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Russ Cox a11643df8f math/big: replace addVW/subVW assembly with fast pure Go 
The vast majority of the time, carry propagation is limited and
addVW/subVW only need to consider a single word for carry propagation.
As Josh Bleecher-Snyder pointed out in 2019 (CL 164968), once carrying
is done, the remaining words can be handled faster with copy (memmove).
In the benchmarks below, this is the data=random case.

Even more important, if the source and destination are the same,
the copy can be optimized away entirely, making a small in-place
addition to a big.Int O(1) instead of O(N). To date, only a few
systems (amd64, arm64, and pure Go, meaning wasm) make use of this
asymptotic improvement. This is the data=shortcut case.

This CL deletes the addVW/subVW assembly and replaces it with
an optimized pure Go version. Using Go makes it easy to call
the real copy builtin, which will use optimized memmove code,
instead of recreating a worse memmove in assembly (as arm64 does)
or omitting the copy optimization entirely (as most others do).

The worst case for the Go version versus assembly is the case
of incrementing 2^N-1 by 1, which has to propagate a carry
the entire length of the array. This is the data=carry case.
On balance, we believe this case is rare enough to be worth
taking a hit in that case, in exchange for significant wins
in the other cases and the deletion of significant amounts of
assembly of varying quality. (Remember that half the assembly has
the copy optimization and shortcut, while half does not.)

In the benchmarks, the systems are:

	c2s16     GOARCH=amd64     c2s16 perf gomote (Intel, Google Cloud)
	c3h88     GOARCH=amd64     c3h88 perf gomote (newer Intel, Google Cloud)
	s7        GOARCH=amd64     rsc basement server (AMD Ryzen 9 7950X)
	c4as16    GOARCH=arm64     c4as16 perf gomote (Google Cloud)
	mac       GOARCH=arm64     Apple M3 Pro in MacBook Pro
	386       GOARCH=386       gotip-linux-386 gomote
	arm       GOARCH=arm       gotip-linux-arm gomote
	loong64   GOARCH=loong64   gotip-linux-loong64 gomote
	ppc64le   GOARCH=ppc64le   gotip-linux-ppc64le gomote
	riscv64   GOARCH=riscv64   gotip-linux-riscv64 gomote

benchmark \ system                    c2s16     c3h88       s7    c4as16       mac       386      arm  loong64   ppc64le  riscv64

AddVW/words=1/data=random            -1.15%    -1.74%   -5.89%    -9.80%   -11.54%   +23.71%  -12.74%  -14.25%   +14.67%  +10.27%
AddVW/words=2/data=random            -2.59%         ~   -4.38%   -19.31%   -15.41%   +24.80%        ~  -19.99%   +13.73%  +19.71%
AddVW/words=3/data=random            -3.75%   -19.10%   -3.79%   -23.15%   -17.04%   +20.04%  -10.07%  -23.20%         ~  +15.39%
AddVW/words=4/data=random            -2.84%    +7.05%   -8.77%   -22.64%   -15.77%   +16.01%   -7.36%  -28.22%         ~  +23.00%
AddVW/words=5/data=random           -10.97%    +2.16%  -12.09%   -20.89%   -17.14%    +9.42%   -4.69%  -32.60%         ~  +10.07%
AddVW/words=6/data=random            -9.87%         ~   -7.54%   -19.08%    -6.46%         ~   -3.44%  -34.61%         ~  +12.19%
AddVW/words=7/data=random           -14.36%         ~  -10.09%   -19.10%   -10.47%    -6.20%   -5.06%  -38.14%   -11.54%   +6.79%
AddVW/words=8/data=random           -17.50%         ~  -11.06%   -25.14%   -12.88%    -8.35%   -5.11%  -41.39%   -14.04%  +11.87%
AddVW/words=9/data=random           -19.76%    -4.05%  -15.47%   -24.08%   -16.50%   -12.34%  -21.56%  -44.25%   -14.82%        ~
AddVW/words=10/data=random          -13.89%         ~   -9.69%   -23.06%    -8.04%   -12.58%  -19.25%  -32.80%   -11.68%        ~
AddVW/words=16/data=random          -29.36%   -15.35%  -21.86%   -25.04%   -19.89%   -32.26%  -16.29%  -42.66%   -25.92%   -3.01%
AddVW/words=32/data=random          -39.02%   -28.76%  -39.87%   -11.22%    -2.85%   -55.40%  -31.17%  -55.37%   -37.92%  -16.28%
AddVW/words=64/data=random          -25.94%   -19.09%  -20.60%    -6.90%    +8.91%   -51.00%  -43.72%  -62.27%   -44.11%  -28.74%
AddVW/words=100/data=random         -22.79%   -18.13%  -18.25%         ~   +33.89%   -67.40%  -51.77%  -63.54%   -53.75%  -30.97%
AddVW/words=1000/data=random         -8.98%    -3.84%        ~    -3.15%         ~   -93.35%  -63.92%  -65.66%   -68.67%  -42.30%
AddVW/words=10000/data=random        -1.38%    -0.38%        ~         ~         ~   -89.16%  -65.18%  -44.65%   -70.35%  -20.08%
AddVW/words=100000/data=random            ~         ~        ~         ~         ~   -87.03%  -64.51%  -36.08%   -61.40%  -16.53%

