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797 Commits
| Author | SHA1 | Message | Date | |
|---|---|---|---|---|
Julian Zhu
|
e7e45d770c |
math: add assembly func archExp and archExp2 for riscv64
goos: linux
goarch: riscv64
pkg: math
│ math-old │ math-new │
│ sec/op │ sec/op vs base │
Exp-64 41.21n ± 0% 32.03n ± 0% -22.28% (p=0.000 n=8)
Exp2-64 38.86n ± 1% 28.18n ± 0% -27.49% (p=0.000 n=8)
Exp2Go-64 40.36n ± 1% 40.51n ± 1% +0.36% (p=0.049 n=8)
Frexp-64 5.681n ± 1% 5.446n ± 0% -4.14% (p=0.000 n=8)
Ldexp-64 7.676n ± 1% 7.555n ± 0% -1.58% (p=0.001 n=8)
Change-Id: Ic122bf9598302f947c6dbf751db591f403c50373
Reviewed-on: https://go-review.googlesource.com/c/go/+/754687
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Carlos Amedee <carlos@golang.org>
Reviewed-by: Meng Zhuo <mengzhuo1203@gmail.com>
Reviewed-by: Dmitri Shuralyov <dmitshur@google.com>
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Meng Zhuo
|
f6be78b539 |
math: add benchmark for float32/float64 conversions
This CL adds benchmarks for float32/float64 conversions for following functions: - Abs - Sqrt - Round - RoundToEven - Floor - Ceil - Trunc Update #75463 Change-Id: Idb57e2e28a0fb59321e480cd676115c6e540cf4f Reviewed-on: https://go-review.googlesource.com/c/go/+/734680 LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Junyang Shao <shaojunyang@google.com> Reviewed-by: Joel Sing <joel@sing.id.au> Reviewed-by: David Chase <drchase@google.com> |
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limeidan
|
287451f09c |
math/big: optimize the implementation of lshVU on loong64
Change-Id: I1aac166aea4f907a7fb93028a39ef9d1e3888c9c Reviewed-on: https://go-review.googlesource.com/c/go/+/743800 Reviewed-by: Michael Pratt <mpratt@google.com> Auto-Submit: Michael Pratt <mpratt@google.com> Reviewed-by: Junyang Shao <shaojunyang@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: abner chenc <chenguoqi@loongson.cn> |
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Xiaolin Zhao
|
7f0f671951 |
math: optimize the floating-point pipeline on loong64
Using the FSEL instruction on loong64 to eliminate branches and reduce
pipeline interruptions.
On the Loongson CPU 3A6000, there is a 0.09% performance improvement, as follows:
goos: linux
goarch: loong64
pkg: math/big
cpu: Loongson-3A6000-HV @ 2500.00MHz
│ old.bench │ new.bench │
│ sec/op │ sec/op vs base │
Exp 7.748m ± 0% 7.740m ± 0% -0.10% (p=0.001 n=10)
Exp2 7.747m ± 0% 7.741m ± 0% -0.09% (p=0.002 n=10)
geomean 7.747m 7.740m -0.09%
Change-Id: If62f2e81bf345c83a1fa9350ace131240cfa3b9b
Reviewed-on: https://go-review.googlesource.com/c/go/+/693458
Reviewed-by: Dmitri Shuralyov <dmitshur@google.com>
Reviewed-by: Cherry Mui <cherryyz@google.com>
Reviewed-by: abner chenc <chenguoqi@loongson.cn>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Meidan Li <limeidan@loongson.cn>
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mohanson
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c04335e33a |
math/pow10: remove overlapping boundary (n=0)
Both the first and second conditions include n=0, creating an implicit logic that relies on order of evaluation. Change-Id: Iefbc25a676242fabf272203a3e845363585bff56 Reviewed-on: https://go-review.googlesource.com/c/go/+/730060 Reviewed-by: Robert Griesemer <gri@google.com> Reviewed-by: Carlos Amedee <carlos@golang.org> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Auto-Submit: Robert Griesemer <gri@google.com> |
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mohanson
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23f7ba554d |
math: use shared signMask constant
In abs.go and copysign.go, magic numbers and local constants are used for the sign bit mask (1 << 63), even though a shared constant signMask already exists in bits.go. Change-Id: Ic3aeb9b52674538443cbe074acfeb373a3c74a8e Reviewed-on: https://go-review.googlesource.com/c/go/+/732060 LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Auto-Submit: Robert Griesemer <gri@google.com> Reviewed-by: Carlos Amedee <carlos@golang.org> Reviewed-by: Robert Griesemer <gri@google.com> |
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Srinivas Pokala
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489d3dafb7 |
math: switch s390x math.Pow to generic implementation
The s390x assembly implementation of math.Pow incorrectly handles certain subnormal cases. This change switches the function to use the generic implementation instead. Updates #76247 Cq-Include-Trybots: luci.golang.try:gotip-linux-s390x Change-Id: I794339080d5a7acf79bbffaeb0214809006fd30c Reviewed-on: https://go-review.googlesource.com/c/go/+/720540 Reviewed-by: Vishwanatha HD <vishwanatha.hd@ibm.com> Reviewed-by: Michael Pratt <mpratt@google.com> Auto-Submit: Michael Pratt <mpratt@google.com> Reviewed-by: Kiran M Vijay IBM <kiran.m.vijay@ibm.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Mark Freeman <markfreeman@google.com> |
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Alan Donovan
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4bfc3a9d14 |
std,cmd: go fix -any std cmd
This change mechanically replaces all occurrences of interface{}
by 'any' (where deemed safe by the 'any' modernizer) throughout
std and cmd, minus their vendor trees.
