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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>
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Also fix a few real but currently harmless bugs from CL 664895.
There were a few places that were still wrong if z != x or if a != 0.
Change-Id: Id8971e2505523bc4708780c82bf998a546f4f081
Reviewed-on: https://go-review.googlesource.com/c/go/+/664897
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Alan Donovan <adonovan@google.com>
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It is annoying that non-x86 implementations of shlVU and shrVU
have to go out of their way to handle the trivial case shift==0
with their own copy loops. Instead, arrange to never call them
with shift==0, so that the code can be removed.
Unfortunately, there are linknames of shlVU, so we cannot
change that function. But we can rename the functions and
then leave behind a shlVU wrapper, so do that.
Since the big.Int API calls the operations Lsh and Rsh, rename
shlVU/shrVU to lshVU/rshVU. Also rename various other shl/shr
methods and functions to lsh/rsh.
Change-Id: Ieaf54e0110a298730aa3e4566ce5be57ba7fc121
Reviewed-on: https://go-review.googlesource.com/c/go/+/664896
Reviewed-by: Alan Donovan <adonovan@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
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addMulVVW is an unnecessarily special case.
All other assembly routines taking []Word (V as in vector) arguments
take separate source and destination. For example:
addVV: z = x+y
mulAddVWW: z = x*m+a
addMulVVW uses the z parameter as both destination and source:
addMulVVW: z = z+x*m
Even looking at the signatures is confusing: all the VV routines take
two input vectors x and y, but addMulVVW takes only x: where is y?
(The answer is that the two inputs are z and x.)
It would be nice to fix this, both for understandability and regularity,
and to simplify a future assembly generator.
We cannot remove or redefine addMulVVW, because it has been used
in linknames. Instead, the CL adds a new final addend argument ‘a’
like in mulAddVWW, making the natural name addMulVVWW
(two input vectors, two input words):
addMulVVWW: z = x+y*m+a
This CL updates all the assembly implementations to rename the
inputs z, x, y -> x, y, m, and then introduces a separate destination z.
Change-Id: Ib76c80b53f6d1f4a901f663566e9c4764bb20488
Reviewed-on: https://go-review.googlesource.com/c/go/+/664895
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Alan Donovan <adonovan@google.com>
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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>
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Montgomery multiplication can be used for Exp mod even m
by splitting it into two steps - Exp mod an odd number and
Exp mod a power of two - and then combining the two results
using the Chinese Remainder Theorem.
For more details, see Ç. K. Koç, “Montgomery Reduction with Even Modulus”,
IEE Proceedings: Computers and Digital Techniques, 141(5) 314-316, September 1994.
http://www.people.vcu.edu/~jwang3/CMSC691/j34monex.pdf
Thanks to Guido Vranken for suggesting that we use a faster algorithm.
name old time/op new time/op delta
ExpMont/Odd-16 240µs ± 2% 239µs ± 2% ~ (p=0.853 n=10+10)
ExpMont/Even1-16 757µs ± 3% 249µs ± 6% -67.17% (p=0.000 n=10+10)
ExpMont/Even2-16 755µs ± 1% 244µs ± 4% -67.64% (p=0.000 n=8+10)
ExpMont/Even3-16 771µs ± 3% 240µs ± 2% -68.90% (p=0.000 n=10+10)
ExpMont/Even4-16 775µs ± 3% 241µs ± 2% -68.91% (p=0.000 n=10+10)
ExpMont/Even8-16 779µs ± 2% 241µs ± 3% -69.06% (p=0.000 n=9+10)
ExpMont/Even32-16 778µs ± 3% 240µs ± 4% -69.11% (p=0.000 n=9+9)
ExpMont/Even64-16 774µs ± 6% 186µs ± 2% -76.00% (p=0.000 n=10+10)
ExpMont/Even96-16 776µs ± 4% 186µs ± 6% -76.09% (p=0.000 n=9+10)
ExpMont/Even128-16 764µs ± 2% 143µs ± 3% -81.24% (p=0.000 n=10+10)
ExpMont/Even255-16 761µs ± 3% 109µs ± 2% -85.73% (p=0.000 n=10+10)
ExpMont/SmallEven1-16 45.6µs ± 1% 36.3µs ± 3% -20.49% (p=0.000 n=9+10)
ExpMont/SmallEven2-16 44.3µs ± 2% 37.5µs ± 2% -15.26% (p=0.000 n=9+10)
ExpMont/SmallEven3-16 44.1µs ± 5% 37.3µs ± 3% -15.32% (p=0.000 n=9+10)
ExpMont/SmallEven4-16 47.1µs ± 6% 38.0µs ± 5% -19.40% (p=0.000 n=10+9)
name old alloc/op new alloc/op delta
ExpMont/Odd-16 2.53kB ± 0% 2.53kB ± 0% ~ (p=0.137 n=8+10)
ExpMont/Even1-16 2.57kB ± 0% 3.31kB ± 0% +28.90% (p=0.000 n=8+10)
ExpMont/Even2-16 2.57kB ± 0% 3.37kB ± 0% +31.09% (p=0.000 n=9+10)
ExpMont/Even3-16 2.57kB ± 0% 3.37kB ± 0% +31.08% (p=0.000 n=8+8)
ExpMont/Even4-16 2.57kB ± 0% 3.37kB ± 0% +31.09% (p=0.000 n=9+10)
ExpMont/Even8-16 2.57kB ± 0% 3.37kB ± 0% +31.09% (p=0.000 n=9+10)
ExpMont/Even32-16 2.57kB ± 0% 3.37kB ± 0% +31.14% (p=0.000 n=10+10)
ExpMont/Even64-16 2.57kB ± 0% 3.16kB ± 0% +22.99% (p=0.000 n=9+9)
ExpMont/Even96-16 2.57kB ± 0% 3.44kB ± 0% +33.90% (p=0.000 n=10+8)
ExpMont/Even128-16 2.57kB ± 0% 2.88kB ± 0% +12.10% (p=0.000 n=10+10)
ExpMont/Even255-16 2.57kB ± 0% 2.54kB ± 0% -1.30% (p=0.000 n=9+10)
ExpMont/SmallEven1-16 872B ± 0% 1232B ± 0% +41.28% (p=0.000 n=10+10)
ExpMont/SmallEven2-16 872B ± 0% 1233B ± 0% +41.40% (p=0.000 n=10+9)
ExpMont/SmallEven3-16 872B ± 0% 1289B ± 0% +47.82% (p=0.000 n=10+10)
ExpMont/SmallEven4-16 872B ± 0% 1241B ± 0% +42.32% (p=0.000 n=10+10)
name old allocs/op new allocs/op delta
ExpMont/Odd-16 21.0 ± 0% 21.0 ± 0% ~ (all equal)
ExpMont/Even1-16 24.0 ± 0% 38.0 ± 0% +58.33% (p=0.000 n=10+10)
ExpMont/Even2-16 24.0 ± 0% 40.0 ± 0% +66.67% (p=0.000 n=10+10)
ExpMont/Even3-16 24.0 ± 0% 40.0 ± 0% +66.67% (p=0.000 n=10+10)
ExpMont/Even4-16 24.0 ± 0% 40.0 ± 0% +66.67% (p=0.000 n=10+10)
ExpMont/Even8-16 24.0 ± 0% 40.0 ± 0% +66.67% (p=0.000 n=10+10)
ExpMont/Even32-16 24.0 ± 0% 40.0 ± 0% +66.67% (p=0.000 n=10+10)
ExpMont/Even64-16 24.0 ± 0% 39.0 ± 0% +62.50% (p=0.000 n=10+10)
ExpMont/Even96-16 24.0 ± 0% 42.0 ± 0% +75.00% (p=0.000 n=10+10)
ExpMont/Even128-16 24.0 ± 0% 40.0 ± 0% +66.67% (p=0.000 n=10+10)
ExpMont/Even255-16 24.0 ± 0% 38.0 ± 0% +58.33% (p=0.000 n=10+10)
ExpMont/SmallEven1-16 16.0 ± 0% 35.0 ± 0% +118.75% (p=0.000 n=10+10)
ExpMont/SmallEven2-16 16.0 ± 0% 35.0 ± 0% +118.75% (p=0.000 n=10+10)
ExpMont/SmallEven3-16 16.0 ± 0% 37.0 ± 0% +131.25% (p=0.000 n=10+10)
ExpMont/SmallEven4-16 16.0 ± 0% 36.0 ± 0% +125.00% (p=0.000 n=10+10)
Change-Id: Ib7f70290f8f087b78805ec3120baf17dd7737ac3
Reviewed-on: https://go-review.googlesource.com/c/go/+/420897
Run-TryBot: Russ Cox <rsc@golang.org>
Reviewed-by: Roland Shoemaker <roland@golang.org>
Auto-Submit: Russ Cox <rsc@golang.org>
TryBot-Result: Gopher Robot <gobot@golang.org>
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Now gc can generate the same assembly code.
Change-Id: Iac503003e14045d63e2def66408c13cee516aa37
Reviewed-on: https://go-review.googlesource.com/c/go/+/402575
TryBot-Result: Gopher Robot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
Reviewed-by: Dmitri Shuralyov <dmitshur@google.com>
Run-TryBot: Wayne Zuo <wdvxdr@golangcn.org>
Auto-Submit: Keith Randall <khr@golang.org>
Reviewed-by: Keith Randall <khr@google.com>
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For whatever reason (perhaps some tool does this), a handful of comments,
including some doc comments, have TODOs formatted like:
// TODO(name): Text here and
// more text aligned
// under first text.
In doc comments the second line turns into a <pre> block,
which is undesirable in this context.
Rewrite those to unindent, like this instead:
// TODO(name): Text here and
// more text aligned
// at left column.
For #51082.
Change-Id: Ibf5145659a61ebf9496f016752a709a7656d2d4b
Reviewed-on: https://go-review.googlesource.com/c/go/+/384258
Trust: Russ Cox <rsc@golang.org>
Run-TryBot: Russ Cox <rsc@golang.org>
Reviewed-by: Ian Lance Taylor <iant@golang.org>
TryBot-Result: Gopher Robot <gobot@golang.org>
|
|
Change-Id: Id67d6ac856bd9271de99c3381bde910aa0c166e0
Reviewed-on: https://go-review.googlesource.com/c/go/+/296011
Trust: Josh Bleecher Snyder <josharian@gmail.com>
Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com>
TryBot-Result: Go Bot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
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The s390x assembly for shlVU does a forward copy when the shift amount s
is 0. This causes corruption of the result z when z is aliased to the
input x.
This fix removes the s390x assembly for both shlVU and shrVU so the pure
go implementations will be used.
Test cases have been added to the existing TestShiftOverlap test to
cover shift values of 0, 1 and (_W - 1).
Fixes #42838
Change-Id: I75ca0e98f3acfaa6366a26355dcd9dd82499a48b
Reviewed-on: https://go-review.googlesource.com/c/go/+/274442
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Go Bot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
Reviewed-by: Matthew Dempsky <mdempsky@google.com>
Trust: Robert Griesemer <gri@golang.org>
|
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Division is much slower than multiplication. And the method of using
multiplication by multiplying reciprocal and replacing division with it
can increase the speed of divWVW algorithm by three times,and at the
same time increase the speed of nats division.