SubVW/words=1/data=random            -3.67%         ~   -8.38%   -10.26%    -3.07%   +45.78%   -6.06%  -11.17%         ~        ~
SubVW/words=2/data=random            -3.48%   -10.07%   -5.76%   -20.14%    -8.45%   +44.28%        ~  -19.09%         ~  +16.98%
SubVW/words=3/data=random            -7.11%   -26.64%   -4.48%   -22.07%    -9.21%   +35.61%        ~  -23.93%   -18.20%        ~
SubVW/words=4/data=random            -4.23%    +7.19%   -8.95%   -22.62%   -13.89%   +33.20%   -8.96%  -29.96%         ~  +22.23%
SubVW/words=5/data=random           -11.49%    +1.92%  -10.86%   -22.27%   -17.53%   +24.48%   -2.88%  -35.19%   -19.55%        ~
SubVW/words=6/data=random            -7.67%         ~   -7.72%   -18.44%    -6.24%   +12.03%   -2.00%  -39.68%   -10.73%        ~
SubVW/words=7/data=random           -13.69%   -18.32%  -11.82%   -18.92%   -11.57%    +6.63%        ~  -43.54%   -30.81%        ~
SubVW/words=8/data=random           -16.02%         ~  -11.07%   -24.50%   -11.92%    +4.32%   -3.01%  -46.95%   -24.14%        ~
SubVW/words=9/data=random           -18.76%    -3.34%  -14.84%   -23.79%   -17.50%         ~  -21.80%  -49.98%   -29.62%        ~
SubVW/words=10/data=random          -13.23%         ~   -9.25%   -21.26%   -11.63%         ~  -18.58%  -39.19%   -20.09%        ~
SubVW/words=16/data=random          -28.25%   -13.24%  -22.66%   -27.18%   -19.13%   -23.38%  -20.24%  -51.01%   -28.06%   -3.05%
SubVW/words=32/data=random          -38.41%   -28.88%  -40.12%   -11.20%    -2.80%   -49.17%  -34.67%  -63.29%   -39.25%  -15.20%
SubVW/words=64/data=random          -25.51%   -19.24%  -22.20%    -6.57%    +9.98%   -48.52%  -48.14%  -69.50%   -49.44%  -27.92%
SubVW/words=100/data=random         -21.69%   -18.51%        ~    +1.92%   +34.42%   -65.88%  -54.67%  -71.24%   -58.88%  -30.71%
SubVW/words=1000/data=random         -9.81%    -4.05%   -2.14%    -3.06%         ~   -93.37%  -67.33%  -74.12%   -68.36%  -42.17%
SubVW/words=10000/data=random             ~    -0.52%        ~         ~         ~   -88.87%  -68.54%  -44.94%   -70.63%  -19.95%
SubVW/words=100000/data=random            ~         ~        ~         ~         ~   -86.69%  -68.09%  -48.36%   -62.42%  -19.32%

