Add an optimization for addVW and subVW over large-sized vectors, it switches
from add/sub with carry to copy the rest of the vector when we are done with
carries. Consistent performance improvement are observed on various arm64
machines.

Add additional tests and benchmarks to increase the test coverage.
TestFunVWExt:
  Testing with various types of input vector, using the result from go-version
  addVW/subVW as golden reference.
BenchmarkAddVWext and BenchmarkSubVWext:
  Benchmarking using input vector having all 1s or all 0s, for evaluating the
  overhead of worst case.

1. Perf. comparison over randomly generated input vectors:

Server 1:
name             old time/op    new time/op    delta
AddVW/1            12.3ns ± 3%    12.0ns ± 0%    -2.60%  (p=0.001 n=10+8)
AddVW/2            12.5ns ± 2%    12.3ns ± 0%    -1.84%  (p=0.001 n=10+8)
AddVW/3            12.6ns ± 2%    12.3ns ± 0%    -1.91%  (p=0.009 n=10+10)
AddVW/4            13.1ns ± 3%    12.7ns ± 0%    -2.98%  (p=0.006 n=10+8)
AddVW/5            14.4ns ± 1%    13.9ns ± 0%    -3.81%  (p=0.000 n=10+10)
AddVW/10           11.7ns ± 0%    11.7ns ± 0%      ~     (all equal)
AddVW/100          47.8ns ± 0%    29.9ns ± 2%   -37.38%  (p=0.000 n=10+9)
AddVW/1000          446ns ± 0%     207ns ± 0%   -53.59%  (p=0.000 n=10+10)
AddVW/10000        4.35µs ± 1%    2.92µs ± 0%   -32.85%  (p=0.000 n=10+10)
AddVW/100000       43.6µs ± 0%    29.7µs ± 0%   -31.92%  (p=0.000 n=8+10)
SubVW/1            12.6ns ± 0%    12.3ns ± 2%    -2.22%  (p=0.000 n=7+10)
SubVW/2            12.7ns ± 0%    12.6ns ± 1%    -0.39%  (p=0.046 n=8+10)
SubVW/3            12.7ns ± 1%    12.6ns ± 1%      ~     (p=0.410 n=10+10)
SubVW/4            13.3ns ± 3%    13.1ns ± 3%      ~     (p=0.072 n=10+10)
SubVW/5            14.2ns ± 0%    14.1ns ± 1%    -0.63%  (p=0.046 n=8+10)
SubVW/10           11.7ns ± 0%    11.7ns ± 0%      ~     (all equal)
SubVW/100          47.8ns ± 0%    33.1ns ±19%   -30.71%  (p=0.000 n=10+10)
SubVW/1000          446ns ± 0%     207ns ± 0%   -53.59%  (p=0.000 n=10+10)
SubVW/10000        4.33µs ± 1%    2.92µs ± 0%   -32.66%  (p=0.000 n=10+6)
SubVW/100000       43.4µs ± 0%    29.6µs ± 0%   -31.90%  (p=0.000 n=10+9)

Server 2:
name             old time/op    new time/op    delta
AddVW/1            5.49ns ± 0%    5.53ns ± 2%     ~     (p=1.000 n=9+10)
AddVW/2            5.96ns ± 2%    5.92ns ± 1%   -0.69%  (p=0.039 n=10+10)
AddVW/3            6.72ns ± 0%    6.73ns ± 0%     ~     (p=0.078 n=10+10)
AddVW/4            7.07ns ± 0%    6.75ns ± 2%   -4.55%  (p=0.000 n=10+10)
AddVW/5            8.14ns ± 0%    8.17ns ± 0%   +0.46%  (p=0.003 n=8+8)
AddVW/10           10.0ns ± 0%    10.1ns ± 1%   +0.70%  (p=0.003 n=10+10)
AddVW/100          43.0ns ± 0%    33.5ns ± 0%  -22.09%  (p=0.000 n=9+9)
AddVW/1000          394ns ± 0%     278ns ± 0%  -29.44%  (p=0.000 n=10+10)
AddVW/10000        4.18µs ± 0%    3.14µs ± 0%  -24.81%  (p=0.000 n=8+8)
AddVW/100000       68.3µs ± 3%    62.1µs ± 5%   -9.13%  (p=0.000 n=10+10)
SubVW/1            5.37ns ± 2%    5.42ns ± 1%     ~     (p=0.990 n=10+10)
SubVW/2            5.89ns ± 0%    5.92ns ± 1%   +0.58%  (p=0.000 n=8+10)
SubVW/3            6.64ns ± 1%    6.82ns ± 3%   +2.63%  (p=0.000 n=9+10)
SubVW/4            7.17ns ± 0%    6.69ns ± 2%   -6.74%  (p=0.000 n=10+9)
SubVW/5            8.22ns ± 0%    8.18ns ± 0%   -0.46%  (p=0.001 n=8+9)
SubVW/10           10.0ns ± 1%    10.1ns ± 1%     ~     (p=0.341 n=10+10)
SubVW/100          43.0ns ± 0%    33.5ns ± 0%  -22.09%  (p=0.000 n=7+10)
SubVW/1000          394ns ± 0%     278ns ± 0%  -29.44%  (p=0.000 n=10+10)
SubVW/10000        4.18µs ± 0%    3.15µs ± 0%  -24.62%  (p=0.000 n=9+9)
SubVW/100000       67.7µs ± 4%    62.4µs ± 2%   -7.92%  (p=0.000 n=10+10)