The benchmark test on arm64 is as follows:
name old time/op new time/op delta
DivWVW/1-4 13.1ns ± 4% 13.3ns ± 4% ~ (p=0.444 n=5+5)
DivWVW/2-4 48.6ns ± 1% 51.2ns ± 2% +5.39% (p=0.008 n=5+5)
DivWVW/3-4 82.0ns ± 1% 69.7ns ± 1% -15.03% (p=0.008 n=5+5)
DivWVW/4-4 116ns ± 1% 71ns ± 2% -38.88% (p=0.008 n=5+5)
DivWVW/5-4 152ns ± 1% 84ns ± 4% -44.70% (p=0.008 n=5+5)
DivWVW/10-4 319ns ± 1% 155ns ± 4% -51.50% (p=0.008 n=5+5)
DivWVW/100-4 3.44µs ± 3% 1.30µs ± 8% -62.30% (p=0.008 n=5+5)
DivWVW/1000-4 33.8µs ± 0% 10.9µs ± 1% -67.74% (p=0.008 n=5+5)
DivWVW/10000-4 343µs ± 4% 111µs ± 5% -67.63% (p=0.008 n=5+5)
DivWVW/100000-4 3.35ms ± 1% 1.25ms ± 3% -62.79% (p=0.008 n=5+5)
QuoRem-4 3.08µs ± 2% 2.21µs ± 4% -28.40% (p=0.008 n=5+5)
ModSqrt225_Tonelli-4 444µs ± 2% 457µs ± 3% ~ (p=0.095 n=5+5)
ModSqrt225_3Mod4-4 136µs ± 1% 138µs ± 3% ~ (p=0.151 n=5+5)
ModSqrt231_Tonelli-4 473µs ± 3% 483µs ± 4% ~ (p=0.548 n=5+5)
ModSqrt231_5Mod8-4 164µs ± 9% 169µs ±12% ~ (p=0.421 n=5+5)
Sqrt-4 36.8µs ± 1% 28.6µs ± 0% -22.17% (p=0.016 n=5+4)
Div/20/10-4 50.0ns ± 3% 51.3ns ± 6% ~ (p=0.238 n=5+5)
Div/40/20-4 49.8ns ± 2% 51.3ns ± 6% ~ (p=0.222 n=5+5)
Div/100/50-4 85.8ns ± 4% 86.5ns ± 5% ~ (p=0.246 n=5+5)
Div/200/100-4 335ns ± 3% 296ns ± 2% -11.60% (p=0.008 n=5+5)
Div/400/200-4 442ns ± 2% 359ns ± 5% -18.81% (p=0.008 n=5+5)
Div/1000/500-4 858ns ± 3% 643ns ± 6% -25.06% (p=0.008 n=5+5)
Div/2000/1000-4 1.70µs ± 3% 1.28µs ± 4% -24.80% (p=0.008 n=5+5)
Div/20000/10000-4 45.0µs ± 5% 41.8µs ± 4% -7.17% (p=0.016 n=5+5)
Div/200000/100000-4 1.51ms ± 7% 1.43ms ± 3% -5.42% (p=0.016 n=5+5)
Div/2000000/1000000-4 57.6ms ± 4% 57.5ms ± 3% ~ (p=1.000 n=5+5)
Div/20000000/10000000-4 2.08s ± 3% 2.04s ± 1% ~ (p=0.095 n=5+5)
name old speed new speed delta
DivWVW/1-4 4.87GB/s ± 4% 4.80GB/s ± 4% ~ (p=0.310 n=5+5)
DivWVW/2-4 2.63GB/s ± 1% 2.50GB/s ± 2% -5.07% (p=0.008 n=5+5)
DivWVW/3-4 2.34GB/s ± 1% 2.76GB/s ± 1% +17.70% (p=0.008 n=5+5)
DivWVW/4-4 2.21GB/s ± 1% 3.61GB/s ± 2% +63.42% (p=0.008 n=5+5)
DivWVW/5-4 2.10GB/s ± 2% 3.81GB/s ± 4% +80.89% (p=0.008 n=5+5)
DivWVW/10-4 2.01GB/s ± 0% 4.13GB/s ± 4% +105.91% (p=0.008 n=5+5)
DivWVW/100-4 1.86GB/s ± 2% 4.95GB/s ± 7% +165.63% (p=0.008 n=5+5)
DivWVW/1000-4 1.89GB/s ± 0% 5.86GB/s ± 1% +209.96% (p=0.008 n=5+5)
DivWVW/10000-4 1.87GB/s ± 4% 5.76GB/s ± 5% +208.96% (p=0.008 n=5+5)
DivWVW/100000-4 1.91GB/s ± 1% 5.14GB/s ± 3% +168.85% (p=0.008 n=5+5)
Change-Id: I049f1196562b20800e6ef8a6493fd147f93ad830
Reviewed-on: https://go-review.googlesource.com/c/go/+/250417
Trust: Giovanni Bajo <rasky@develer.com>
Trust: Keith Randall <khr@golang.org>
Run-TryBot: Giovanni Bajo <rasky@develer.com>
TryBot-Result: Go Bot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
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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>
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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>
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For the case where the addresses of parameter z and x of the function
shlVU overlap and the address of z is greater than x, x (input value)
can be polluted during the calculation when the high words of x are
overlapped with the low words of z (output value).
Fixes #31084
Change-Id: I9bb0266a1d7856b8faa9a9b1975d6f57dece0479
Reviewed-on: https://go-review.googlesource.com/c/go/+/169780
Run-TryBot: Cherry Zhang <cherryyz@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Cherry Zhang <cherryyz@google.com>
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Unroll the cycle 4 times to reduce load overhead.
Benchmarks:
name old time/op new time/op delta
MulAddVWW/1-8 15.9ns ± 0% 11.9ns ± 0% -24.92% (p=0.000 n=8+8)
MulAddVWW/2-8 16.1ns ± 0% 13.9ns ± 1% -13.82% (p=0.000 n=8+8)
MulAddVWW/3-8 18.9ns ± 0% 17.3ns ± 0% -8.47% (p=0.000 n=8+8)
MulAddVWW/4-8 21.7ns ± 0% 19.5ns ± 0% -10.14% (p=0.000 n=8+8)
MulAddVWW/5-8 25.1ns ± 0% 22.5ns ± 0% -10.27% (p=0.000 n=8+8)
MulAddVWW/10-8 41.6ns ± 0% 40.0ns ± 0% -3.79% (p=0.000 n=8+8)
MulAddVWW/100-8 368ns ± 0% 363ns ± 0% -1.36% (p=0.000 n=8+8)
MulAddVWW/1000-8 3.52µs ± 0% 3.52µs ± 0% -0.14% (p=0.000 n=8+8)
MulAddVWW/10000-8 35.1µs ± 0% 35.1µs ± 0% -0.01% (p=0.000 n=7+6)
MulAddVWW/100000-8 351µs ± 0% 351µs ± 0% +0.15% (p=0.038 n=8+8)
Change-Id: I052a4db286ac6e4f3293289c7e9a82027da0405e
Reviewed-on: https://go-review.googlesource.com/c/go/+/155780
Run-TryBot: Cherry Zhang <cherryyz@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Cherry Zhang <cherryyz@google.com>
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While we're here, delete addWW_g and subWW_g, per the TODO.
They are now obsolete.
Benchmarks on amd64 with -tags=math_big_pure_go.
name old time/op new time/op delta
AddVV/1-8 5.24ns ± 2% 5.12ns ± 1% -2.11% (p=0.000 n=82+87)
AddVV/2-8 6.44ns ± 1% 6.33ns ± 2% -1.82% (p=0.000 n=77+82)
AddVV/3-8 7.89ns ± 8% 6.97ns ± 4% -11.71% (p=0.000 n=100+96)
AddVV/4-8 8.60ns ± 0% 7.72ns ± 4% -10.24% (p=0.000 n=90+96)
AddVV/5-8 10.3ns ± 4% 8.5ns ± 1% -17.02% (p=0.000 n=96+91)
AddVV/10-8 16.2ns ± 5% 12.8ns ± 1% -21.11% (p=0.000 n=97+86)
AddVV/100-8 148ns ± 1% 117ns ± 5% -21.07% (p=0.000 n=66+98)
AddVV/1000-8 1.41µs ± 4% 1.13µs ± 3% -19.90% (p=0.000 n=97+97)
AddVV/10000-8 14.2µs ± 5% 11.2µs ± 1% -20.82% (p=0.000 n=99+84)
AddVV/100000-8 142µs ± 4% 113µs ± 4% -20.40% (p=0.000 n=91+92)
SubVV/1-8 5.29ns ± 1% 5.11ns ± 0% -3.30% (p=0.000 n=87+88)
SubVV/2-8 6.36ns ± 4% 6.33ns ± 2% -0.56% (p=0.002 n=98+73)
SubVV/3-8 7.58ns ± 5% 6.98ns ± 4% -8.01% (p=0.000 n=97+91)
SubVV/4-8 8.61ns ± 3% 7.98ns ± 2% -7.31% (p=0.000 n=95+83)
SubVV/5-8 10.6ns ± 2% 8.5ns ± 1% -19.56% (p=0.000 n=79+89)
SubVV/10-8 16.3ns ± 4% 12.7ns ± 1% -21.97% (p=0.000 n=98+82)
SubVV/100-8 124ns ± 1% 118ns ± 1% -4.83% (p=0.000 n=85+81)
SubVV/1000-8 1.14µs ± 5% 1.12µs ± 2% -1.17% (p=0.000 n=97+81)
SubVV/10000-8 11.6µs ±10% 11.2µs ± 1% -3.39% (p=0.000 n=100+84)
SubVV/100000-8 114µs ± 6% 114µs ± 5% ~ (p=0.396 n=83+94)
AddVW/1-8 4.04ns ± 4% 4.34ns ± 4% +7.57% (p=0.000 n=96+98)
AddVW/2-8 4.34ns ± 5% 4.40ns ± 5% +1.40% (p=0.000 n=99+98)
AddVW/3-8 5.43ns ± 0% 5.54ns ± 2% +1.97% (p=0.000 n=85+94)
AddVW/4-8 6.23ns ± 1% 6.18ns ± 2% -0.66% (p=0.000 n=77+78)
AddVW/5-8 6.78ns ± 2% 6.90ns ± 4% +1.77% (p=0.000 n=80+99)
AddVW/10-8 10.5ns ± 4% 9.9ns ± 1% -5.77% (p=0.000 n=97+69)
AddVW/100-8 114ns ± 3% 91ns ± 0% -20.38% (p=0.000 n=98+77)
AddVW/1000-8 1.12µs ± 1% 0.87µs ± 1% -22.80% (p=0.000 n=82+68)
AddVW/10000-8 11.2µs ± 2% 8.5µs ± 5% -23.85% (p=0.000 n=85+100)
AddVW/100000-8 112µs ± 2% 85µs ± 5% -24.22% (p=0.000 n=71+96)
SubVW/1-8 4.09ns ± 2% 4.18ns ± 4% +2.32% (p=0.000 n=78+96)
SubVW/2-8 4.59ns ± 5% 4.52ns ± 7% -1.54% (p=0.000 n=98+94)
SubVW/3-8 5.41ns ±10% 5.55ns ± 1% +2.48% (p=0.000 n=100+89)
SubVW/4-8 6.51ns ± 2% 6.19ns ± 0% -4.85% (p=0.000 n=97+81)
SubVW/5-8 7.25ns ± 3% 6.90ns ± 4% -4.93% (p=0.000 n=97+96)
SubVW/10-8 10.6ns ± 4% 9.8ns ± 2% -7.32% (p=0.000 n=95+96)
SubVW/100-8 90.4ns ± 0% 90.8ns ± 0% +0.43% (p=0.000 n=83+78)
SubVW/1000-8 853ns ± 4% 857ns ± 2% +0.42% (p=0.000 n=100+98)
SubVW/10000-8 8.52µs ± 4% 8.53µs ± 2% ~ (p=0.061 n=99+97)
SubVW/100000-8 84.8µs ± 5% 84.2µs ± 2% -0.78% (p=0.000 n=99+93)
AddMulVVW/1-8 8.73ns ± 0% 5.33ns ± 3% -38.91% (p=0.000 n=91+96)
AddMulVVW/2-8 14.8ns ± 3% 6.5ns ± 2% -56.33% (p=0.000 n=100+79)
AddMulVVW/3-8 18.6ns ± 2% 7.8ns ± 5% -57.84% (p=0.000 n=89+96)
AddMulVVW/4-8 24.0ns ± 2% 9.8ns ± 0% -59.09% (p=0.000 n=95+67)
AddMulVVW/5-8 29.0ns ± 2% 11.5ns ± 5% -60.44% (p=0.000 n=90+97)
AddMulVVW/10-8 54.1ns ± 0% 18.8ns ± 1% -65.37% (p=0.000 n=82+84)
AddMulVVW/100-8 508ns ± 2% 165ns ± 4% -67.62% (p=0.000 n=72+98)
AddMulVVW/1000-8 4.96µs ± 3% 1.55µs ± 1% -68.86% (p=0.000 n=99+91)
AddMulVVW/10000-8 50.0µs ± 4% 15.5µs ± 4% -68.95% (p=0.000 n=97+97)
AddMulVVW/100000-8 491µs ± 1% 156µs ± 8% -68.22% (p=0.000 n=79+95)
Change-Id: I4c6ae0b4065f371aea8103f6a85d9e9274bf01d0
Reviewed-on: https://go-review.googlesource.com/c/go/+/164965
Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
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The biggest hot spot of the existing implementation is "load" operations, which lead to poor performance.