AddVW/words=1/data=shortcut         -29.38%   -25.38%  -27.37%   -23.15%   -25.41%    +3.01%  -33.60%  -36.12%   -15.76%        ~
AddVW/words=2/data=shortcut         -32.79%   -34.72%  -31.47%   -24.47%   -28.21%    -3.75%  -34.66%  -43.89%   -23.65%  -21.56%
AddVW/words=3/data=shortcut         -38.50%   -46.83%  -35.67%   -26.38%   -30.29%   -10.41%  -44.89%  -47.68%   -30.93%  -26.85%
AddVW/words=4/data=shortcut         -40.40%   -28.85%  -34.19%   -29.83%   -32.95%   -16.09%  -42.86%  -51.02%   -34.19%  -26.69%
AddVW/words=5/data=shortcut         -43.87%   -35.42%  -36.46%   -32.59%   -37.72%   -20.82%  -45.14%  -54.01%   -35.49%  -30.48%
AddVW/words=6/data=shortcut         -46.98%   -39.34%  -42.22%   -35.43%   -38.18%   -27.46%  -46.72%  -56.61%   -40.21%  -34.07%
AddVW/words=7/data=shortcut         -49.63%   -47.97%  -46.61%   -35.28%   -41.93%   -31.14%  -49.29%  -58.89%   -41.10%  -37.01%
AddVW/words=8/data=shortcut         -50.48%   -42.33%  -45.40%   -40.24%   -41.74%   -32.92%  -50.62%  -60.98%   -44.85%  -38.10%
AddVW/words=9/data=shortcut         -54.27%   -43.52%  -49.06%   -42.16%   -45.22%   -37.57%  -51.84%  -62.91%   -46.04%  -40.82%
AddVW/words=10/data=shortcut        -56.01%   -45.40%  -51.42%   -43.29%   -46.14%   -38.65%  -53.65%  -64.62%   -47.05%  -43.21%
AddVW/words=16/data=shortcut        -62.73%   -55.66%  -59.31%   -56.38%   -54.31%   -53.16%  -61.03%  -72.29%   -58.24%  -52.57%
AddVW/words=32/data=shortcut        -74.00%   -69.42%  -71.75%   -33.65%   -37.35%   -71.73%  -72.59%  -82.44%   -70.87%  -67.69%
AddVW/words=64/data=shortcut        -56.69%   -52.72%  -52.09%   -35.48%   -36.87%   -84.24%  -83.10%  -90.37%   -82.56%  -80.81%
AddVW/words=100/data=shortcut       -56.68%   -53.18%  -51.49%   -33.49%   -37.72%   -89.95%  -88.21%  -93.37%   -88.47%  -86.52%
AddVW/words=1000/data=shortcut      -56.68%   -52.45%  -51.66%   -35.31%   -36.65%   -98.88%  -98.62%  -99.24%   -98.78%  -98.41%
AddVW/words=10000/data=shortcut     -56.70%   -52.40%  -51.92%   -33.49%   -36.98%   -99.89%  -99.86%  -99.92%   -99.87%  -99.91%
AddVW/words=100000/data=shortcut    -56.67%   -52.46%  -52.38%   -35.31%   -37.20%   -99.99%  -99.99%  -99.99%   -99.99%  -99.99%