Since this fix is relatively numerous, it gets its own CL.
Also, 'go generate go/types'.
Change-Id: I14a6b52856c3291c1d27935409bca8d5fd4242a2
Reviewed-on: https://go-review.googlesource.com/c/go/+/719702
Commit-Queue: Alan Donovan <adonovan@google.com>
Reviewed-by: Dmitri Shuralyov <dmitshur@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Dmitri Shuralyov <dmitshur@golang.org>
Auto-Submit: Alan Donovan <adonovan@google.com>
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Joel Sing
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bc5ffe5c79 |
internal/runtime/sys,math/bits: eliminate bounds checks on len8tab
The compiler cannot currently determine that the accesses to len8tab are within bounds. Cast to uint8 to avoid unnecessary bounds checks. Fixes #76166 Change-Id: I1fd930bba2b20d3998252c476308642e08ce00b4 Reviewed-on: https://go-review.googlesource.com/c/go/+/718040 Reviewed-by: Meng Zhuo <mengzhuo1203@gmail.com> Reviewed-by: Keith Randall <khr@google.com> Reviewed-by: Keith Randall <khr@golang.org> Auto-Submit: Keith Randall <khr@golang.org> Reviewed-by: Junyang Shao <shaojunyang@google.com> Auto-Submit: Joel Sing <joel@sing.id.au> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> |
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Tobias Klauser
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b5aefe07e5 |
all: remove unnecessary loop variable copies in tests
Copying the loop variable is no longer necessary since Go 1.22. Change-Id: Iebb21dac44a20ec200567f1d786f105a4ee4999d Reviewed-on: https://go-review.googlesource.com/c/go/+/711640 Reviewed-by: Florian Lehner <lehner.florian86@gmail.com> Auto-Submit: Damien Neil <dneil@google.com> Reviewed-by: Dmitri Shuralyov <dmitshur@google.com> Reviewed-by: Damien Neil <dneil@google.com> Auto-Submit: Tobias Klauser <tobias.klauser@gmail.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> |
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Michael Munday
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3e596d448f |
math: rename Modf parameter int to integer
Avoid using int as a parameter name. Also, rename frac to fractional for consistency. Addresses comment on CL 694896: https://go-review.googlesource.com/c/go/+/694896/comment/a9723a07_8352e3aa/ Change-Id: Icedeecf65ad2f51d4e8d5bcf6e64c0eae9885dec Reviewed-on: https://go-review.googlesource.com/c/go/+/699035 Auto-Submit: Sean Liao <sean@liao.dev> Reviewed-by: Cherry Mui <cherryyz@google.com> Reviewed-by: Michael Pratt <mpratt@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Sean Liao <sean@liao.dev> Reviewed-by: Joel Sing <joel@sing.id.au> |
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Michael Munday
|
25c2d4109f |
math: use Trunc to implement Modf
By implementing Modf using Trunc, rather than the other way round,
we can get a significant performance improvement on platforms where
Trunc is implemented as an intrinsic.
Trunc is implemented as an intrinsic on ppc64x and arm64 so the assembly
implementations of Modf are no longer needed (the compiler can generate
very similar code that can now potentially be inlined).
GOAMD64=v1
goos: linux
goarch: amd64
pkg: math
cpu: 12th Gen Intel(R) Core(TM) i7-12700T
│ sec/op │ sec/op vs base │
Gamma 4.257n ± 0% 3.890n ± 0% -8.61% (p=0.000 n=10)
Modf 1.6110n ± 0% 0.4243n ± 0% -73.67% (p=0.000 n=10)
geomean 2.619n 1.285n -50.94%
GOAMD64=v2
goos: linux
goarch: amd64
pkg: math
cpu: 12th Gen Intel(R) Core(TM) i7-12700T
│ sec/op │ sec/op vs base │
Gamma 4.100n ± 1% 3.717n ± 0% -9.35% (p=0.000 n=10)
Modf 1.6070n ± 0% 0.2158n ± 1% -86.57% (p=0.000 n=10)
geomean 2.567n 0.8957n -65.11%
Change-Id: I689a560c344cf1d39ef002b540749bacc3179786
Reviewed-on: https://go-review.googlesource.com/c/go/+/694896
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Sean Liao <sean@liao.dev>
Reviewed-by: Cherry Mui <cherryyz@google.com>
Reviewed-by: Keith Randall <khr@google.com>
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Michael Munday
|
4e05a070c4 |
math: implement IsInf using Abs
Abs is an intrinsic (or a relatively cheap operation) on most
architectures. Using it in IsInf typically saves a branch when
`sign` is 0 (note the `sign` variable is typically a constant).