By unrolling the cycle 4 times and 2 times, and using "LDP", "STP" instructions,
this CL can reduce the "load" cost and improve performance.
Benchmarks:
name old time/op new time/op delta
AddVV/1-8 21.5ns ± 0% 21.5ns ± 0% ~ (all equal)
AddVV/2-8 13.5ns ± 0% 13.5ns ± 0% ~ (all equal)
AddVV/3-8 15.5ns ± 0% 15.5ns ± 0% ~ (all equal)
AddVV/4-8 17.5ns ± 0% 17.5ns ± 0% ~ (all equal)
AddVV/5-8 19.5ns ± 0% 19.5ns ± 0% ~ (all equal)
AddVV/10-8 29.5ns ± 0% 29.5ns ± 0% ~ (all equal)
AddVV/100-8 217ns ± 0% 217ns ± 0% ~ (all equal)
AddVV/1000-8 2.02µs ± 0% 2.02µs ± 0% ~ (all equal)
AddVV/10000-8 20.3µs ± 0% 20.3µs ± 0% ~ (p=0.603 n=5+5)
AddVV/100000-8 223µs ± 7% 228µs ± 8% ~ (p=0.548 n=5+5)
AddVW/1-8 9.32ns ± 0% 9.26ns ± 0% -0.64% (p=0.008 n=5+5)
AddVW/2-8 19.8ns ± 3% 10.5ns ± 0% -46.92% (p=0.008 n=5+5)
AddVW/3-8 11.5ns ± 0% 11.0ns ± 0% -4.35% (p=0.008 n=5+5)
AddVW/4-8 13.0ns ± 0% 12.0ns ± 0% -7.69% (p=0.008 n=5+5)
AddVW/5-8 14.5ns ± 0% 12.5ns ± 0% -13.79% (p=0.008 n=5+5)
AddVW/10-8 22.0ns ± 0% 15.5ns ± 0% -29.55% (p=0.008 n=5+5)
AddVW/100-8 167ns ± 0% 81ns ± 0% -51.44% (p=0.008 n=5+5)
AddVW/1000-8 1.52µs ± 0% 0.64µs ± 0% -57.58% (p=0.008 n=5+5)
AddVW/10000-8 15.1µs ± 0% 7.2µs ± 0% -52.55% (p=0.008 n=5+5)
AddVW/100000-8 150µs ± 0% 71µs ± 0% -52.95% (p=0.008 n=5+5)
SubVW/1-8 9.32ns ± 0% 9.26ns ± 0% -0.64% (p=0.008 n=5+5)
SubVW/2-8 19.7ns ± 2% 10.5ns ± 0% -46.70% (p=0.008 n=5+5)
SubVW/3-8 11.5ns ± 0% 11.0ns ± 0% -4.35% (p=0.008 n=5+5)
SubVW/4-8 13.0ns ± 0% 12.0ns ± 0% -7.69% (p=0.008 n=5+5)
SubVW/5-8 14.5ns ± 0% 12.5ns ± 0% -13.79% (p=0.008 n=5+5)
SubVW/10-8 22.0ns ± 0% 15.5ns ± 0% -29.55% (p=0.008 n=5+5)
SubVW/100-8 167ns ± 0% 81ns ± 0% -51.44% (p=0.008 n=5+5)
SubVW/1000-8 1.52µs ± 0% 0.64µs ± 0% -57.58% (p=0.008 n=5+5)
SubVW/10000-8 15.1µs ± 0% 7.2µs ± 0% -52.49% (p=0.008 n=5+5)
SubVW/100000-8 150µs ± 0% 71µs ± 0% -52.91% (p=0.008 n=5+5)
AddMulVVW/1-8 32.4ns ± 1% 32.6ns ± 1% ~ (p=0.119 n=5+5)
AddMulVVW/2-8 57.0ns ± 0% 57.0ns ± 0% ~ (p=0.643 n=5+5)
AddMulVVW/3-8 90.8ns ± 0% 90.7ns ± 0% ~ (p=0.524 n=5+5)
AddMulVVW/4-8 118ns ± 0% 118ns ± 1% ~ (p=1.000 n=4+5)
AddMulVVW/5-8 144ns ± 1% 144ns ± 0% ~ (p=0.794 n=5+4)
AddMulVVW/10-8 294ns ± 1% 296ns ± 0% +0.48% (p=0.040 n=5+5)
AddMulVVW/100-8 2.73µs ± 0% 2.73µs ± 0% ~ (p=0.278 n=5+5)
AddMulVVW/1000-8 26.0µs ± 0% 26.5µs ± 0% +2.14% (p=0.008 n=5+5)
AddMulVVW/10000-8 297µs ± 0% 297µs ± 0% +0.24% (p=0.008 n=5+5)
AddMulVVW/100000-8 3.15ms ± 1% 3.13ms ± 0% ~ (p=0.690 n=5+5)
DecimalConversion-8 311µs ± 2% 309µs ± 2% ~ (p=0.310 n=5+5)
FloatString/100-8 2.55µs ± 2% 2.54µs ± 2% ~ (p=1.000 n=5+5)
FloatString/1000-8 58.1µs ± 0% 58.1µs ± 0% ~ (p=0.151 n=5+5)
FloatString/10000-8 4.59ms ± 0% 4.59ms ± 0% ~ (p=0.151 n=5+5)
FloatString/100000-8 446ms ± 0% 446ms ± 0% +0.01% (p=0.016 n=5+5)
FloatAdd/10-8 183ns ± 0% 183ns ± 0% ~ (p=0.333 n=4+5)
FloatAdd/100-8 187ns ± 1% 192ns ± 2% ~ (p=0.056 n=5+5)
FloatAdd/1000-8 369ns ± 0% 371ns ± 0% +0.54% (p=0.016 n=4+5)
FloatAdd/10000-8 1.88µs ± 0% 1.88µs ± 0% -0.14% (p=0.000 n=4+5)
FloatAdd/100000-8 17.2µs ± 0% 17.1µs ± 0% -0.37% (p=0.008 n=5+5)
FloatSub/10-8 147ns ± 0% 147ns ± 0% ~ (all equal)
FloatSub/100-8 145ns ± 0% 146ns ± 0% ~ (p=0.238 n=5+4)
FloatSub/1000-8 241ns ± 0% 241ns ± 0% ~ (p=0.333 n=5+4)
FloatSub/10000-8 1.06µs ± 0% 1.06µs ± 0% ~ (p=0.444 n=5+5)
FloatSub/100000-8 9.50µs ± 0% 9.48µs ± 0% -0.14% (p=0.008 n=5+5)
ParseFloatSmallExp-8 28.4µs ± 2% 28.5µs ± 1% ~ (p=0.690 n=5+5)
ParseFloatLargeExp-8 125µs ± 1% 124µs ± 1% ~ (p=0.095 n=5+5)
GCD10x10/WithoutXY-8 277ns ± 2% 278ns ± 3% ~ (p=0.937 n=5+5)
GCD10x10/WithXY-8 2.08µs ± 3% 2.15µs ± 3% ~ (p=0.056 n=5+5)
GCD10x100/WithoutXY-8 592ns ± 3% 613ns ± 4% ~ (p=0.056 n=5+5)
GCD10x100/WithXY-8 3.40µs ± 2% 3.42µs ± 4% ~ (p=0.841 n=5+5)
GCD10x1000/WithoutXY-8 1.37µs ± 2% 1.35µs ± 3% ~ (p=0.460 n=5+5)
GCD10x1000/WithXY-8 7.34µs ± 2% 7.33µs ± 4% ~ (p=0.841 n=5+5)
GCD10x10000/WithoutXY-8 8.52µs ± 0% 8.51µs ± 1% ~ (p=0.421 n=5+5)
GCD10x10000/WithXY-8 27.5µs ± 2% 27.2µs ± 1% ~ (p=0.151 n=5+5)
GCD10x100000/WithoutXY-8 78.3µs ± 1% 78.5µs ± 1% ~ (p=0.690 n=5+5)
GCD10x100000/WithXY-8 231µs ± 0% 229µs ± 1% -1.11% (p=0.016 n=5+5)
GCD100x100/WithoutXY-8 1.86µs ± 2% 1.86µs ± 2% ~ (p=0.881 n=5+5)
GCD100x100/WithXY-8 27.1µs ± 2% 27.2µs ± 1% ~ (p=0.421 n=5+5)
GCD100x1000/WithoutXY-8 4.44µs ± 2% 4.41µs ± 1% ~ (p=0.310 n=5+5)
GCD100x1000/WithXY-8 36.3µs ± 1% 36.2µs ± 1% ~ (p=0.310 n=5+5)
GCD100x10000/WithoutXY-8 22.6µs ± 2% 22.5µs ± 1% ~ (p=0.690 n=5+5)
GCD100x10000/WithXY-8 145µs ± 1% 145µs ± 1% ~ (p=1.000 n=5+5)
GCD100x100000/WithoutXY-8 195µs ± 0% 196µs ± 1% ~ (p=0.548 n=5+5)
GCD100x100000/WithXY-8 1.10ms ± 0% 1.10ms ± 0% -0.30% (p=0.016 n=5+5)
GCD1000x1000/WithoutXY-8 25.0µs ± 1% 25.2µs ± 2% ~ (p=0.222 n=5+5)
GCD1000x1000/WithXY-8 520µs ± 0% 520µs ± 1% ~ (p=0.151 n=5+5)
GCD1000x10000/WithoutXY-8 57.0µs ± 1% 56.9µs ± 1% ~ (p=0.690 n=5+5)
GCD1000x10000/WithXY-8 1.21ms ± 0% 1.21ms ± 1% ~ (p=0.881 n=5+5)
GCD1000x100000/WithoutXY-8 358µs ± 0% 359µs ± 1% ~ (p=0.548 n=5+5)
GCD1000x100000/WithXY-8 8.73ms ± 0% 8.73ms ± 0% ~ (p=0.548 n=5+5)
GCD10000x10000/WithoutXY-8 686µs ± 0% 687µs ± 0% ~ (p=0.548 n=5+5)
GCD10000x10000/WithXY-8 15.9ms ± 0% 15.9ms ± 0% ~ (p=0.841 n=5+5)
GCD10000x100000/WithoutXY-8 2.08ms ± 0% 2.08ms ± 0% ~ (p=1.000 n=5+5)
GCD10000x100000/WithXY-8 86.7ms ± 0% 86.7ms ± 0% ~ (p=1.000 n=5+5)
GCD100000x100000/WithoutXY-8 51.1ms ± 0% 51.0ms ± 0% ~ (p=0.151 n=5+5)
GCD100000x100000/WithXY-8 1.23s ± 0% 1.23s ± 0% ~ (p=0.841 n=5+5)
Hilbert-8 2.41ms ± 1% 2.42ms ± 2% ~ (p=0.690 n=5+5)
Binomial-8 4.86µs ± 1% 4.86µs ± 1% ~ (p=0.889 n=5+5)
QuoRem-8 7.09µs ± 0% 7.08µs ± 0% -0.09% (p=0.024 n=5+5)
Exp-8 161ms ± 0% 161ms ± 0% -0.08% (p=0.032 n=5+5)
Exp2-8 161ms ± 0% 161ms ± 0% ~ (p=1.000 n=5+5)
Bitset-8 40.7ns ± 0% 40.6ns ± 0% ~ (p=0.095 n=4+5)
BitsetNeg-8 159ns ± 4% 148ns ± 0% -6.92% (p=0.016 n=5+4)
BitsetOrig-8 378ns ± 1% 378ns ± 1% ~ (p=0.937 n=5+5)
BitsetNegOrig-8 647ns ± 5% 647ns ± 4% ~ (p=1.000 n=5+5)
ModSqrt225_Tonelli-8 7.26ms ± 0% 7.27ms ± 0% ~ (p=1.000 n=5+5)
ModSqrt224_3Mod4-8 2.24ms ± 0% 2.24ms ± 0% ~ (p=0.690 n=5+5)
ModSqrt5430_Tonelli-8 62.8s ± 1% 62.5s ± 0% ~ (p=0.063 n=5+4)