SubVW/words=1/data=shortcut         -29.80%   -20.71%  -26.94%   -23.24%   -25.33%   +26.97%  -32.02%  -37.85%   -40.20%  -12.67%
SubVW/words=2/data=shortcut         -35.47%   -36.38%  -31.93%   -25.43%   -30.18%   +18.96%  -33.48%  -46.48%   -39.38%  -18.65%
SubVW/words=3/data=shortcut         -39.22%   -49.96%  -36.90%   -25.82%   -30.96%   +12.53%  -40.67%  -51.07%   -43.71%  -23.78%
SubVW/words=4/data=shortcut         -40.46%   -24.90%  -34.66%   -29.87%   -33.97%    +4.60%  -42.32%  -54.92%   -42.83%  -22.45%
SubVW/words=5/data=shortcut         -43.84%   -34.17%  -38.00%   -32.55%   -37.27%    -2.46%  -43.09%  -58.18%   -45.70%  -26.45%
SubVW/words=6/data=shortcut         -47.69%   -37.49%  -42.73%   -35.90%   -37.73%    -8.52%  -46.55%  -61.01%   -44.00%  -30.14%
SubVW/words=7/data=shortcut         -49.45%   -50.66%  -46.88%   -34.77%   -41.64%   -14.46%  -48.92%  -63.46%   -50.47%  -33.39%
SubVW/words=8/data=shortcut         -50.45%   -39.31%  -47.14%   -40.47%   -41.70%   -15.77%  -50.21%  -65.64%   -47.71%  -34.01%
SubVW/words=9/data=shortcut         -54.28%   -43.07%  -49.42%   -41.34%   -44.99%   -19.39%  -51.55%  -67.61%   -56.92%  -36.82%
SubVW/words=10/data=shortcut        -56.85%   -47.88%  -50.92%   -42.76%   -45.67%   -23.60%  -53.04%  -69.34%   -60.18%  -39.43%
SubVW/words=16/data=shortcut        -62.36%   -54.83%  -58.80%   -55.83%   -53.74%   -41.04%  -60.16%  -76.75%   -60.56%  -48.63%
SubVW/words=32/data=shortcut        -73.68%   -68.64%  -71.57%   -33.52%   -37.34%   -64.73%  -72.67%  -85.89%   -71.87%  -64.56%
SubVW/words=64/data=shortcut        -56.68%   -51.66%  -52.56%   -34.75%   -37.54%   -80.30%  -83.58%  -92.39%   -83.41%  -78.70%
SubVW/words=100/data=shortcut       -56.68%   -50.97%  -51.57%   -33.68%   -36.78%   -87.42%  -88.53%  -94.84%   -88.87%  -84.96%
SubVW/words=1000/data=shortcut      -56.68%   -50.89%  -52.10%   -34.94%   -37.77%   -98.59%  -98.71%  -99.43%   -98.80%  -98.20%
SubVW/words=10000/data=shortcut     -56.68%   -51.00%  -52.44%   -33.65%   -37.27%   -99.86%  -99.87%  -99.94%   -99.88%  -99.90%
SubVW/words=100000/data=shortcut    -56.68%   -50.80%  -52.20%   -34.79%   -37.46%   -99.99%  -99.99%  -99.99%   -99.99%  -99.99%

AddVW/words=1/data=carry             -0.51%    -5.29%  -24.03%   -26.48%         ~         ~  -33.14%  -30.23%         ~  -20.74%
AddVW/words=2/data=carry             -6.36%         ~  -21.05%   -39.40%         ~   +10.72%  -29.12%  -31.34%         ~  -17.29%
AddVW/words=3/data=carry                  ~         ~  -17.46%   -19.53%   +17.58%         ~  -26.23%  -23.61%    +7.80%  -14.34%
AddVW/words=4/data=carry            +19.02%   +16.80%        ~         ~   +28.25%         ~  -27.90%  -20.31%   +19.16%        ~
AddVW/words=5/data=carry             +3.97%   +53.02%        ~         ~   +11.31%         ~  -19.05%  -17.47%   +16.81%        ~
AddVW/words=6/data=carry             +2.98%   +19.83%        ~         ~   +14.84%         ~  -18.48%  -14.92%   +18.25%        ~
AddVW/words=7/data=carry                  ~         ~        ~         ~   +27.17%         ~  -15.50%  -12.74%   +13.00%        ~
AddVW/words=8/data=carry             +0.58%   +22.32%        ~    +6.10%   +29.63%         ~  -13.04%        ~   +28.46%   +2.95%
AddVW/words=9/data=carry                  ~   +31.53%        ~         ~   +14.42%         ~  -11.32%        ~   +18.37%   +3.28%
AddVW/words=10/data=carry            +3.94%   +22.36%        ~    +6.29%   +19.22%         ~  -11.27%        ~   +20.10%   +3.91%
AddVW/words=16/data=carry            +2.82%   +14.23%        ~   +10.06%   +25.91%   -16.12%        ~        ~   +52.28%  +10.40%
AddVW/words=32/data=carry                 ~   +25.35%  +13.66%         ~   +34.89%   -34.39%   +6.51%  -18.71%   +41.06%  +19.42%
AddVW/words=64/data=carry           -42.03%         ~  -39.70%    +6.65%   +32.29%   -39.94%  +14.34%        ~   +19.68%  +20.86%
AddVW/words=100/data=carry          -33.95%   -34.28%  -39.65%         ~   +27.72%   -26.80%  +17.40%        ~   +26.39%  +23.32%
AddVW/words=1000/data=carry         -42.49%   -47.87%  -47.44%    +1.25%    +4.25%   -41.76%  +23.40%        ~   +25.48%  +27.99%
AddVW/words=10000/data=carry        -41.85%   -48.49%  -49.43%         ~         ~   -42.09%  +24.61%  -10.32%   +40.55%  +18.35%
AddVW/words=100000/data=carry       -28.18%   -48.13%  -48.24%    +1.35%         ~   -42.90%  +24.73%   -9.79%   +22.55%  +17.16%