This change doesn't make a huge difference on amd64 (these
benchmarks are fairly noisy too) but removing the branch will
allow rewrite rules to detect and optimize infinity checks on
other architectures. For example, riscv64 can check for
infinities with the FCLASSD instruction and s390x can use the
TCDB instruction.
goos: linux
goarch: amd64
pkg: math
cpu: 12th Gen Intel(R) Core(TM) i7-12700T
│ sec/op │ sec/op vs base │
Acos 4.317n ± 1% 4.321n ± 0% ~ (p=0.466 n=10)
Acosh 8.857n ± 1% 8.411n ± 2% -5.05% (p=0.001 n=10)
Asin 4.260n ± 1% 4.204n ± 6% -1.31% (p=0.021 n=10)
Asinh 10.63n ± 2% 10.37n ± 0% -2.49% (p=0.000 n=10)
Atan 2.493n ± 1% 2.368n ± 0% -5.01% (p=0.000 n=10)
Atanh 8.820n ± 4% 8.770n ± 2% ~ (p=0.579 n=10)
Atan2 4.212n ± 1% 4.066n ± 11% -3.45% (p=0.023 n=10)
Cbrt 4.859n ± 0% 4.845n ± 0% -0.29% (p=0.000 n=10)
Ceil 0.3877n ± 3% 0.2514n ± 0% -35.17% (p=0.000 n=10)
Copysign 0.3479n ± 2% 0.4179n ± 0% +20.14% (p=0.000 n=10)
Cos 4.734n ± 2% 4.486n ± 0% -5.26% (p=0.000 n=10)
Cosh 5.244n ± 0% 5.071n ± 0% -3.29% (p=0.000 n=10)
Erf 2.975n ± 1% 2.788n ± 0% -6.29% (p=0.000 n=10)
Erfc 3.259n ± 1% 3.121n ± 0% -4.23% (p=0.000 n=10)
Erfinv 4.015n ± 1% 3.904n ± 0% -2.76% (p=0.000 n=10)
Erfcinv 4.166n ± 1% 4.039n ± 0% -3.04% (p=0.000 n=10)
Exp 3.567n ± 1% 3.429n ± 0% -3.87% (p=0.000 n=10)
ExpGo 9.173n ± 1% 8.368n ± 2% -8.78% (p=0.000 n=10)
Expm1 4.466n ± 3% 4.419n ± 0% -1.05% (p=0.000 n=10)
Exp2 8.328n ± 0% 8.046n ± 0% -3.39% (p=0.000 n=10)
Exp2Go 8.796n ± 5% 8.237n ± 2% -6.36% (p=0.000 n=10)
Abs 0.2400n ± 2% 0.2144n ± 0% -10.71% (p=0.000 n=10)
Dim 0.4077n ± 3% 0.3795n ± 1% -6.91% (p=0.000 n=10)
Floor 0.3616n ± 2% 0.2528n ± 3% -30.10% (p=0.000 n=10)
Max 1.401n ± 1% 1.344n ± 1% -4.14% (p=0.000 n=10)
Min 1.391n ± 1% 1.345n ± 1% -3.27% (p=0.000 n=10)
Mod 15.45n ± 1% 15.62n ± 2% ~ (p=0.066 n=10)
Frexp 1.838n ± 2% 1.605n ± 1% -12.70% (p=0.000 n=10)
Gamma 4.465n ± 1% 4.458n ± 1% ~ (p=0.256 n=10)
Hypot 2.237n ± 1% 2.208n ± 0% -1.32% (p=0.000 n=10)
HypotGo 2.610n ± 3% 2.663n ± 5% ~ (p=0.280 n=10)
Ilogb 1.793n ± 1% 1.566n ± 1% -12.66% (p=0.000 n=10)
J0 22.11n ± 1% 21.45n ± 1% -2.99% (p=0.000 n=10)
J1 21.71n ± 1% 21.38n ± 1% -1.54% (p=0.000 n=10)
Jn 46.43n ± 1% 45.83n ± 1% -1.30% (p=0.001 n=10)
Ldexp 2.360n ± 1% 2.111n ± 1% -10.51% (p=0.000 n=10)
Lgamma 4.728n ± 1% 4.850n ± 2% +2.59% (p=0.000 n=10)
Log 4.304n ± 2% 4.228n ± 1% -1.78% (p=0.000 n=10)
Logb 1.833n ± 2% 1.635n ± 2% -10.80% (p=0.000 n=10)
Log1p 5.262n ± 2% 5.173n ± 2% -1.69% (p=0.001 n=10)
Log10 4.534n ± 1% 4.474n ± 1% -1.33% (p=0.024 n=10)
Log2 2.510n ± 2% 2.246n ± 2% -10.48% (p=0.000 n=10)
Modf 1.712n ± 3% 1.700n ± 1% ~ (p=0.055 n=10)
Nextafter32 2.190n ± 3% 2.187n ± 0% ~ (p=0.266 n=10)
Nextafter64 2.184n ± 0% 2.183n ± 0% -0.05% (p=0.017 n=10)
PowInt 11.45n ± 7% 11.32n ± 9% ~ (p=0.137 n=10)
PowFrac 27.46n ± 3% 27.04n ± 1% -1.55% (p=0.001 n=10)
Pow10Pos 0.5367n ± 3% 0.5466n ± 2% +1.84% (p=0.009 n=10)
Pow10Neg 0.8939n ± 1% 0.8720n ± 2% -2.45% (p=0.000 n=10)
Round 1.218n ± 1% 1.198n ± 1% -1.56% (p=0.005 n=10)
RoundToEven 1.711n ± 0% 1.710n ± 0% ~ (p=0.464 n=10)
Remainder 12.87n ± 10% 13.79n ± 14% +7.11% (p=0.027 n=10)