ModSqrt5430_3Mod4-8 20.8s ± 0% 20.8s ± 0% ~ (p=0.310 n=5+5)
Sqrt-8 101µs ± 1% 101µs ± 0% -0.35% (p=0.032 n=5+5)
IntSqr/1-8 32.3ns ± 1% 32.5ns ± 1% ~ (p=0.421 n=5+5)
IntSqr/2-8 157ns ± 5% 156ns ± 5% ~ (p=0.651 n=5+5)
IntSqr/3-8 292ns ± 2% 291ns ± 3% ~ (p=0.881 n=5+5)
IntSqr/5-8 738ns ± 6% 740ns ± 5% ~ (p=0.841 n=5+5)
IntSqr/8-8 1.82µs ± 4% 1.83µs ± 4% ~ (p=0.730 n=5+5)
IntSqr/10-8 2.92µs ± 1% 2.93µs ± 1% ~ (p=0.643 n=5+5)
IntSqr/20-8 6.28µs ± 2% 6.28µs ± 2% ~ (p=1.000 n=5+5)
IntSqr/30-8 13.8µs ± 2% 13.9µs ± 3% ~ (p=1.000 n=5+5)
IntSqr/50-8 37.8µs ± 4% 37.9µs ± 4% ~ (p=0.690 n=5+5)
IntSqr/80-8 95.9µs ± 1% 95.8µs ± 1% ~ (p=0.841 n=5+5)
IntSqr/100-8 148µs ± 1% 148µs ± 1% ~ (p=0.310 n=5+5)
IntSqr/200-8 586µs ± 1% 586µs ± 1% ~ (p=0.841 n=5+5)
IntSqr/300-8 1.32ms ± 0% 1.31ms ± 0% ~ (p=0.222 n=5+5)
IntSqr/500-8 2.48ms ± 0% 2.48ms ± 0% ~ (p=0.556 n=5+4)
IntSqr/800-8 4.68ms ± 0% 4.68ms ± 0% ~ (p=0.548 n=5+5)
IntSqr/1000-8 7.57ms ± 0% 7.56ms ± 0% ~ (p=0.421 n=5+5)
Mul-8 311ms ± 0% 311ms ± 0% ~ (p=0.548 n=5+5)
Exp3Power/0x10-8 559ns ± 1% 560ns ± 1% ~ (p=0.984 n=5+5)
Exp3Power/0x40-8 641ns ± 1% 634ns ± 1% ~ (p=0.063 n=5+5)
Exp3Power/0x100-8 1.39µs ± 2% 1.40µs ± 2% ~ (p=0.381 n=5+5)
Exp3Power/0x400-8 8.27µs ± 1% 8.26µs ± 0% ~ (p=0.571 n=5+5)
Exp3Power/0x1000-8 59.9µs ± 0% 59.7µs ± 0% -0.23% (p=0.008 n=5+5)
Exp3Power/0x4000-8 816µs ± 0% 816µs ± 0% ~ (p=1.000 n=5+5)
Exp3Power/0x10000-8 7.77ms ± 0% 7.77ms ± 0% ~ (p=0.841 n=5+5)
Exp3Power/0x40000-8 73.4ms ± 0% 73.4ms ± 0% ~ (p=0.690 n=5+5)
Exp3Power/0x100000-8 665ms ± 0% 664ms ± 0% -0.14% (p=0.008 n=5+5)
Exp3Power/0x400000-8 5.98s ± 0% 5.98s ± 0% -0.09% (p=0.008 n=5+5)
Fibo-8 116ms ± 0% 116ms ± 0% -0.25% (p=0.008 n=5+5)
NatSqr/1-8 115ns ± 3% 116ns ± 2% ~ (p=0.238 n=5+5)
NatSqr/2-8 237ns ± 1% 237ns ± 1% ~ (p=0.683 n=5+5)
NatSqr/3-8 367ns ± 3% 368ns ± 3% ~ (p=0.817 n=5+5)
NatSqr/5-8 807ns ± 3% 812ns ± 3% ~ (p=0.913 n=5+5)
NatSqr/8-8 1.93µs ± 2% 1.93µs ± 3% ~ (p=0.651 n=5+5)
NatSqr/10-8 2.98µs ± 2% 2.99µs ± 2% ~ (p=0.690 n=5+5)
NatSqr/20-8 6.49µs ± 2% 6.46µs ± 2% ~ (p=0.548 n=5+5)
NatSqr/30-8 14.4µs ± 2% 14.3µs ± 2% ~ (p=0.690 n=5+5)
NatSqr/50-8 38.6µs ± 2% 38.7µs ± 2% ~ (p=0.841 n=5+5)
NatSqr/80-8 96.1µs ± 2% 95.8µs ± 2% ~ (p=0.548 n=5+5)
NatSqr/100-8 149µs ± 1% 149µs ± 1% ~ (p=0.841 n=5+5)
NatSqr/200-8 593µs ± 1% 590µs ± 1% ~ (p=0.421 n=5+5)
NatSqr/300-8 1.32ms ± 0% 1.32ms ± 1% ~ (p=0.222 n=5+5)
NatSqr/500-8 2.49ms ± 0% 2.49ms ± 0% ~ (p=0.690 n=5+5)
NatSqr/800-8 4.69ms ± 0% 4.69ms ± 0% ~ (p=1.000 n=5+5)
NatSqr/1000-8 7.59ms ± 0% 7.58ms ± 0% ~ (p=0.841 n=5+5)
ScanPi-8 322µs ± 0% 321µs ± 0% ~ (p=0.095 n=5+5)
StringPiParallel-8 71.4µs ± 5% 68.8µs ± 4% ~ (p=0.151 n=5+5)
Scan/10/Base2-8 1.10µs ± 0% 1.09µs ± 0% -0.36% (p=0.032 n=5+5)
Scan/100/Base2-8 7.78µs ± 0% 7.79µs ± 0% +0.14% (p=0.008 n=5+5)
Scan/1000/Base2-8 78.8µs ± 0% 79.0µs ± 0% +0.24% (p=0.008 n=5+5)
Scan/10000/Base2-8 1.22ms ± 0% 1.22ms ± 0% ~ (p=0.056 n=5+5)
Scan/100000/Base2-8 55.1ms ± 0% 55.0ms ± 0% -0.15% (p=0.008 n=5+5)
Scan/10/Base8-8 514ns ± 0% 515ns ± 0% ~ (p=0.079 n=5+5)
Scan/100/Base8-8 2.89µs ± 0% 2.89µs ± 0% +0.15% (p=0.008 n=5+5)
Scan/1000/Base8-8 31.0µs ± 0% 31.1µs ± 0% +0.12% (p=0.008 n=5+5)
Scan/10000/Base8-8 740µs ± 0% 740µs ± 0% ~ (p=0.222 n=5+5)
Scan/100000/Base8-8 50.6ms ± 0% 50.5ms ± 0% -0.06% (p=0.016 n=4+5)
Scan/10/Base10-8 492ns ± 1% 490ns ± 1% ~ (p=0.310 n=5+5)
Scan/100/Base10-8 2.67µs ± 0% 2.67µs ± 0% ~ (p=0.056 n=5+5)
Scan/1000/Base10-8 28.7µs ± 0% 28.7µs ± 0% ~ (p=1.000 n=5+5)
Scan/10000/Base10-8 717µs ± 0% 716µs ± 0% ~ (p=0.222 n=5+5)
Scan/100000/Base10-8 50.2ms ± 0% 50.3ms ± 0% +0.05% (p=0.008 n=5+5)
Scan/10/Base16-8 442ns ± 1% 442ns ± 0% ~ (p=0.468 n=5+5)
Scan/100/Base16-8 2.46µs ± 0% 2.45µs ± 0% ~ (p=0.159 n=5+5)
Scan/1000/Base16-8 27.2µs ± 0% 27.2µs ± 0% ~ (p=0.841 n=5+5)
Scan/10000/Base16-8 721µs ± 0% 722µs ± 0% ~ (p=0.548 n=5+5)
Scan/100000/Base16-8 52.6ms ± 0% 52.6ms ± 0% +0.07% (p=0.008 n=5+5)
String/10/Base2-8 244ns ± 1% 242ns ± 1% ~ (p=0.103 n=5+5)
String/100/Base2-8 1.48µs ± 0% 1.48µs ± 1% ~ (p=0.786 n=5+5)
String/1000/Base2-8 13.3µs ± 1% 13.3µs ± 0% ~ (p=0.222 n=5+5)
String/10000/Base2-8 132µs ± 1% 132µs ± 1% ~ (p=1.000 n=5+5)
String/100000/Base2-8 1.30ms ± 1% 1.30ms ± 1% ~ (p=1.000 n=5+5)
String/10/Base8-8 167ns ± 1% 168ns ± 1% ~ (p=0.135 n=5+5)
String/100/Base8-8 623ns ± 1% 626ns ± 1% ~ (p=0.151 n=5+5)
String/1000/Base8-8 5.24µs ± 1% 5.24µs ± 0% ~ (p=1.000 n=5+5)
String/10000/Base8-8 50.0µs ± 1% 50.0µs ± 1% ~ (p=1.000 n=5+5)
String/100000/Base8-8 492µs ± 1% 489µs ± 1% ~ (p=0.056 n=5+5)
String/10/Base10-8 503ns ± 1% 501ns ± 0% ~ (p=0.183 n=5+5)
String/100/Base10-8 1.96µs ± 0% 1.97µs ± 0% ~ (p=0.389 n=5+5)
String/1000/Base10-8 12.4µs ± 1% 12.4µs ± 1% ~ (p=0.841 n=5+5)
String/10000/Base10-8 56.7µs ± 1% 56.6µs ± 0% ~ (p=1.000 n=5+5)
String/100000/Base10-8 25.6ms ± 0% 25.6ms ± 0% ~ (p=0.222 n=5+5)
String/10/Base16-8 147ns ± 0% 148ns ± 2% ~ (p=1.000 n=4+5)
String/100/Base16-8 505ns ± 0% 505ns ± 1% ~ (p=0.778 n=5+5)
String/1000/Base16-8 3.94µs ± 0% 3.94µs ± 0% ~ (p=0.841 n=5+5)
String/10000/Base16-8 37.4µs ± 1% 37.2µs ± 1% ~ (p=0.095 n=5+5)
String/100000/Base16-8 367µs ± 1% 367µs ± 0% ~ (p=1.000 n=5+5)
LeafSize/0-8 6.64ms ± 0% 6.65ms ± 0% ~ (p=0.690 n=5+5)
LeafSize/1-8 72.5µs ± 1% 72.4µs ± 1% ~ (p=0.841 n=5+5)
LeafSize/2-8 72.6µs ± 1% 72.6µs ± 1% ~ (p=1.000 n=5+5)
LeafSize/3-8 377µs ± 0% 377µs ± 0% ~ (p=0.421 n=5+5)
LeafSize/4-8 71.2µs ± 1% 71.3µs ± 0% ~ (p=0.278 n=5+5)
LeafSize/5-8 469µs ± 0% 469µs ± 0% ~ (p=0.310 n=5+5)
LeafSize/6-8 376µs ± 0% 376µs ± 0% ~ (p=0.841 n=5+5)
LeafSize/7-8 244µs ± 0% 244µs ± 0% ~ (p=0.841 n=5+5)
LeafSize/8-8 71.9µs ± 1% 72.1µs ± 1% ~ (p=0.548 n=5+5)
LeafSize/9-8 536µs ± 0% 536µs ± 0% ~ (p=0.151 n=5+5)
LeafSize/10-8 470µs ± 0% 471µs ± 0% +0.10% (p=0.032 n=5+5)
LeafSize/11-8 458µs ± 0% 458µs ± 0% ~ (p=0.881 n=5+5)
LeafSize/12-8 376µs ± 0% 376µs ± 0% ~ (p=0.548 n=5+5)
LeafSize/13-8 341µs ± 0% 342µs ± 0% ~ (p=0.222 n=5+5)
LeafSize/14-8 246µs ± 0% 245µs ± 0% ~ (p=0.167 n=5+5)
LeafSize/15-8 168µs ± 0% 168µs ± 0% ~ (p=0.548 n=5+5)
LeafSize/16-8 72.1µs ± 1% 72.2µs ± 1% ~ (p=0.690 n=5+5)
