p=0.021 n=15)
NatMul/100000-88           295.1m ± 0%   297.9m ± 0%   +0.94% (p=0.000 n=15)
geomean                    14.96µ        14.33µ        -4.23%

                 │     old      │                   new                   │
                 │     B/op     │     B/op       vs base                  │
NatMul/10-88         192.0 ± 0%     192.0 ±  0%        ~ (p=1.000 n=15) ¹
NatMul/100-88      4.750Ki ± 0%   1.758Ki ±  0%  -62.99% (p=0.000 n=15)
NatMul/1000-88     48.44Ki ± 0%   16.08Ki ±  0%  -66.80% (p=0.000 n=15)
NatMul/10000-88    489.7Ki ± 1%   166.1Ki ±  3%  -66.08% (p=0.000 n=15)
NatMul/100000-88   5.546Mi ± 0%   3.819Mi ± 60%  -31.15% (p=0.000 n=15)
geomean            41.29Ki        20.30Ki        -50.85%
¹ all samples are equal

                 │     old     │                 new                  │
                 │  allocs/op  │  allocs/op   vs base                 │
NatMul/10-88       1.000 ±  0%   1.000 ±  0%       ~ (p=1.000 n=15) ¹
NatMul/100-88      1.000 ±  0%   1.000 ±  0%       ~ (p=1.000 n=15) ¹
NatMul/1000-88     1.000 ±  0%   1.000 ±  0%       ~ (p=1.000 n=15) ¹
NatMul/10000-88    1.000 ±  0%   1.000 ±  0%       ~ (p=1.000 n=15) ¹
NatMul/100000-88   5.000 ± 20%   6.000 ± 67%       ~ (p=0.672 n=15)
geomean            1.380         1.431        +3.71%
¹ all samples are equal

goos: linux
goarch: arm64
pkg: math/big
                         │     old     │                 new                 │
                         │   sec/op    │   sec/op     vs base                │
Div/20/10-16               15.85n ± 0%   15.23n ± 0%   -3.91% (p=0.000 n=15)
Div/40/20-16               15.88n ± 0%   15.22n ± 0%   -4.16% (p=0.000 n=15)
Div/100/50-16              29.69n ± 0%   26.39n ± 0%  -11.11% (p=0.000 n=15)
Div/200/100-16             149.2n ± 0%   123.3n ± 0%  -17.36% (p=0.000 n=15)
Div/400/200-16             160.3n ± 0%   139.2n ± 0%  -13.16% (p=0.000 n=15)
Div/1000/500-16            271.0n ± 0%   256.1n ± 0%   -5.50% (p=0.000 n=15)
Div/2000/1000-16           545.3n ± 0%   527.0n ± 0%   -3.36% (p=0.000 n=15)
Div/20000/10000-16         22.60µ ± 0%   22.20µ ± 0%   -1.77% (p=0.000 n=15)
Div/200000/100000-16       889.0µ ± 0%   892.2µ ± 0%   +0.35% (p=0.000 n=15)
Div/2000000/1000000-16     38.01m ± 0%   38.12m ± 0%   +0.30% (p=0.000 n=15)
Div/20000000/10000000-16    1.437 ± 0%    1.444 ± 0%   +0.50% (p=0.000 n=15)
NatMul/10-16               166.4n ± 2%   169.5n ± 1%   +1.86% (p=0.000 n=15)
NatMul/100-16              5.733µ ± 1%   5.570µ ± 1%   -2.84% (p=0.000 n=15)
NatMul/1000-16             232.6µ ± 1%   229.8µ ± 0%   -1.22% (p=0.000 n=15)
NatMul/10000-16            9.039m ± 1%   8.969m ± 0%   -0.77% (p=0.000 n=15)
NatMul/100000-16           367.0m ± 0%   368.8m ± 0%   +0.48% (p=0.000 n=15)
geomean                    16.15µ        15.50µ        -4.01%

                 │     old      │                  new                   │
                 │     B/op     │     B/op      vs base                  │
NatMul/10-16         192.0 ± 0%     192.0 ± 0%        ~ (p=1.000 n=15) ¹
NatMul/100-16      4.750Ki ± 0%   1.751Ki ± 0%  -63.14% (p=0.000 n=15)
NatMul/1000-16     48.33Ki ± 0%   16.02Ki ± 0%  -66.85% (p=0.000 n=15)
NatMul/10000-16    536.5Ki ± 1%   165.7Ki ± 3%  -69.12% (p=0.000 n=15)
NatMul/100000-16   6.078Mi ± 6%   4.197Mi ± 0%  -30.94% (p=0.000 n=15)
geomean            42.81Ki        20.64Ki       -51.78%
¹ all samples are equal