Signbit 0.4072n ± 2% 0.3839n ± 2% -5.71% (p=0.000 n=10)
Sin 4.102n ± 1% 4.058n ± 3% ~ (p=0.138 n=10)
Sincos 5.837n ± 1% 5.715n ± 2% -2.10% (p=0.000 n=10)
Sinh 5.622n ± 1% 5.567n ± 2% -0.96% (p=0.006 n=10)
SqrtIndirect 0.4284n ± 0% 0.4279n ± 0% ~ (p=0.084 n=10)
SqrtLatency 2.779n ± 0% 2.777n ± 0% ~ (p=0.089 n=10)
SqrtIndirectLatency 2.777n ± 0% 2.778n ± 0% ~ (p=0.305 n=10)
SqrtGoLatency 24.00n ± 0% 24.51n ± 0% +2.12% (p=0.000 n=10)
SqrtPrime 673.0n ± 0% 673.0n ± 0% ~ (p=0.574 n=10)
Tan 4.111n ± 4% 4.123n ± 5% ~ (p=0.424 n=10)
Tanh 5.787n ± 1% 5.723n ± 1% -1.11% (p=0.010 n=10)
Trunc 0.3441n ± 3% 0.2596n ± 2% -24.56% (p=0.000 n=10)
Y0 21.63n ± 2% 21.07n ± 2% -2.61% (p=0.001 n=10)
Y1 21.42n ± 1% 20.93n ± 3% -2.29% (p=0.041 n=10)
Yn 45.78n ± 1% 45.83n ± 1% ~ (p=0.671 n=10)
Float64bits 0.2187n ± 2% 0.2199n ± 2% ~ (p=0.138 n=10)
Float64frombits 0.2198n ± 1% 0.2199n ± 1% ~ (p=0.956 n=10)
Float32bits 0.2237n ± 2% 0.2213n ± 1% ~ (p=0.060 n=10)
Float32frombits 0.2251n ± 1% 0.2219n ± 2% -1.42% (p=0.000 n=10)
FMA 0.8557n ± 1% 0.8555n ± 0% ~ (p=0.286 n=10)
geomean 3.186n 3.070n -3.61%
Change-Id: I4814bb1e3d9d20e9d8cd7689e8d5383e36b00331
Reviewed-on: https://go-review.googlesource.com/c/go/+/694955
Reviewed-by: Cherry Mui <cherryyz@google.com>
Reviewed-by: Sean Liao <sean@liao.dev>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Keith Randall <khr@google.com>
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Michael Munday
|
1eed4f32a0 |
math: optimize Signbit implementation slightly
This small tweak to Signbit improves code generation on riscv64 and
possibly other architectures by removing the need to apply a 64 bit
mask.
Before:
MOV $-9223372036854775808, X6
AND X6, X5, X5
SNEZ X5, X10
After:
SLTI $0, X5, X10
This transformation could also be added to the optimization rules
but it is quite a special case.
goos: linux
goarch: riscv64
pkg: math
cpu: Spacemit(R) X60
│ sec/op │ sec/op vs base │
Signbit 13.05n ± 0% 11.42n ± 0% -12.49% (p=0.000 n=10)
Change-Id: Ic218017c5bbb720ec24c6fe7cc230df539b2630c
Reviewed-on: https://go-review.googlesource.com/c/go/+/698419
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Sean Liao <sean@liao.dev>
Reviewed-by: Cherry Mui <cherryyz@google.com>
Auto-Submit: Sean Liao <sean@liao.dev>
Reviewed-by: Florian Lehner <lehner.florian86@gmail.com>
Reviewed-by: Carlos Amedee <carlos@golang.org>
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Michael Munday
|
0201524c52 |
math: remove redundant infinity tests
These cases are covered by existing comparisons against constants. Change-Id: I19ad530e95d2437a8617f5229495da591ceb779a Reviewed-on: https://go-review.googlesource.com/c/go/+/692255 Reviewed-by: Dmitri Shuralyov <dmitshur@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Sean Liao <sean@liao.dev> Reviewed-by: Russ Cox <rsc@golang.org> Auto-Submit: Sean Liao <sean@liao.dev> |
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ICHINOSE Shogo
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498899e205 |
math: fix portable FMA implementation when x*y ~ 0, x*y < 0 and z = 0
Adding zero usually does not change the original value.