2. Perf. comparison over input vectors of all 1s or all 0s

Server 1:
name             old time/op    new time/op    delta
AddVWext/1         12.6ns ± 0%    12.0ns ± 0%    -4.76%  (p=0.000 n=6+10)
AddVWext/2         12.7ns ± 0%    12.4ns ± 1%    -2.52%  (p=0.000 n=10+10)
AddVWext/3         12.7ns ± 0%    12.4ns ± 0%    -2.36%  (p=0.000 n=9+7)
AddVWext/4         13.2ns ± 4%    12.7ns ± 0%    -3.71%  (p=0.001 n=10+9)
AddVWext/5         14.6ns ± 0%    13.9ns ± 0%    -4.79%  (p=0.000 n=10+8)
AddVWext/10        11.7ns ± 0%    11.7ns ± 0%      ~     (all equal)
AddVWext/100       47.8ns ± 0%    47.4ns ± 0%    -0.84%  (p=0.000 n=10+10)
AddVWext/1000       446ns ± 0%     399ns ± 0%   -10.54%  (p=0.000 n=10+10)
AddVWext/10000     4.34µs ± 1%    3.90µs ± 0%   -10.12%  (p=0.000 n=10+10)
AddVWext/100000    43.9µs ± 1%    39.4µs ± 0%   -10.18%  (p=0.000 n=10+10)
SubVWext/1         12.6ns ± 0%    12.3ns ± 2%    -2.70%  (p=0.000 n=7+10)
SubVWext/2         12.6ns ± 1%    12.6ns ± 2%      ~     (p=0.234 n=10+10)
SubVWext/3         12.7ns ± 0%    12.6ns ± 2%    -0.71%  (p=0.033 n=10+10)
SubVWext/4         13.4ns ± 0%    13.1ns ± 3%    -2.01%  (p=0.006 n=8+10)
SubVWext/5         14.2ns ± 0%    14.1ns ± 1%    -0.85%  (p=0.003 n=10+10)
SubVWext/10        11.7ns ± 0%    11.7ns ± 0%      ~     (all equal)
SubVWext/100       47.8ns ± 0%    47.4ns ± 0%    -0.84%  (p=0.000 n=10+10)
SubVWext/1000       446ns ± 0%     399ns ± 0%   -10.54%  (p=0.000 n=10+10)
SubVWext/10000     4.33µs ± 1%    3.90µs ± 0%   -10.02%  (p=0.000 n=10+10)
SubVWext/100000    43.5µs ± 0%    39.5µs ± 1%    -9.16%  (p=0.000 n=7+10)

Server 2:
name             old time/op    new time/op    delta
AddVWext/1         5.48ns ± 0%    5.43ns ± 1%   -0.97%  (p=0.000 n=9+9)
AddVWext/2         5.99ns ± 2%    5.93ns ± 1%     ~     (p=0.054 n=10+10)
AddVWext/3         6.74ns ± 0%    6.79ns ± 1%   +0.80%  (p=0.000 n=9+10)
AddVWext/4         7.18ns ± 0%    7.21ns ± 1%   +0.36%  (p=0.034 n=9+10)
AddVWext/5         7.93ns ± 3%    8.18ns ± 0%   +3.18%  (p=0.000 n=10+8)
AddVWext/10        10.0ns ± 0%    10.1ns ± 1%   +0.60%  (p=0.011 n=10+10)
AddVWext/100       43.0ns ± 0%    47.7ns ± 0%  +10.93%  (p=0.000 n=9+10)
AddVWext/1000       394ns ± 0%     399ns ± 0%   +1.27%  (p=0.000 n=10+10)
AddVWext/10000     4.18µs ± 0%    4.50µs ± 0%   +7.73%  (p=0.000 n=9+10)
AddVWext/100000    67.6µs ± 2%    68.4µs ± 3%     ~     (p=0.139 n=9+8)
SubVWext/1         5.46ns ± 1%    5.43ns ± 0%   -0.55%  (p=0.002 n=9+9)
SubVWext/2         5.89ns ± 0%    5.93ns ± 1%   +0.68%  (p=0.000 n=8+10)
SubVWext/3         6.72ns ± 1%    6.79ns ± 1%   +1.07%  (p=0.000 n=10+10)
SubVWext/4         6.98ns ± 1%    7.21ns ± 0%   +3.25%  (p=0.000 n=10+10)
SubVWext/5         8.22ns ± 0%    7.99ns ± 3%   -2.83%  (p=0.000 n=8+10)
SubVWext/10        10.0ns ± 1%    10.1ns ± 1%     ~     (p=0.239 n=10+10)
SubVWext/100       43.0ns ± 0%    47.7ns ± 0%  +10.93%  (p=0.000 n=8+10)
SubVWext/1000       394ns ± 0%     399ns ± 0%   +1.27%  (p=0.000 n=10+10)
SubVWext/10000     4.18µs ± 0%    4.51µs ± 0%   +7.86%  (p=0.000 n=8+8)
SubVWext/100000    68.3µs ± 2%    68.0µs ± 3%     ~     (p=0.515 n=10+8)