                 │     old     │                  new                  │
                 │  allocs/op  │  allocs/op   vs base                  │
NatMul/10-16       1.000 ±  0%   1.000 ±  0%        ~ (p=1.000 n=15) ¹
NatMul/100-16      1.000 ±  0%   1.000 ±  0%        ~ (p=1.000 n=15) ¹
NatMul/1000-16     1.000 ±  0%   1.000 ±  0%        ~ (p=1.000 n=15) ¹
NatMul/10000-16    2.000 ± 50%   1.000 ±  0%  -50.00% (p=0.001 n=15)
NatMul/100000-16   9.000 ± 11%   8.000 ± 12%  -11.11% (p=0.001 n=15)
geomean            1.783         1.516        -14.97%
¹ all samples are equal

goos: darwin
goarch: arm64
pkg: math/big
cpu: Apple M3 Pro
                         │     old      │                new                 │
                         │    sec/op    │   sec/op     vs base               │
Div/20/10-12                9.850n ± 1%   9.405n ± 1%  -4.52% (p=0.000 n=15)
Div/40/20-12                9.858n ± 0%   9.403n ± 1%  -4.62% (p=0.000 n=15)
Div/100/50-12               16.40n ± 1%   14.81n ± 0%  -9.70% (p=0.000 n=15)
Div/200/100-12              88.48n ± 2%   80.88n ± 0%  -8.59% (p=0.000 n=15)
Div/400/200-12             107.90n ± 1%   99.28n ± 1%  -7.99% (p=0.000 n=15)
Div/1000/500-12             188.8n ± 1%   178.6n ± 1%  -5.40% (p=0.000 n=15)
Div/2000/1000-12            399.9n ± 0%   389.1n ± 0%  -2.70% (p=0.000 n=15)
Div/20000/10000-12          13.94µ ± 2%   13.81µ ± 1%       ~ (p=0.574 n=15)
Div/200000/100000-12        523.8µ ± 0%   521.7µ ± 0%  -0.40% (p=0.000 n=15)
Div/2000000/1000000-12      21.46m ± 0%   21.48m ± 0%       ~ (p=0.067 n=15)
Div/20000000/10000000-12    812.5m ± 0%   812.9m ± 0%       ~ (p=0.061 n=15)
NatMul/10-12                77.14n ± 0%   78.35n ± 1%  +1.57% (p=0.000 n=15)
NatMul/100-12               2.999µ ± 0%   2.871µ ± 1%  -4.27% (p=0.000 n=15)
NatMul/1000-12              126.2µ ± 0%   126.8µ ± 0%  +0.51% (p=0.011 n=15)
NatMul/10000-12             5.099m ± 0%   5.125m ± 0%  +0.51% (p=0.000 n=15)
NatMul/100000-12            206.7m ± 0%   208.4m ± 0%  +0.80% (p=0.000 n=15)
geomean                     9.512µ        9.236µ       -2.91%

                 │     old      │                   new                    │
                 │     B/op     │      B/op       vs base                  │
NatMul/10-12         192.0 ± 0%     192.0 ±   0%        ~ (p=1.000 n=15) ¹
NatMul/100-12      4.750Ki ± 0%   1.750Ki ±   0%  -63.16% (p=0.000 n=15)
NatMul/1000-12     48.13Ki ± 0%   16.01Ki ±   0%  -66.73% (p=0.000 n=15)
NatMul/10000-12    483.5Ki ± 1%   163.2Ki ±   2%  -66.24% (p=0.000 n=15)
NatMul/100000-12   5.480Mi ± 4%   1.532Mi ± 104%  -72.05% (p=0.000 n=15)
geomean            41.03Ki        16.82Ki         -59.01%
¹ all samples are equal

                 │    old     │                  new                   │
                 │ allocs/op  │  allocs/op    vs base                  │
NatMul/10-12       1.000 ± 0%   1.000 ±   0%        ~ (p=1.000 n=15) ¹
NatMul/100-12      1.000 ± 0%   1.000 ±   0%        ~ (p=1.000 n=15) ¹
NatMul/1000-12     1.000 ± 0%   1.000 ±   0%        ~ (p=1.000 n=15) ¹
NatMul/10000-12    1.000 ± 0%   1.000 ±   0%        ~ (p=1.000 n=15) ¹
NatMul/100000-12   5.000 ± 0%   1.000 ± 400%  -80.00% (p=0.007 n=15)
geomean            1.380        1.000         -27.52%
¹ all samples are equal

Change-Id: I7efa6fe37971ed26ae120a32250fcb47ece0a011
Reviewed-on: https://go-review.googlesource.com/c/go/+/650638
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Auto-Submit: Russ Cox <rsc@golang.org>
Reviewed-by: Ian Lance Taylor <iant@google.com>
Reviewed-by: Alan Donovan <adonovan@google.com>
 		2025-02-27 05:58:09 -08:00
.github .github: update language change proposal template 2024-08-08 19:02:29 +00:00
api go/parser: deprecate parser.ParseDir 2025-02-19 11:49:13 -08:00
doc crypto/tls: require EMS in FIPS 140-3 mode 2025-02-25 11:50:05 -08:00
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: replace nat pool with Word stack 2025-02-27 05:58:09 -08:00
test cmd/compile: simplify intrinsification of TrailingZeros16 and TrailingZeros8 2025-02-27 03:45:44 -08:00
.gitattributes
…
.gitignore runtime,internal: move runtime/internal/sys to internal/runtime/sys 2024-07-23 19:05:35 +00:00
CONTRIBUTING.md
…
LICENSE LICENSE: update per Google Legal 2024-08-09 14:54:31 +00:00
PATENTS
…
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
codereview.cfg
…
go.env cmd/go: additional doc-inspired tests and bug fixes 2023-06-06 19:18:46 +00:00

README.md

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