LeafSize/32-8 81.5µs ± 1% 81.4µs ± 1% ~ (p=1.000 n=5+5)
LeafSize/64-8 133µs ± 1% 134µs ± 1% ~ (p=0.690 n=5+5)
ProbablyPrime/n=0-8 44.3ms ± 0% 44.2ms ± 0% -0.28% (p=0.008 n=5+5)
ProbablyPrime/n=1-8 64.8ms ± 0% 64.7ms ± 0% -0.15% (p=0.008 n=5+5)
ProbablyPrime/n=5-8 147ms ± 0% 147ms ± 0% -0.11% (p=0.008 n=5+5)
ProbablyPrime/n=10-8 250ms ± 0% 250ms ± 0% ~ (p=0.056 n=5+5)
ProbablyPrime/n=20-8 456ms ± 0% 455ms ± 0% -0.05% (p=0.008 n=5+5)
ProbablyPrime/Lucas-8 23.6ms ± 0% 23.5ms ± 0% -0.29% (p=0.008 n=5+5)
ProbablyPrime/MillerRabinBase2-8 20.6ms ± 0% 20.6ms ± 0% ~ (p=0.690 n=5+5)
FloatSqrt/64-8 2.01µs ± 1% 2.02µs ± 1% ~ (p=0.421 n=5+5)
FloatSqrt/128-8 4.43µs ± 2% 4.38µs ± 2% ~ (p=0.222 n=5+5)
FloatSqrt/256-8 6.64µs ± 1% 6.68µs ± 2% ~ (p=0.516 n=5+5)
FloatSqrt/1000-8 31.9µs ± 0% 31.8µs ± 0% ~ (p=0.095 n=5+5)
FloatSqrt/10000-8 595µs ± 0% 594µs ± 0% ~ (p=0.056 n=5+5)
FloatSqrt/100000-8 17.9ms ± 0% 17.9ms ± 0% ~ (p=0.151 n=5+5)
FloatSqrt/1000000-8 1.52s ± 0% 1.52s ± 0% ~ (p=0.841 n=5+5)
name old speed new speed delta
AddVV/1-8 2.97GB/s ± 0% 2.97GB/s ± 0% ~ (p=0.971 n=4+4)
AddVV/2-8 9.47GB/s ± 0% 9.47GB/s ± 0% +0.01% (p=0.016 n=5+5)
AddVV/3-8 12.4GB/s ± 0% 12.4GB/s ± 0% ~ (p=0.548 n=5+5)
AddVV/4-8 14.6GB/s ± 0% 14.6GB/s ± 0% ~ (p=1.000 n=5+5)
AddVV/5-8 16.4GB/s ± 0% 16.4GB/s ± 0% ~ (p=1.000 n=5+5)
AddVV/10-8 21.7GB/s ± 0% 21.7GB/s ± 0% ~ (p=0.548 n=5+5)
AddVV/100-8 29.4GB/s ± 0% 29.4GB/s ± 0% ~ (p=1.000 n=5+5)
AddVV/1000-8 31.7GB/s ± 0% 31.7GB/s ± 0% ~ (p=0.524 n=5+4)
AddVV/10000-8 31.5GB/s ± 0% 31.5GB/s ± 0% ~ (p=0.690 n=5+5)
AddVV/100000-8 28.8GB/s ± 7% 28.1GB/s ± 8% ~ (p=0.548 n=5+5)
AddVW/1-8 859MB/s ± 0% 864MB/s ± 0% +0.61% (p=0.008 n=5+5)
AddVW/2-8 809MB/s ± 2% 1520MB/s ± 0% +87.78% (p=0.008 n=5+5)
AddVW/3-8 2.08GB/s ± 0% 2.18GB/s ± 0% +4.54% (p=0.008 n=5+5)
AddVW/4-8 2.46GB/s ± 0% 2.66GB/s ± 0% +8.33% (p=0.016 n=4+5)
AddVW/5-8 2.76GB/s ± 0% 3.20GB/s ± 0% +16.03% (p=0.008 n=5+5)
AddVW/10-8 3.63GB/s ± 0% 5.15GB/s ± 0% +41.83% (p=0.008 n=5+5)
AddVW/100-8 4.79GB/s ± 0% 9.87GB/s ± 0% +106.12% (p=0.008 n=5+5)
AddVW/1000-8 5.27GB/s ± 0% 12.42GB/s ± 0% +135.74% (p=0.008 n=5+5)
AddVW/10000-8 5.31GB/s ± 0% 11.19GB/s ± 0% +110.71% (p=0.008 n=5+5)
AddVW/100000-8 5.32GB/s ± 0% 11.32GB/s ± 0% +112.56% (p=0.008 n=5+5)
SubVW/1-8 859MB/s ± 0% 864MB/s ± 0% +0.61% (p=0.008 n=5+5)
SubVW/2-8 812MB/s ± 2% 1520MB/s ± 0% +87.09% (p=0.008 n=5+5)
SubVW/3-8 2.08GB/s ± 0% 2.18GB/s ± 0% +4.55% (p=0.008 n=5+5)
SubVW/4-8 2.46GB/s ± 0% 2.66GB/s ± 0% +8.33% (p=0.008 n=5+5)
SubVW/5-8 2.75GB/s ± 0% 3.20GB/s ± 0% +16.03% (p=0.008 n=5+5)
SubVW/10-8 3.63GB/s ± 0% 5.15GB/s ± 0% +41.82% (p=0.008 n=5+5)
SubVW/100-8 4.79GB/s ± 0% 9.87GB/s ± 0% +106.13% (p=0.008 n=5+5)
SubVW/1000-8 5.27GB/s ± 0% 12.42GB/s ± 0% +135.74% (p=0.008 n=5+5)
SubVW/10000-8 5.31GB/s ± 0% 11.17GB/s ± 0% +110.44% (p=0.008 n=5+5)
SubVW/100000-8 5.32GB/s ± 0% 11.31GB/s ± 0% +112.35% (p=0.008 n=5+5)
AddMulVVW/1-8 1.97GB/s ± 1% 1.96GB/s ± 1% ~ (p=0.151 n=5+5)
AddMulVVW/2-8 2.24GB/s ± 0% 2.25GB/s ± 0% ~ (p=0.095 n=5+5)
AddMulVVW/3-8 2.11GB/s ± 0% 2.12GB/s ± 0% ~ (p=0.548 n=5+5)
AddMulVVW/4-8 2.17GB/s ± 1% 2.17GB/s ± 1% ~ (p=0.548 n=5+5)
AddMulVVW/5-8 2.22GB/s ± 1% 2.21GB/s ± 1% ~ (p=0.421 n=5+5)
AddMulVVW/10-8 2.17GB/s ± 1% 2.16GB/s ± 0% ~ (p=0.095 n=5+5)
AddMulVVW/100-8 2.35GB/s ± 0% 2.35GB/s ± 0% ~ (p=0.421 n=5+5)
AddMulVVW/1000-8 2.47GB/s ± 0% 2.41GB/s ± 0% -2.09% (p=0.008 n=5+5)
AddMulVVW/10000-8 2.16GB/s ± 0% 2.15GB/s ± 0% -0.23% (p=0.008 n=5+5)
AddMulVVW/100000-8 2.03GB/s ± 1% 2.04GB/s ± 0% ~ (p=0.690 n=5+5)
name old alloc/op new alloc/op delta
FloatString/100-8 400B ± 0% 400B ± 0% ~ (all equal)
FloatString/1000-8 3.22kB ± 0% 3.22kB ± 0% ~ (all equal)
FloatString/10000-8 55.6kB ± 0% 55.5kB ± 0% ~ (p=0.206 n=5+5)
FloatString/100000-8 627kB ± 0% 627kB ± 0% ~ (all equal)
FloatAdd/10-8 0.00B 0.00B ~ (all equal)
FloatAdd/100-8 0.00B 0.00B ~ (all equal)
FloatAdd/1000-8 0.00B 0.00B ~ (all equal)
FloatAdd/10000-8 0.00B 0.00B ~ (all equal)
FloatAdd/100000-8 0.00B 0.00B ~ (all equal)
FloatSub/10-8 0.00B 0.00B ~ (all equal)
FloatSub/100-8 0.00B 0.00B ~ (all equal)
FloatSub/1000-8 0.00B 0.00B ~ (all equal)
FloatSub/10000-8 0.00B 0.00B ~ (all equal)
FloatSub/100000-8 0.00B 0.00B ~ (all equal)
FloatSqrt/64-8 416B ± 0% 416B ± 0% ~ (all equal)
FloatSqrt/128-8 720B ± 0% 720B ± 0% ~ (all equal)
FloatSqrt/256-8 816B ± 0% 816B ± 0% ~ (all equal)
FloatSqrt/1000-8 2.50kB ± 0% 2.50kB ± 0% ~ (all equal)
FloatSqrt/10000-8 23.5kB ± 0% 23.5kB ± 0% ~ (all equal)
FloatSqrt/100000-8 251kB ± 0% 251kB ± 0% ~ (all equal)
FloatSqrt/1000000-8 4.61MB ± 0% 4.61MB ± 0% ~ (all equal)
name old allocs/op new allocs/op delta
FloatString/100-8 8.00 ± 0% 8.00 ± 0% ~ (all equal)
FloatString/1000-8 10.0 ± 0% 10.0 ± 0% ~ (all equal)
FloatString/10000-8 42.0 ± 0% 42.0 ± 0% ~ (all equal)
FloatString/100000-8 346 ± 0% 346 ± 0% ~ (all equal)
FloatAdd/10-8 0.00 0.00 ~ (all equal)
FloatAdd/100-8 0.00 0.00 ~ (all equal)
FloatAdd/1000-8 0.00 0.00 ~ (all equal)
FloatAdd/10000-8 0.00 0.00 ~ (all equal)
FloatAdd/100000-8 0.00 0.00 ~ (all equal)
FloatSub/10-8 0.00 0.00 ~ (all equal)
FloatSub/100-8 0.00 0.00 ~ (all equal)
FloatSub/1000-8 0.00 0.00 ~ (all equal)
FloatSub/10000-8 0.00 0.00 ~ (all equal)
FloatSub/100000-8 0.00 0.00 ~ (all equal)
FloatSqrt/64-8 9.00 ± 0% 9.00 ± 0% ~ (all equal)
FloatSqrt/128-8 13.0 ± 0% 13.0 ± 0% ~ (all equal)
FloatSqrt/256-8 12.0 ± 0% 12.0 ± 0% ~ (all equal)
FloatSqrt/1000-8 19.0 ± 0% 19.0 ± 0% ~ (all equal)
FloatSqrt/10000-8 35.0 ± 0% 35.0 ± 0% ~ (all equal)
FloatSqrt/100000-8 55.0 ± 0% 55.0 ± 0% ~ (all equal)
FloatSqrt/1000000-8 122 ± 0% 122 ± 0% ~ (all equal)
Change-Id: I6888d84c037d91f9e2199f3492ea3f6a0ed77b24
Reviewed-on: https://go-review.googlesource.com/77832
Reviewed-by: Vlad Krasnov <vlad@cloudflare.com>
Reviewed-by: Cherry Zhang <cherryyz@google.com>
Run-TryBot: Cherry Zhang <cherryyz@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
|
|
The biggest hot spot of the existing implementation is "load" operations, which lead to poor performance.
By unrolling the cycle 4x and 2x, and using "LDP", "STP" instructions, this CL can reduce the "load" cost and improve performance.