SubVW/words=1/data=carry            -10.32%   -17.16%  -24.14%   -26.24%         ~   +18.43%  -34.10%  -29.54%    -9.57%        ~
SubVW/words=2/data=carry            -19.45%   -23.31%  -20.74%   -39.73%         ~   +15.74%  -28.13%  -30.21%         ~  -18.74%
SubVW/words=3/data=carry                  ~   -16.18%  -15.34%   -19.54%   +17.62%   +12.39%  -27.64%  -27.09%         ~  -14.97%
SubVW/words=4/data=carry            +11.67%   +24.42%        ~         ~   +25.11%   +14.07%  -28.08%  -26.18%         ~        ~
SubVW/words=5/data=carry             +8.08%   +25.64%        ~         ~   +10.35%    +8.12%  -21.75%  -25.50%         ~   -4.86%
SubVW/words=6/data=carry                  ~   +13.82%        ~         ~   +12.92%    +6.79%  -20.25%  -24.70%         ~   -2.74%
SubVW/words=7/data=carry                  ~         ~   +8.29%    +4.51%   +26.59%    +4.62%  -18.01%  -24.09%         ~   -1.26%
SubVW/words=8/data=carry                  ~   +23.16%  +16.19%    +6.16%   +25.46%    +6.74%  -15.57%  -22.74%         ~   +1.44%
SubVW/words=9/data=carry                  ~   +30.71%  +20.81%         ~   +12.36%         ~  -12.99%        ~         ~   +3.13%
SubVW/words=10/data=carry            +5.03%   +19.53%  +14.84%   +14.16%   +16.12%         ~  -11.64%  -16.00%   +15.45%   +3.29%
SubVW/words=16/data=carry           +14.42%   +15.58%  +33.07%   +11.43%   +24.65%         ~        ~  -21.90%   +25.59%   +9.40%
SubVW/words=32/data=carry                 ~   +27.57%  +46.58%         ~   +35.35%    -8.49%        ~  -24.04%   +11.86%  +18.40%
SubVW/words=64/data=carry           -24.34%   -27.83%  -20.90%   +13.34%   +37.17%   -14.90%        ~   -8.81%   +12.88%  +18.92%
SubVW/words=100/data=carry          -25.19%   -34.70%  -27.45%   +12.86%   +28.42%   -14.48%        ~        ~   +25.71%  +21.93%
SubVW/words=1000/data=carry         -24.93%   -47.86%  -47.26%    +2.66%         ~   -23.88%        ~        ~   +25.99%  +27.81%
SubVW/words=10000/data=carry        -24.17%   -36.48%  -49.41%    +1.06%         ~   -25.06%        ~  -26.50%   +27.94%  +18.36%
SubVW/words=100000/data=carry       -22.51%   -35.86%  -49.46%    +3.96%         ~   -25.18%        ~  -22.15%   +26.86%  +15.44%

Change-Id: I8f252073040e674780ac6ec9912082fb205329dd
Reviewed-on: https://go-review.googlesource.com/c/go/+/664898
Reviewed-by: Alan Donovan <adonovan@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
 		2025-04-18 15:07:59 -07:00
.github .github: update language change proposal template 2024-08-08 19:02:29 +00:00
api unicode: add CategoryAliases, Cn, LC 2025-04-18 14:13:31 -07:00
doc regexp/syntax: recognize category aliases like \p{Letter} 2025-04-18 14:13:38 -07:00
lib lib/time: build with Ubuntu backward compatibility options 2025-02-06 17:10:15 -08:00
misc misc/linkcheck: remove unused tool 2025-03-20 04:38:55 -07:00
src math/big: replace addVW/subVW assembly with fast pure Go 2025-04-18 15:07:59 -07:00
test cmd/compile: set unalignedOK to make memcombine work properly on loong64 2025-04-09 09:18:20 -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
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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
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README.md

The Go Programming Language

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

Gopher image Gopher image by Renee French, licensed under Creative Commons 4.0 Attribution license.

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.