However, there is an exception with negative zero. (e.g. (-0) + (+0) = (+0))
This applies when x * y is negative and underflows.
Fixes #73757
Change-Id: Ib7b54bdacd1dcfe3d392802ea35cdb4e989f9371
GitHub-Last-Rev:
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Julian Zhu
|
6109185cf9 |
math/big: fix incorrect register allocation for mipsx/mips64x
According to the MIPS ABI, R26/R27 are reserved for OS kernel, and may be clobbered by it. They must not be used by user mode. See Figure 3-18 of MIPS ELF ABI specification: https://refspecs.linuxfoundation.org/elf/mipsabi.pdf Fixes #73472 Change-Id: Ifda692a803176bfaab2c70d6623636c5d135f42e Reviewed-on: https://go-review.googlesource.com/c/go/+/667816 Reviewed-by: Alan Donovan <adonovan@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Dmitri Shuralyov <dmitshur@google.com> Reviewed-by: Keith Randall <khr@google.com> |
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Russ Cox
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a4d0269a4f |
math/big: use clearer loop bounds check elimination
Checking that the lengths are equal and panicking teaches the compiler that it can assume “i in range for z” implies “i in range for x”, letting us simplify the actual loops a bit. It also turns up a few places in math/big that were playing maybe a little too fast and loose with slice lengths. Update those to explicitly set all the input slices to the same length. These speedups are basically irrelevant, since they only happen in real code if people are compiling with -tags math_big_pure_go. But at least the code is clearer. benchmark \ system c3h88 c2s16 s7 386 s7-386 c4as16 mac arm loong64 ppc64le riscv64 s390x AddVV/words=1/impl=go ~ +11.20% +5.11% -7.67% -7.77% +1.90% +10.76% -33.22% ~ +10.98% ~ +6.60% AddVV/words=10/impl=go -22.12% -13.48% -10.37% -17.95% -18.07% -24.58% -22.04% -29.95% -14.22% ~ -6.33% +3.66% AddVV/words=16/impl=go -9.75% -13.73% ~ -21.90% -18.66% -30.03% -20.45% -28.09% -17.33% -7.15% -8.96% +12.55% AddVV/words=100/impl=go -5.91% -1.02% ~ -29.23% -22.18% -25.62% -6.49% -23.59% -22.31% -1.88% -14.13% +9.23% AddVV/words=1000/impl=go -0.52% -0.19% -3.58% -33.89% -23.46% -22.46% ~ -24.00% -24.73% +0.93% -15.79% +12.32% AddVV/words=10000/impl=go ~ ~ ~ -33.79% -23.72% -23.79% -5.98% -23.92% ~ +0.78% -15.45% +8.59% AddVV/words=100000/impl=go ~ ~ ~ -33.90% -24.25% -22.82% -4.09% -24.63% ~ +1.00% -13.56% ~ SubVV/words=1/impl=go ~ +11.64% +14.05% ~ -4.07% ~ +10.79% -33.69% ~ ~ +3.89% +12.33% SubVV/words=10/impl=go -10.31% -14.09% -7.38% +13.76% -13.25% -18.05% -20.08% -24.97% -14.15% +10.13% -0.97% -2.51% SubVV/words=16/impl=go -8.06% -13.73% -5.70% +17.00% -12.83% -23.76% -17.52% -25.25% -17.30% -2.80% -4.96% -18.25% SubVV/words=100/impl=go -9.22% -1.30% -2.76% +20.88% -14.35% -15.29% -8.49% -19.64% -22.31% -0.68% -14.30% -9.04% SubVV/words=1000/impl=go -0.60% ~ -3.43% +23.08% -16.14% -11.96% ~ -28.52% -24.73% ~ -15.95% -9.91% SubVV/words=10000/impl=go ~ ~ ~ +26.01% -15.24% -11.92% ~ -28.26% +4.25% ~ -15.42% -5.95% SubVV/words=100000/impl=go ~ ~ ~ +25.71% -15.83% -12.13% ~ -27.88% -1.27% ~ -13.57% -6.72% LshVU/words=1/impl=go +0.56% +0.36% ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ LshVU/words=10/impl=go +13.37% +4.63% ~ ~ ~ ~ ~ -2.90% ~ ~ ~ ~ LshVU/words=16/impl=go +22.83% +6.47% ~ ~ ~ ~ ~ ~ +0.80% ~ ~ +5.88% LshVU/words=100/impl=go +7.56% +13.95% ~ ~ ~ ~ ~ ~ +0.33% -2.50% ~ ~ LshVU/words=1000/impl=go +0.64% +17.92% ~ ~ ~ ~ ~ -6.52% ~ -2.58% ~ ~ LshVU/words=10000/impl=go ~ +17.60% ~ ~ ~ ~ ~ -6.64% -6.22% -1.40% ~ ~ LshVU/words=100000/impl=go ~ +14.57% ~ ~ ~ ~ ~ ~ -5.47% ~ ~ ~ RshVU/words=1/impl=go ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ +2.72% RshVU/words=10/impl=go ~ ~ ~ ~ ~ ~ ~ +2.50% ~ ~ ~ ~ RshVU/words=16/impl=go ~ +0.53% ~ ~ ~ ~ ~ +3.82% ~ ~ ~ ~ RshVU/words=100/impl=go ~ ~ ~ ~ ~ ~ ~ +6.18% ~ ~ ~ ~ RshVU/words=1000/impl=go ~ ~ ~ ~ ~ ~ ~ +7.00% ~ ~ ~ ~ RshVU/words=10000/impl=go ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ RshVU/words=100000/impl=go ~ ~ ~ ~ ~ ~ ~ +7.05% ~ ~ ~ ~ MulAddVWW/words=1/impl=go -10.34% +4.43% +10.62% -1.62% -4.74% -2.86% +11.75% ~ -8.00% +8.89% +3.87% ~ MulAddVWW/words=10/impl=go -1.61% -5.87% ~ -8.30% -4.55% +0.87% ~ -5.28% -20.82% ~ ~ -2.32% MulAddVWW/words=16/impl=go -2.96% -5.28% ~ -9.22% -5.28% ~ ~ -3.74% -19.52% -1.48% -2.53% -9.52% MulAddVWW/words=100/impl=go -3.89% -7.53% +1.93% -10.49% -4.87% -8.27% ~ ~ -0.65% -0.61% -7.59% -20.61% MulAddVWW/words=1000/impl=go -0.45% -3.91% +4.54% -11.46% -4.69% -8.53% ~ ~ -0.05% ~ -8.88% -19.77% MulAddVWW/words=10000/impl=go ~ -3.30% +4.10% -11.34% -4.10% -9.43% ~ -0.61% ~ -0.55% -8.21% -18.48% MulAddVWW/words=100000/impl=go -0.30% -3.03% +4.31% -11.55% -4.41% -9.74% ~ -0.75% +0.63% ~ -7.80% -19.82% AddMulVVWW/words=1/impl=go ~ +13.09% +12.50% -7.05% -10.41% +2.53% +13.32% -3.49% ~ +15.56% +3.62% ~ AddMulVVWW/words=10/impl=go -15.96% -9.06% -5.06% -14.56% -11.83% -5.44% -26.30% -14.23% -11.44% -1.79% -5.93% -6.60% AddMulVVWW/words=16/impl=go -19.05% -12.43% -6.19% -14.24% -12.67% -8.65% -18.64% -16.56% -10.64% -3.00% -7.61% -12.80% AddMulVVWW/words=100/impl=go -22.13% -16.59% -13.04% -13.79% -11.46% -12.01% -6.46% -21.80% -5.08% -3.13% -13.60% -22.53% AddMulVVWW/words=1000/impl=go -17.07% -17.05% -14.08% -13.59% -12.13% -11.21% ~ -22.81% -4.27% -1.27% -16.35% -23.47% AddMulVVWW/words=10000/impl=go -15.03% -16.78% -14.23% -13.86% -11.84% -11.69% ~ -22.75% -13.39% -1.10% -14.37% -22.01% AddMulVVWW/words=100000/impl=go -13.70% -14.90% -14.26% -13.55% -12.04% -11.63% ~ -22.61% ~ -2.53% -10.42% -23.16% Change-Id: Ic6f64344484a762b818c7090d1396afceb638607 Reviewed-on: https://go-review.googlesource.com/c/go/+/665155 Auto-Submit: Russ Cox <rsc@golang.org> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Alan Donovan <adonovan@google.com> |
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Russ Cox
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7f516a31b0 |
math/big: replace assembly with mini-compiler output
Step 4 of the mini-compiler: switch to the new generated assembly. No systematic performance regressions, and many many improvements. In the benchmarks, the systems are: c3h88 GOARCH=amd64 c3h88 perf gomote (newer Intel, Google Cloud) c2s16 GOARCH=amd64 c2s16 perf gomote (Intel, Google Cloud) s7 GOARCH=amd64 rsc basement server (AMD Ryzen 9 7950X) 386 GOARCH=386 gotip-linux-386 gomote (Intel, Google Cloud) s7-386 GOARCH=386 rsc basement server (AMD Ryzen 9 7950X) c4as16 GOARCH=arm64 c4as16 perf gomote (Google Cloud) mac GOARCH=arm64 Apple M3 Pro in MacBook Pro 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 s390x GOARCH=s390x linux-s390x-ibm old gomote benchmark \ system c3h88 c2s16 s7 386 s7-386 c4as16 mac arm loong64 ppc64le riscv64 s390x AddVV/words=1 -4.03% +5.21% -4.04% +4.94% ~ ~ ~ ~ -19.51% ~ ~ ~ AddVV/words=10 -10.20% +0.34% -3.46% -11.50% -7.46% +7.66% +5.97% ~ -17.90% ~ ~ ~ AddVV/words=16 -10.91% -6.45% -8.45% -21.86% -17.90% +2.73% -1.61% ~ -22.47% -3.54% ~ ~ AddVV/words=100 -3.77% -4.30% -3.17% -47.27% -45.34% -0.78% ~ -8.74% -27.19% ~ ~ ~ AddVV/words=1000 -0.08% -0.71% ~ -49.21% -48.07% ~ ~ -16.80% -24.74% ~ ~ ~ AddVV/words=10000 ~ ~ ~ -48.73% -48.56% -0.06% ~ -17.08% ~ ~ -4.81% ~ AddVV/words=100000 ~ ~ ~ -47.80% -48.38% ~ ~ -15.10% -25.06% ~ -5.34% ~ SubVV/words=1 -0.84% +3.43% -3.62% +1.34% ~ -0.76% ~ ~ -18.18% +5.58% ~ ~ SubVV/words=10 -9.99% +0.34% ~ -11.23% -8.24% +7.53% +6.15% ~ -17.55% +2.77% -2.08% ~ SubVV/words=16 -11.94% -6.45% -6.81% -21.82% -18.11% +1.58% -1.21% ~ -20.36% ~ ~ ~ SubVV/words=100 -3.38% -4.32% -1.80% -46.14% -46.43% +0.41% ~ -7.20% -26.17% ~ -0.42% ~ SubVV/words=1000 -0.38% -0.80% ~ -49.22% -48.90% ~ ~ -15.86% -24.73% ~ ~ ~ SubVV/words=10000 ~ ~ ~ -49.57% -49.64% -0.03% ~ -15.85% -26.52% ~ -5.05% ~ SubVV/words=100000 ~ ~ ~ -46.88% -49.66% ~ ~ -15.45% -16.11% ~ -4.99% ~ LshVU/words=1 ~ +5.78% ~ ~ -2.48% +1.61% +2.18% +2.70% -18.16% -34.16% -21.29% ~ LshVU/words=10 -18.34% -3.78% +2.21% ~ ~ -2.81% -12.54% ~ -25.02% -24.78% -38.11% -66.98% LshVU/words=16 -23.15% +1.03% +7.74% +0.73% ~ +8.88% +1.56% ~ -25.37% -28.46% -41.27% ~ LshVU/words=100 -32.85% -8.86% -2.58% ~ +2.69% +1.24% ~ -20.63% -44.14% -42.68% -53.09% ~ LshVU/words=1000 -37.30% -0.20% +5.67% ~ ~ +1.44% ~ -27.83% -45.01% -37.07% -57.02% -46.57% LshVU/words=10000 -36.84% -2.30% +3.82% ~ +1.86% +1.57% -66.81% -28.00% -13.15% -35.40% -41.97% ~ LshVU/words=100000 -40.30% ~ +3.96% ~ ~ ~ ~ -24.91% -19.06% -36.14% -40.99% -66.03% RshVU/words=1 -3.17% +4.76% -4.06% +4.31% +4.55% ~ ~ ~ -20.61% ~ -26.20% -51.33% RshVU/words=10 -22.08% -4.41% -17.99% +3.64% -11.87% ~ -16.30% ~ -30.01% ~ -40.37% -63.05% RshVU/words=16 -26.03% -8.50% -18.09% ~ -17.52% +6.50% ~ -2.85% -30.24% ~ -42.93% -63.13% RshVU/words=100 -20.87% -28.83% -29.45% ~ -26.25% +1.46% -1.14% -16.20% -45.65% -16.20% -53.66% -77.27% RshVU/words=1000 -24.03% -21.37% -26.71% ~ -28.95% +0.98% ~ -18.82% -45.21% -23.55% -57.09% -71.18% RshVU/words=10000 -24.56% -22.44% -27.01% ~ -28.88% +0.78% -5.35% -17.47% -16.87% -20.67% -41.97% ~ RshVU/words=100000 -23.36% -15.65% -27.54% ~ -29.26% +1.73% -6.67% -13.68% -21.40% -23.02% -40.37% -66.31% MulAddVWW/words=1 +2.37% +8.14% ~ +4.10% +3.71% ~ ~ ~ -21.62% ~ +1.12% ~ MulAddVWW/words=10 ~ -2.72% -15.15% +8.04% ~ ~ ~ -2.52% -19.48% ~ -6.18% ~ MulAddVWW/words=16 ~ +1.49% ~ +4.49% +6.58% -8.70% -7.16% -12.08% -21.43% -6.59% -9.05% ~ MulAddVWW/words=100 +0.37% +1.11% -4.51% -13.59% ~ -11.10% -3.63% -21.40% -22.27% -2.92% -14.41% ~ MulAddVWW/words=1000 ~ +0.90% -7.13% -18.94% ~ -14.02% -9.97% -28.31% -18.72% -2.32% -15.80% ~ MulAddVWW/words=10000 ~ +1.08% -6.75% -19.10% ~ -14.61% -9.04% -28.48% -14.29% -2.25% -9.40% ~ MulAddVWW/words=100000 ~ ~ -6.93% -18.09% ~ -14.33% -9.66% -28.92% -16.63% -2.43% -8.23% ~ AddMulVVWW/words=1 +2.30% +4.83% -11.37% +4.58% ~ -3.14% ~ ~ -10.58% +30.35% ~ ~ AddMulVVWW/words=10 -3.27% ~ +8.96% +5.74% ~ +2.67% -1.44% -7.64% -13.41% ~ ~ ~ AddMulVVWW/words=16 -6.12% ~ ~ ~ +1.91% -7.90% -16.22% -14.07% -14.26% -4.15% -7.30% ~ AddMulVVWW/words=100 -5.48% -2.14% ~ -9.40% +9.98% -1.43% -12.35% -18.56% -21.94% ~ -9.84% ~ AddMulVVWW/words=1000 -11.35% -3.40% -3.64% -11.04% +12.82% -1.33% -15.63% -20.50% -20.95% ~ -11.06% -51.97% AddMulVVWW/words=10000 -10.31% -1.61% -8.41% -12.15% +13.10% -1.03% -16.34% -22.46% -1.00% ~ -10.33% -49.80% AddMulVVWW/words=100000 -13.71% ~ -8.31% -12.18% +12.98% -1.35% -15.20% -21.89% ~ ~ -9.38% -48.30% Change-Id: I0a33c33602c0d053c84d9946e662500cfa048e2d Reviewed-on: https://go-review.googlesource.com/c/go/+/664938 Reviewed-by: Alan Donovan <adonovan@google.com> Auto-Submit: Russ Cox <rsc@golang.org> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> |
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Russ Cox
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39070da4f8 |
math/big: add shift and mul to mini-compiler