Benchmarks:
name old time/op new time/op delta
AddVV/1-8 21.5ns ± 0% 11.5ns ± 0% -46.51% (p=0.008 n=5+5)
AddVV/2-8 13.5ns ± 0% 12.0ns ± 0% -11.11% (p=0.008 n=5+5)
AddVV/3-8 15.5ns ± 0% 13.0ns ± 0% -16.13% (p=0.008 n=5+5)
AddVV/4-8 17.5ns ± 0% 13.5ns ± 0% -22.86% (p=0.008 n=5+5)
AddVV/5-8 19.5ns ± 0% 14.5ns ± 0% -25.64% (p=0.008 n=5+5)
AddVV/10-8 29.5ns ± 0% 18.0ns ± 0% -38.98% (p=0.008 n=5+5)
AddVV/100-8 217ns ± 0% 94ns ± 0% -56.64% (p=0.008 n=5+5)
AddVV/1000-8 2.02µs ± 0% 1.03µs ± 0% -48.85% (p=0.008 n=5+5)
AddVV/10000-8 20.5µs ± 0% 11.3µs ± 0% -44.70% (p=0.008 n=5+5)
AddVV/100000-8 247µs ± 3% 154µs ± 0% -37.52% (p=0.008 n=5+5)
SubVV/1-8 21.5ns ± 0% 11.5ns ± 0% ~ (p=0.079 n=4+5)
SubVV/2-8 13.5ns ± 0% 12.0ns ± 0% -11.11% (p=0.008 n=5+5)
SubVV/3-8 15.5ns ± 0% 13.0ns ± 0% -16.13% (p=0.008 n=5+5)
SubVV/4-8 17.5ns ± 0% 13.5ns ± 0% -22.86% (p=0.008 n=5+5)
SubVV/5-8 19.5ns ± 0% 14.5ns ± 0% -25.64% (p=0.008 n=5+5)
SubVV/10-8 29.5ns ± 0% 18.0ns ± 0% -38.98% (p=0.008 n=5+5)
SubVV/100-8 217ns ± 0% 94ns ± 0% -56.64% (p=0.008 n=5+5)
SubVV/1000-8 2.02µs ± 0% 0.80µs ± 0% -60.50% (p=0.008 n=5+5)
SubVV/10000-8 20.5µs ± 0% 11.3µs ± 0% -44.99% (p=0.008 n=5+5)
SubVV/100000-8 221µs ±11% 223µs ±16% ~ (p=0.690 n=5+5)
AddVW/1-8 9.32ns ± 0% 9.32ns ± 0% ~ (all equal)
AddVW/2-8 19.7ns ± 1% 19.7ns ± 0% ~ (p=0.381 n=5+4)
AddVW/3-8 11.5ns ± 0% 11.5ns ± 0% ~ (all equal)
AddVW/4-8 13.0ns ± 0% 13.0ns ± 0% ~ (all equal)
AddVW/5-8 14.5ns ± 0% 14.5ns ± 0% ~ (all equal)
AddVW/10-8 22.0ns ± 0% 22.0ns ± 0% ~ (all equal)
AddVW/100-8 167ns ± 0% 167ns ± 0% ~ (all equal)
AddVW/1000-8 1.52µs ± 0% 1.52µs ± 0% +0.40% (p=0.008 n=5+5)
AddVW/10000-8 15.1µs ± 0% 15.1µs ± 0% ~ (p=0.556 n=5+4)
AddVW/100000-8 152µs ± 1% 152µs ± 1% ~ (p=0.690 n=5+5)
AddMulVVW/1-8 33.3ns ± 0% 32.7ns ± 1% -1.86% (p=0.008 n=5+5)
AddMulVVW/2-8 59.3ns ± 1% 56.9ns ± 1% -4.15% (p=0.008 n=5+5)
AddMulVVW/3-8 80.5ns ± 1% 85.4ns ± 3% +6.19% (p=0.008 n=5+5)
AddMulVVW/4-8 127ns ± 0% 111ns ± 1% -13.19% (p=0.008 n=5+5)
AddMulVVW/5-8 144ns ± 0% 149ns ± 0% +3.47% (p=0.016 n=4+5)
AddMulVVW/10-8 298ns ± 1% 283ns ± 0% -4.77% (p=0.008 n=5+5)
AddMulVVW/100-8 3.06µs ± 0% 2.99µs ± 0% -2.21% (p=0.008 n=5+5)
AddMulVVW/1000-8 31.3µs ± 0% 26.9µs ± 0% -14.17% (p=0.008 n=5+5)
AddMulVVW/10000-8 316µs ± 0% 305µs ± 0% -3.51% (p=0.008 n=5+5)
AddMulVVW/100000-8 3.17ms ± 0% 3.17ms ± 1% ~ (p=0.690 n=5+5)
DecimalConversion-8 316µs ± 1% 313µs ± 2% ~ (p=0.095 n=5+5)
FloatString/100-8 2.53µs ± 1% 2.56µs ± 2% ~ (p=0.222 n=5+5)
FloatString/1000-8 58.4µs ± 0% 58.5µs ± 0% ~ (p=0.206 n=5+5)
FloatString/10000-8 4.59ms ± 0% 4.58ms ± 0% -0.31% (p=0.008 n=5+5)
FloatString/100000-8 446ms ± 0% 444ms ± 0% -0.31% (p=0.008 n=5+5)
FloatAdd/10-8 184ns ± 0% 172ns ± 0% -6.30% (p=0.008 n=5+5)
FloatAdd/100-8 189ns ± 2% 191ns ± 4% ~ (p=0.381 n=5+5)
FloatAdd/1000-8 371ns ± 0% 347ns ± 1% -6.42% (p=0.008 n=5+5)
FloatAdd/10000-8 1.87µs ± 0% 1.68µs ± 0% -10.16% (p=0.008 n=5+5)
FloatAdd/100000-8 17.1µs ± 0% 15.6µs ± 0% -8.74% (p=0.016 n=5+4)
FloatSub/10-8 152ns ± 0% 138ns ± 0% -9.47% (p=0.000 n=4+5)
FloatSub/100-8 148ns ± 0% 142ns ± 0% -4.05% (p=0.000 n=5+4)
FloatSub/1000-8 245ns ± 1% 217ns ± 0% -11.28% (p=0.000 n=5+4)
FloatSub/10000-8 1.07µs ± 0% 0.88µs ± 1% -18.14% (p=0.008 n=5+5)
FloatSub/100000-8 9.58µs ± 0% 7.96µs ± 0% -16.84% (p=0.008 n=5+5)
ParseFloatSmallExp-8 28.8µs ± 1% 29.0µs ± 1% ~ (p=0.095 n=5+5)
ParseFloatLargeExp-8 126µs ± 1% 126µs ± 1% ~ (p=0.841 n=5+5)
GCD10x10/WithoutXY-8 277ns ± 2% 281ns ± 4% ~ (p=0.746 n=5+5)
GCD10x10/WithXY-8 2.10µs ± 1% 2.12µs ± 3% ~ (p=0.548 n=5+5)
GCD10x100/WithoutXY-8 615ns ± 3% 607ns ± 2% ~ (p=0.135 n=5+5)
GCD10x100/WithXY-8 3.50µs ± 2% 3.62µs ± 5% ~ (p=0.151 n=5+5)
GCD10x1000/WithoutXY-8 1.39µs ± 2% 1.39µs ± 3% ~ (p=0.690 n=5+5)
GCD10x1000/WithXY-8 7.39µs ± 1% 7.34µs ± 2% ~ (p=0.135 n=5+5)
GCD10x10000/WithoutXY-8 8.66µs ± 1% 8.68µs ± 1% ~ (p=0.421 n=5+5)
GCD10x10000/WithXY-8 28.1µs ± 2% 27.0µs ± 2% -3.81% (p=0.008 n=5+5)
GCD10x100000/WithoutXY-8 79.3µs ± 1% 79.3µs ± 1% ~ (p=0.841 n=5+5)
GCD10x100000/WithXY-8 238µs ± 0% 227µs ± 1% -4.74% (p=0.008 n=5+5)
GCD100x100/WithoutXY-8 1.89µs ± 1% 1.88µs ± 2% ~ (p=0.968 n=5+5)
GCD100x100/WithXY-8 26.7µs ± 1% 27.0µs ± 1% +1.44% (p=0.032 n=5+5)
GCD100x1000/WithoutXY-8 4.48µs ± 1% 4.45µs ± 2% ~ (p=0.341 n=5+5)
GCD100x1000/WithXY-8 36.3µs ± 1% 35.1µs ± 1% -3.27% (p=0.008 n=5+5)
GCD100x10000/WithoutXY-8 22.8µs ± 0% 22.7µs ± 1% ~ (p=0.056 n=5+5)
GCD100x10000/WithXY-8 145µs ± 1% 133µs ± 1% -8.33% (p=0.008 n=5+5)
GCD100x100000/WithoutXY-8 198µs ± 0% 195µs ± 0% -1.56% (p=0.008 n=5+5)
GCD100x100000/WithXY-8 1.11ms ± 0% 1.00ms ± 0% -10.04% (p=0.008 n=5+5)
GCD1000x1000/WithoutXY-8 25.2µs ± 1% 24.8µs ± 1% -1.63% (p=0.016 n=5+5)
GCD1000x1000/WithXY-8 513µs ± 0% 517µs ± 2% ~ (p=0.421 n=5+5)
GCD1000x10000/WithoutXY-8 57.0µs ± 0% 52.7µs ± 1% -7.56% (p=0.008 n=5+5)
GCD1000x10000/WithXY-8 1.20ms ± 0% 1.10ms ± 0% -8.70% (p=0.008 n=5+5)
GCD1000x100000/WithoutXY-8 358µs ± 0% 318µs ± 1% -11.03% (p=0.008 n=5+5)
GCD1000x100000/WithXY-8 8.71ms ± 0% 7.65ms ± 0% -12.19% (p=0.008 n=5+5)
GCD10000x10000/WithoutXY-8 690µs ± 0% 630µs ± 0% -8.71% (p=0.008 n=5+5)
GCD10000x10000/WithXY-8 16.0ms ± 1% 14.9ms ± 0% -6.85% (p=0.008 n=5+5)
GCD10000x100000/WithoutXY-8 2.09ms ± 0% 1.75ms ± 0% -16.09% (p=0.016 n=5+4)
GCD10000x100000/WithXY-8 86.8ms ± 0% 76.3ms ± 0% -12.09% (p=0.008 n=5+5)
GCD100000x100000/WithoutXY-8 51.1ms ± 0% 46.0ms ± 0% -9.97% (p=0.008 n=5+5)
GCD100000x100000/WithXY-8 1.25s ± 0% 1.15s ± 0% -7.92% (p=0.008 n=5+5)
Hilbert-8 2.45ms ± 1% 2.49ms ± 1% +1.99% (p=0.008 n=5+5)
Binomial-8 4.98µs ± 3% 4.90µs ± 2% ~ (p=0.421 n=5+5)
QuoRem-8 7.10µs ± 0% 6.21µs ± 0% -12.55% (p=0.016 n=5+4)
Exp-8 161ms ± 0% 161ms ± 0% ~ (p=0.421 n=5+5)
Exp2-8 161ms ± 0% 161ms ± 0% ~ (p=0.151 n=5+5)
Bitset-8 40.4ns ± 0% 40.3ns ± 0% ~ (p=0.190 n=5+5)
BitsetNeg-8 163ns ± 3% 137ns ± 2% -15.91% (p=0.008 n=5+5)
BitsetOrig-8 377ns ± 1% 372ns ± 1% -1.22% (p=0.024 n=5+5)
BitsetNegOrig-8 631ns ± 1% 605ns ± 1% -4.09% (p=0.008 n=5+5)
ModSqrt225_Tonelli-8 7.26ms ± 0% 7.26ms ± 0% ~ (p=0.548 n=5+5)
ModSqrt224_3Mod4-8 2.24ms ± 0% 2.24ms ± 0% ~ (p=1.000 n=5+5)
ModSqrt5430_Tonelli-8 62.4s ± 0% 62.4s ± 0% ~ (p=0.841 n=5+5)
ModSqrt5430_3Mod4-8 20.8s ± 0% 20.7s ± 0% ~ (p=0.056 n=5+5)
Sqrt-8 101µs ± 0% 89µs ± 0% -12.17% (p=0.008 n=5+5)
IntSqr/1-8 32.5ns ± 1% 32.7ns ± 1% ~ (p=0.056 n=5+5)
IntSqr/2-8 160ns ± 5% 158ns ± 0% ~ (p=0.397 n=5+4)
IntSqr/3-8 298ns ± 4% 296ns ± 4% ~ (p=0.667 n=5+5)
IntSqr/5-8 737ns ± 5% 761ns ± 3% +3.34% (p=0.016 n=5+5)
IntSqr/8-8 1.87µs ± 4% 1.90µs ± 3% ~ (p=0.222 n=5+5)
IntSqr/10-8 2.96µs ± 4% 2.92µs ± 6% ~ (p=0.310 n=5+5)
IntSqr/20-8 6.28µs ± 3% 6.21µs ± 2% ~ (p=0.310 n=5+5)
IntSqr/30-8 14.0µs ± 2% 13.9µs ± 2% ~ (p=0.548 n=5+5)
IntSqr/50-8 37.7µs ± 3% 38.3µs ± 2% ~ (p=0.095 n=5+5)
IntSqr/80-8 95.9µs ± 2% 95.1µs ± 1% ~ (p=0.310 n=5+5)
IntSqr/100-8 148µs ± 1% 148µs ± 1% ~ (p=0.841 n=5+5)
IntSqr/200-8 586µs ± 1% 587µs ± 1% ~ (p=1.000 n=5+5)
IntSqr/300-8 1.32ms ± 0% 1.31ms ± 1% -0.73% (p=0.032 n=5+5)
IntSqr/500-8 2.48ms ± 0% 2.45ms ± 0% -1.15% (p=0.008 n=5+5)
IntSqr/800-8 4.68ms ± 0% 4.62ms ± 0% -1.23% (p=0.008 n=5+5)
IntSqr/1000-8 7.57ms ± 0% 7.50ms ± 0% -0.84% (p=0.008 n=5+5)
Mul-8 311ms ± 0% 308ms ± 0% -0.81% (p=0.008 n=5+5)