Change-Id: I134a5194b8a2deaaebbaa2b771baf72846971d58
Reviewed-on: https://go-review.googlesource.com/c/go/+/229739
Reviewed-by: Cherry Zhang <cherryyz@google.com>
Reviewed-by: Robert Griesemer <gri@golang.org>
Run-TryBot: Cherry Zhang <cherryyz@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>

Change-Id: I9ff5d1767cf70648c2251268e5e815944a7cb371
Reviewed-on: https://go-review.googlesource.com/c/go/+/233737
Run-TryBot: Emmanuel Odeke <emm.odeke@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>

While reading the source code of the math/big package, I found the SetString function example of float type missing.

Change-Id: Id8c16a58e2e24f9463e8ff38adbc98f8c418ab26
Reviewed-on: https://go-review.googlesource.com/c/go/+/232804
Run-TryBot: Ian Lance Taylor <iant@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>

Don't overwrite incoming test data.

The change uses copy instead of assigning statement to avoid this.

Change-Id: Ib907101822d811de5c45145cb9d7961907e212c3
Reviewed-on: https://go-review.googlesource.com/c/go/+/250137
Run-TryBot: Emmanuel Odeke <emm.odeke@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>

This changes the assembly implementation on ppc64x
to improve performance by reordering some instructions.
It also eliminates an unnecessary move by changing an
ADDZE to use the correct target register.

Improvement on power9:

MulAddVWW/1         6.89ns ± 0%    7.30ns ± 0%   +5.95%  (p=1.000 n=1+1)
MulAddVWW/2         8.04ns ± 0%    8.06ns ± 0%   +0.25%  (p=1.000 n=1+1)
MulAddVWW/3         9.39ns ± 0%    9.39ns ± 0%     ~     (all equal)
MulAddVWW/4         9.76ns ± 0%    9.48ns ± 0%   -2.87%  (p=1.000 n=1+1)
MulAddVWW/5         10.5ns ± 0%    10.3ns ± 0%   -1.90%  (p=1.000 n=1+1)
MulAddVWW/10        15.4ns ± 0%    14.9ns ± 0%   -3.25%  (p=1.000 n=1+1)
MulAddVWW/100        149ns ± 0%     125ns ± 0%  -16.11%  (p=1.000 n=1+1)
MulAddVWW/1000      1.42µs ± 0%    1.28µs ± 0%   -9.74%  (p=1.000 n=1+1)
MulAddVWW/10000     14.2µs ± 0%    12.8µs ± 0%   -9.73%  (p=1.000 n=1+1)
MulAddVWW/100000     144µs ± 0%     129µs ± 0%  -10.10%  (p=1.000 n=1+1)

Change-Id: I0ae7002a69783ca19d7a4e3e42042ae75dc60069
Reviewed-on: https://go-review.googlesource.com/c/go/+/248721
Run-TryBot: Lynn Boger <laboger@linux.vnet.ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Carlos Eduardo Seo <cseo@linux.vnet.ibm.com>
Reviewed-by: Paul Murphy <murp@ibm.com>

Simplifying some code without compromising performance.
My CPU is Intel Xeon Gold 6161, 2.20GHz, 64-bit operating system.
The memory is 8GB. This is my test environment, I hope to help you judge.

Benchmark:

name      old time/op    new time/op    delta
Log1p-4    21.8ns ± 5%    21.8ns ± 4%   ~     (p=0.973 n=20+20)

Change-Id: Icd8f96f1325b00007602d114300b92d4c57de409
Reviewed-on: https://go-review.googlesource.com/c/go/+/233940
Reviewed-by: Robert Griesemer <gri@golang.org>

Change-Id: Ie5fd026af45d2e7bc371a38d15dbb52a1b4958cd
Reviewed-on: https://go-review.googlesource.com/c/go/+/235717
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

Updates #38850

Change-Id: I33f48762f5520eb0c0a841d8ca1ccdd65ecc20c8
Reviewed-on: https://go-review.googlesource.com/c/go/+/234583
Run-TryBot: Bryan C. Mills <bcmills@google.com>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>

Replaced almost every use of Bytes with FillBytes.

Note that the approved proposal was for

    func (*Int) FillBytes(buf []byte)

while this implements

    func (*Int) FillBytes(buf []byte) []byte

because the latter was far nicer to use in all callsites.

Fixes #35833

Change-Id: Ia912df123e5d79b763845312ea3d9a8051343c0a
Reviewed-on: https://go-review.googlesource.com/c/go/+/230397
Reviewed-by: Robert Griesemer <gri@golang.org>

Change-Id: If34422859d47bc8f44974a00c6b7908e7655ff41
Reviewed-on: https://go-review.googlesource.com/c/go/+/223561
Reviewed-by: Cherry Zhang <cherryyz@google.com>