Exp3Power/0x10-8 574ns ± 1% 578ns ± 2% ~ (p=0.500 n=5+5)
Exp3Power/0x40-8 640ns ± 1% 646ns ± 0% ~ (p=0.056 n=5+5)
Exp3Power/0x100-8 1.42µs ± 1% 1.42µs ± 1% ~ (p=0.246 n=5+5)
Exp3Power/0x400-8 8.30µs ± 1% 8.29µs ± 1% ~ (p=0.802 n=5+5)
Exp3Power/0x1000-8 60.0µs ± 0% 59.9µs ± 0% -0.24% (p=0.016 n=5+5)
Exp3Power/0x4000-8 817µs ± 0% 816µs ± 0% -0.17% (p=0.008 n=5+5)
Exp3Power/0x10000-8 7.80ms ± 1% 7.70ms ± 0% -1.23% (p=0.008 n=5+5)
Exp3Power/0x40000-8 73.4ms ± 0% 72.5ms ± 0% -1.28% (p=0.008 n=5+5)
Exp3Power/0x100000-8 665ms ± 0% 656ms ± 0% -1.34% (p=0.008 n=5+5)
Exp3Power/0x400000-8 5.99s ± 0% 5.90s ± 0% -1.40% (p=0.008 n=5+5)
Fibo-8 116ms ± 0% 50ms ± 0% -57.09% (p=0.008 n=5+5)
NatSqr/1-8 112ns ± 4% 112ns ± 2% ~ (p=0.968 n=5+5)
NatSqr/2-8 251ns ± 2% 250ns ± 1% ~ (p=0.571 n=5+5)
NatSqr/3-8 378ns ± 2% 379ns ± 2% ~ (p=0.794 n=5+5)
NatSqr/5-8 829ns ± 3% 827ns ± 2% ~ (p=1.000 n=5+5)
NatSqr/8-8 1.97µs ± 2% 1.95µs ± 2% ~ (p=0.310 n=5+5)
NatSqr/10-8 3.02µs ± 2% 2.99µs ± 2% ~ (p=0.421 n=5+5)
NatSqr/20-8 6.51µs ± 2% 6.49µs ± 1% ~ (p=0.841 n=5+5)
NatSqr/30-8 14.1µs ± 2% 14.0µs ± 2% ~ (p=0.841 n=5+5)
NatSqr/50-8 38.1µs ± 2% 38.3µs ± 3% ~ (p=0.690 n=5+5)
NatSqr/80-8 95.5µs ± 2% 96.0µs ± 1% ~ (p=0.421 n=5+5)
NatSqr/100-8 150µs ± 1% 148µs ± 2% ~ (p=0.095 n=5+5)
NatSqr/200-8 588µs ± 1% 590µs ± 1% ~ (p=0.421 n=5+5)
NatSqr/300-8 1.32ms ± 1% 1.31ms ± 1% ~ (p=0.841 n=5+5)
NatSqr/500-8 2.50ms ± 0% 2.47ms ± 0% -1.03% (p=0.008 n=5+5)
NatSqr/800-8 4.70ms ± 0% 4.64ms ± 0% -1.31% (p=0.008 n=5+5)
NatSqr/1000-8 7.60ms ± 0% 7.52ms ± 0% -1.01% (p=0.008 n=5+5)
ScanPi-8 326µs ± 0% 326µs ± 0% ~ (p=0.841 n=5+5)
StringPiParallel-8 70.3µs ± 5% 63.8µs ±10% ~ (p=0.056 n=5+5)
Scan/10/Base2-8 1.09µs ± 0% 1.09µs ± 0% ~ (p=0.317 n=5+5)
Scan/100/Base2-8 7.79µs ± 0% 7.78µs ± 0% ~ (p=0.063 n=5+5)
Scan/1000/Base2-8 79.0µs ± 0% 78.9µs ± 0% -0.18% (p=0.008 n=5+5)
Scan/10000/Base2-8 1.22ms ± 0% 1.22ms ± 0% -0.15% (p=0.008 n=5+5)
Scan/100000/Base2-8 55.1ms ± 0% 55.2ms ± 0% +0.20% (p=0.008 n=5+5)
Scan/10/Base8-8 512ns ± 0% 512ns ± 1% ~ (p=0.810 n=5+5)
Scan/100/Base8-8 2.89µs ± 0% 2.89µs ± 0% ~ (p=0.810 n=5+5)
Scan/1000/Base8-8 31.0µs ± 0% 31.0µs ± 0% ~ (p=0.151 n=5+5)
Scan/10000/Base8-8 740µs ± 0% 741µs ± 0% +0.10% (p=0.008 n=5+5)
Scan/100000/Base8-8 50.6ms ± 0% 50.6ms ± 0% +0.08% (p=0.008 n=5+5)
Scan/10/Base10-8 487ns ± 0% 487ns ± 0% ~ (p=0.571 n=5+5)
Scan/100/Base10-8 2.67µs ± 0% 2.67µs ± 0% ~ (p=0.810 n=5+5)
Scan/1000/Base10-8 28.7µs ± 0% 28.7µs ± 0% +0.06% (p=0.008 n=5+5)
Scan/10000/Base10-8 716µs ± 0% 717µs ± 0% ~ (p=0.222 n=5+5)
Scan/100000/Base10-8 50.3ms ± 0% 50.3ms ± 0% +0.10% (p=0.008 n=5+5)
Scan/10/Base16-8 438ns ± 0% 437ns ± 1% ~ (p=0.786 n=5+5)
Scan/100/Base16-8 2.47µs ± 0% 2.47µs ± 0% -0.19% (p=0.048 n=5+5)
Scan/1000/Base16-8 27.2µs ± 0% 27.3µs ± 0% ~ (p=0.087 n=5+5)
Scan/10000/Base16-8 722µs ± 0% 722µs ± 0% +0.11% (p=0.008 n=5+5)
Scan/100000/Base16-8 52.6ms ± 0% 52.7ms ± 0% +0.15% (p=0.008 n=5+5)
String/10/Base2-8 247ns ± 2% 248ns ± 1% ~ (p=0.437 n=5+5)
String/100/Base2-8 1.51µs ± 0% 1.51µs ± 0% -0.37% (p=0.024 n=5+5)
String/1000/Base2-8 13.6µs ± 1% 13.5µs ± 0% ~ (p=0.095 n=5+5)
String/10000/Base2-8 135µs ± 0% 135µs ± 1% ~ (p=0.841 n=5+5)
String/100000/Base2-8 1.32ms ± 1% 1.32ms ± 1% ~ (p=0.690 n=5+5)
String/10/Base8-8 169ns ± 1% 169ns ± 1% ~ (p=1.000 n=5+5)
String/100/Base8-8 636ns ± 0% 634ns ± 1% ~ (p=0.413 n=5+5)
String/1000/Base8-8 5.33µs ± 1% 5.32µs ± 0% ~ (p=0.222 n=5+5)
String/10000/Base8-8 50.9µs ± 1% 50.7µs ± 0% ~ (p=0.151 n=5+5)
String/100000/Base8-8 500µs ± 1% 497µs ± 0% ~ (p=0.421 n=5+5)
String/10/Base10-8 516ns ± 1% 513ns ± 0% -0.62% (p=0.016 n=5+4)
String/100/Base10-8 1.97µs ± 0% 1.96µs ± 0% ~ (p=0.667 n=4+5)
String/1000/Base10-8 12.5µs ± 0% 11.5µs ± 0% -7.92% (p=0.008 n=5+5)
String/10000/Base10-8 57.7µs ± 0% 52.5µs ± 0% -8.93% (p=0.008 n=5+5)
String/100000/Base10-8 25.6ms ± 0% 21.6ms ± 0% -15.94% (p=0.008 n=5+5)
String/10/Base16-8 150ns ± 1% 149ns ± 0% ~ (p=0.413 n=5+4)
String/100/Base16-8 514ns ± 1% 514ns ± 1% ~ (p=0.849 n=5+5)
String/1000/Base16-8 4.01µs ± 0% 4.01µs ± 0% ~ (p=0.421 n=5+5)
String/10000/Base16-8 37.8µs ± 1% 37.8µs ± 1% ~ (p=0.841 n=5+5)
String/100000/Base16-8 373µs ± 2% 373µs ± 0% ~ (p=0.421 n=5+5)
LeafSize/0-8 6.63ms ± 0% 6.63ms ± 0% ~ (p=0.730 n=4+5)
LeafSize/1-8 74.0µs ± 0% 67.7µs ± 1% -8.53% (p=0.008 n=5+5)
LeafSize/2-8 74.2µs ± 0% 68.3µs ± 1% -7.99% (p=0.008 n=5+5)
LeafSize/3-8 379µs ± 0% 309µs ± 0% -18.52% (p=0.008 n=5+5)
LeafSize/4-8 72.7µs ± 1% 66.7µs ± 0% -8.37% (p=0.008 n=5+5)
LeafSize/5-8 471µs ± 0% 384µs ± 0% -18.55% (p=0.008 n=5+5)
LeafSize/6-8 378µs ± 0% 308µs ± 0% -18.59% (p=0.008 n=5+5)
LeafSize/7-8 245µs ± 0% 204µs ± 1% -16.75% (p=0.008 n=5+5)
LeafSize/8-8 73.4µs ± 0% 66.9µs ± 1% -8.79% (p=0.008 n=5+5)
LeafSize/9-8 538µs ± 0% 437µs ± 0% -18.75% (p=0.008 n=5+5)
LeafSize/10-8 472µs ± 0% 396µs ± 1% -16.01% (p=0.008 n=5+5)
LeafSize/11-8 460µs ± 0% 374µs ± 0% -18.58% (p=0.008 n=5+5)
LeafSize/12-8 378µs ± 0% 308µs ± 0% -18.38% (p=0.008 n=5+5)
LeafSize/13-8 343µs ± 0% 284µs ± 0% -17.30% (p=0.008 n=5+5)
LeafSize/14-8 248µs ± 0% 206µs ± 0% -16.94% (p=0.008 n=5+5)
LeafSize/15-8 169µs ± 0% 144µs ± 0% -14.69% (p=0.008 n=5+5)
LeafSize/16-8 72.9µs ± 0% 66.8µs ± 1% -8.27% (p=0.008 n=5+5)
LeafSize/32-8 82.5µs ± 0% 76.7µs ± 0% -7.04% (p=0.008 n=5+5)
LeafSize/64-8 134µs ± 0% 129µs ± 0% -3.80% (p=0.008 n=5+5)
ProbablyPrime/n=0-8 44.2ms ± 0% 43.4ms ± 0% -1.95% (p=0.008 n=5+5)
ProbablyPrime/n=1-8 64.9ms ± 0% 64.0ms ± 0% -1.27% (p=0.008 n=5+5)
ProbablyPrime/n=5-8 147ms ± 0% 146ms ± 0% -0.58% (p=0.008 n=5+5)
ProbablyPrime/n=10-8 250ms ± 0% 249ms ± 0% -0.35% (p=0.008 n=5+5)
ProbablyPrime/n=20-8 456ms ± 0% 455ms ± 0% -0.18% (p=0.008 n=5+5)
ProbablyPrime/Lucas-8 23.6ms ± 0% 22.7ms ± 0% -3.74% (p=0.008 n=5+5)
ProbablyPrime/MillerRabinBase2-8 20.7ms ± 0% 20.6ms ± 0% ~ (p=0.421 n=5+5)
FloatSqrt/64-8 2.25µs ± 1% 2.29µs ± 0% +1.48% (p=0.008 n=5+5)
FloatSqrt/128-8 4.86µs ± 1% 4.92µs ± 1% +1.21% (p=0.032 n=5+5)
FloatSqrt/256-8 13.6µs ± 0% 13.7µs ± 1% +1.31% (p=0.032 n=5+5)
FloatSqrt/1000-8 70.0µs ± 1% 70.1µs ± 0% ~ (p=0.690 n=5+5)
FloatSqrt/10000-8 1.92ms ± 0% 1.90ms ± 0% -0.59% (p=0.008 n=5+5)
FloatSqrt/100000-8 55.3ms ± 0% 54.8ms ± 0% -1.01% (p=0.008 n=5+5)
FloatSqrt/1000000-8 4.56s ± 0% 4.50s ± 0% -1.28% (p=0.008 n=5+5)
name old speed new speed delta
AddVV/1-8 2.97GB/s ± 0% 5.56GB/s ± 0% +86.85% (p=0.008 n=5+5)
AddVV/2-8 9.47GB/s ± 0% 10.66GB/s ± 0% +12.50% (p=0.008 n=5+5)
AddVV/3-8 12.4GB/s ± 0% 14.7GB/s ± 0% +19.10% (p=0.008 n=5+5)
AddVV/4-8 14.6GB/s ± 0% 18.9GB/s ± 0% +29.63% (p=0.016 n=4+5)
AddVV/5-8 16.4GB/s ± 0% 22.0GB/s ± 0% +34.47% (p=0.016 n=5+4)
AddVV/10-8 21.7GB/s ± 0% 35.5GB/s ± 0% +63.89% (p=0.008 n=5+5)
AddVV/100-8 29.4GB/s ± 0% 68.0GB/s ± 0% +131.38% (p=0.008 n=5+5)
AddVV/1000-8 31.7GB/s ± 0% 61.9GB/s ± 0% +95.43% (p=0.008 n=5+5)
AddVV/10000-8 31.2GB/s ± 0% 56.4GB/s ± 0% +80.83% (p=0.008 n=5+5)
AddVV/100000-8 25.9GB/s ± 3% 41.4GB/s ± 0% +59.98% (p=0.008 n=5+5)
SubVV/1-8 2.97GB/s ± 0% 5.56GB/s ± 0% +86.97% (p=0.016 n=4+5)
SubVV/2-8 9.47GB/s ± 0% 10.66GB/s ± 0% +12.51% (p=0.008 n=5+5)
SubVV/3-8 12.4GB/s ± 0% 14.8GB/s ± 0% +19.23% (p=0.016 n=4+5)
SubVV/4-8 14.6GB/s ± 0% 18.9GB/s ± 0% +29.56% (p=0.008 n=5+5)
SubVV/5-8 16.4GB/s ± 0% 22.0GB/s ± 0% +34.47% (p=0.016 n=4+5)
SubVV/10-8 21.7GB/s ± 0% 35.5GB/s ± 0% +63.89% (p=0.008 n=5+5)
SubVV/100-8 29.4GB/s ± 0% 68.0GB/s ± 0% +131.38% (p=0.008 n=5+5)
SubVV/1000-8 31.6GB/s ± 0% 80.1GB/s ± 0% +153.08% (p=0.008 n=5+5)
SubVV/10000-8 31.2GB/s ± 0% 56.7GB/s ± 0% +81.79% (p=0.008 n=5+5)
SubVV/100000-8 29.1GB/s ±10% 29.0GB/s ±18% ~ (p=0.690 n=5+5)
AddVW/1-8 859MB/s ± 0% 859MB/s ± 0% -0.01% (p=0.008 n=5+5)
AddVW/2-8 811MB/s ± 1% 814MB/s ± 0% ~ (p=0.413 n=5+4)
AddVW/3-8 2.08GB/s ± 0% 2.08GB/s ± 0% ~ (p=0.206 n=5+5)
AddVW/4-8 2.46GB/s ± 0% 2.46GB/s ± 0% ~ (p=0.056 n=5+5)
AddVW/5-8 2.75GB/s ± 0% 2.75GB/s ± 0% ~ (p=0.508 n=5+5)
AddVW/10-8 3.63GB/s ± 0% 3.63GB/s ± 0% ~ (p=0.214 n=5+5)
AddVW/100-8 4.79GB/s ± 0% 4.79GB/s ± 0% ~ (p=0.500 n=5+5)
AddVW/1000-8 5.27GB/s ± 0% 5.25GB/s ± 0% -0.43% (p=0.008 n=5+5)
AddVW/10000-8 5.30GB/s ± 0% 5.30GB/s ± 0% ~ (p=0.397 n=5+5)
AddVW/100000-8 5.27GB/s ± 1% 5.25GB/s ± 1% ~ (p=0.690 n=5+5)
AddMulVVW/1-8 1.92GB/s ± 0% 1.96GB/s ± 1% +1.95% (p=0.008 n=5+5)
AddMulVVW/2-8 2.16GB/s ± 1% 2.25GB/s ± 1% +4.32% (p=0.008 n=5+5)
AddMulVVW/3-8 2.39GB/s ± 1% 2.25GB/s ± 3% -5.79% (p=0.008 n=5+5)
AddMulVVW/4-8 2.00GB/s ± 0% 2.31GB/s ± 1% +15.31% (p=0.008 n=5+5)
AddMulVVW/5-8 2.22GB/s ± 0% 2.14GB/s ± 0% -3.86% (p=0.008 n=5+5)
AddMulVVW/10-8 2.15GB/s ± 1% 2.25GB/s ± 0% +5.03% (p=0.008 n=5+5)
AddMulVVW/100-8 2.09GB/s ± 0% 2.14GB/s ± 0% +2.25% (p=0.008 n=5+5)
AddMulVVW/1000-8 2.04GB/s ± 0% 2.38GB/s ± 0% +16.52% (p=0.008 n=5+5)
AddMulVVW/10000-8 2.03GB/s ± 0% 2.10GB/s ± 0% +3.64% (p=0.008 n=5+5)
AddMulVVW/100000-8 2.02GB/s ± 0% 2.02GB/s ± 1% ~ (p=0.690 n=5+5)
Change-Id: Ie482d67a7dbb5af6f5d81af2b3d9d14bd66336db
Reviewed-on: https://go-review.googlesource.com/77831
Reviewed-by: Cherry Zhang <cherryyz@google.com>
Run-TryBot: Cherry Zhang <cherryyz@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
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Verified that BenchmarkBitLen time went down from 2.25 ns/op to 0.65 ns/op
an a 2.3 GHz Intel Core i7, before removing that benchmark (now covered by
math/bits benchmarks).
Change-Id: I3890bb7d1889e95b9a94bd68f0bdf06f1885adeb
Reviewed-on: https://go-review.googlesource.com/38464
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
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No need to test so many sizes in race mode, especially for a package
which doesn't use goroutines.
Reduces test time from 2.5 minutes to 25 seconds.
Updates #17104
Change-Id: I7065b39273f82edece385c0d67b3f2d83d4934b8
Reviewed-on: https://go-review.googlesource.com/29163
Reviewed-by: David Crawshaw <crawshaw@golang.org>
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Follow-up cleanup to https://golang.org/cl/23424/ .
Change-Id: Ifb05c1ff5327df6bc5f4cbc554e18363293f7960
Reviewed-on: https://go-review.googlesource.com/23446
Reviewed-by: Marcel van Lohuizen <mpvl@golang.org>
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shortens code and gives an example of the use of Run.
Change-Id: I75ffaf762218a589274b4b62e19022e31e805d1b
Reviewed-on: https://go-review.googlesource.com/23424
Reviewed-by: Russ Cox <rsc@golang.org>
Run-TryBot: Marcel van Lohuizen <mpvl@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
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This deletes unused code and helpers from tests.
Change-Id: Ie31d46115f558ceb8da6efbf90c3c204e03b0d7e
Reviewed-on: https://go-review.googlesource.com/20927
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
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The tree's pretty inconsistent about single space vs double space
after a period in documentation. Make it consistently a single space,
per earlier decisions. This means contributors won't be confused by
misleading precedence.
This CL doesn't use go/doc to parse. It only addresses // comments.
It was generated with:
$ perl -i -npe 's,^(\s*// .+[a-z]\.) +([A-Z]),$1 $2,' $(git grep -l -E '^\s*//(.+\.) +([A-Z])')
$ go test go/doc -update
Change-Id: Iccdb99c37c797ef1f804a94b22ba5ee4b500c4f7
Reviewed-on: https://go-review.googlesource.com/20022
Reviewed-by: Rob Pike <r@golang.org>
Reviewed-by: Dave Day <djd@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
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Fixes #10525.
Change-Id: I92dc87f5d6db396d8dde2220fc37b7093b772d81
Reviewed-on: https://go-review.googlesource.com/9210
Reviewed-by: Robert Griesemer <gri@golang.org>
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(platforms w/o corresponding assembly kernels)
For short vector adds there's some erradic slow-down, but overall
these routines have become significantly faster. This only matters
for platforms w/o native (assembly) versions of these kernels, so
we are not concerned about the minor slow-down for short vectors.
This code was already reviewed under Mercurial (golang.org/cl/172810043)
but wasn't submitted before the switch to git.
Benchmarks run on 2.3GHz Intel Core i7, running OS X 10.9.5,
with the respective AddVV and AddVW assembly routines disabled.
benchmark old ns/op new ns/op delta
BenchmarkAddVV_1 6.59 7.09 +7.59%
BenchmarkAddVV_2 10.3 10.1 -1.94%
BenchmarkAddVV_3 10.9 12.6 +15.60%
BenchmarkAddVV_4 13.9 15.6 +12.23%
BenchmarkAddVV_5 16.8 17.3 +2.98%
BenchmarkAddVV_1e1 29.5 29.9 +1.36%
BenchmarkAddVV_1e2 246 232 -5.69%
BenchmarkAddVV_1e3 2374 2185 -7.96%
BenchmarkAddVV_1e4 58942 22292 -62.18%
BenchmarkAddVV_1e5 668622 225279 -66.31%
BenchmarkAddVW_1 6.81 5.58 -18.06%
BenchmarkAddVW_2 7.69 6.86 -10.79%
BenchmarkAddVW_3 9.56 8.32 -12.97%
BenchmarkAddVW_4 12.1 9.53 -21.24%
BenchmarkAddVW_5 13.2 10.9 -17.42%
BenchmarkAddVW_1e1 23.4 18.0 -23.08%
BenchmarkAddVW_1e2 175 141 -19.43%
BenchmarkAddVW_1e3 1568 1266 -19.26%
BenchmarkAddVW_1e4 15425 12596 -18.34%
BenchmarkAddVW_1e5 156737 133539 -14.80%
BenchmarkFibo 381678466 132958666 -65.16%
benchmark old MB/s new MB/s speedup
BenchmarkAddVV_1 9715.25 9028.30 0.93x
BenchmarkAddVV_2 12461.72 12622.60 1.01x
BenchmarkAddVV_3 17549.64 15243.82 0.87x
BenchmarkAddVV_4 18392.54 16398.29 0.89x
BenchmarkAddVV_5 18995.23 18496.57 0.97x
BenchmarkAddVV_1e1 21708.98 21438.28 0.99x
BenchmarkAddVV_1e2 25956.53 27506.88 1.06x
BenchmarkAddVV_1e3 26947.93 29286.66 1.09x
BenchmarkAddVV_1e4 10857.96 28709.46 2.64x
BenchmarkAddVV_1e5 9571.91 28409.21 2.97x
BenchmarkAddVW_1 1175.28 1433.98 1.22x
BenchmarkAddVW_2 2080.01 2332.54 1.12x
BenchmarkAddVW_3 2509.28 2883.97 1.15x
BenchmarkAddVW_4 2646.09 3356.83 1.27x
BenchmarkAddVW_5 3020.69 3671.07 1.22x
BenchmarkAddVW_1e1 3425.76 4441.40 1.30x
BenchmarkAddVW_1e2 4553.17 5642.96 1.24x
BenchmarkAddVW_1e3 5100.14 6318.72 1.24x
BenchmarkAddVW_1e4 5186.15 6350.96 1.22x
BenchmarkAddVW_1e5 5104.07 5990.74 1.17x
Change-Id: I7a62023b1105248a0e85e5b9819d3fd4266123d4
Reviewed-on: https://go-review.googlesource.com/2480
Reviewed-by: Russ Cox <rsc@golang.org>
Reviewed-by: Alan Donovan <adonovan@google.com>
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Preparation was in CL 134570043.
This CL contains only the effect of 'hg mv src/pkg/* src'.
For more about the move, see golang.org/s/go14nopkg.
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