Step 3 of the mini-compiler: add the generators for the shift and mul routines. Change-Id: I981d5b7086262c740036f5db768d3e63083984e2 Reviewed-on: https://go-review.googlesource.com/c/go/+/664937 Auto-Submit: Russ Cox <rsc@golang.org> Reviewed-by: Alan Donovan <adonovan@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> |
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Russ Cox
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2a88106617 |
math/big: add all architectures to mini-compiler
Step 2 of the mini-compiler: add all the remaining architectures. Change-Id: I8c5283aa8baa497785a5c15f2248528fa9ae886e Reviewed-on: https://go-review.googlesource.com/c/go/+/664936 LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Alan Donovan <adonovan@google.com> Auto-Submit: Russ Cox <rsc@golang.org> |
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Russ Cox
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8cc98a04ef |
math/big: new mini-compiler for arith assembly
The arith assembly is big enough, and the details that you have to keep in mind are complex enough and varied enough, that it is worth using a Go program to generate the assembly. That way, all the architectures can use the same algorithms, and porting to new architectures will be easier. This is the first of a sequence of CLs to introduce a new mini-compiler for generating the arith assembly, in math/big/internal/asmgen. This CL has the basics of the compiler as well as a couple simple architectures and the generator for addVV/subVV. It does not check in the generated assembly yet. That will happen in a followup CL after the other architectures and generators have been added. Change-Id: Ib704c60fd972fc5690ac04d8fae3712ee2c1a80a Reviewed-on: https://go-review.googlesource.com/c/go/+/664935 LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Alan Donovan <adonovan@google.com> Auto-Submit: Russ Cox <rsc@golang.org> |
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Russ Cox
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a11643df8f |
math/big: replace addVW/subVW assembly with fast pure Go
The vast majority of the time, carry propagation is limited and addVW/subVW only need to consider a single word for carry propagation. As Josh Bleecher-Snyder pointed out in 2019 (CL 164968), once carrying is done, the remaining words can be handled faster with copy (memmove). In the benchmarks below, this is the data=random case. Even more important, if the source and destination are the same, the copy can be optimized away entirely, making a small in-place addition to a big.Int O(1) instead of O(N). To date, only a few systems (amd64, arm64, and pure Go, meaning wasm) make use of this asymptotic improvement. This is the data=shortcut case. This CL deletes the addVW/subVW assembly and replaces it with an optimized pure Go version. Using Go makes it easy to call the real copy builtin, which will use optimized memmove code, instead of recreating a worse memmove in assembly (as arm64 does) or omitting the copy optimization entirely (as most others do). The worst case for the Go version versus assembly is the case of incrementing 2^N-1 by 1, which has to propagate a carry the entire length of the array. This is the data=carry case. On balance, we believe this case is rare enough to be worth taking a hit in that case, in exchange for significant wins in the other cases and the deletion of significant amounts of assembly of varying quality. (Remember that half the assembly has the copy optimization and shortcut, while half does not.) In the benchmarks, the systems are: c2s16 GOARCH=amd64 c2s16 perf gomote (Intel, Google Cloud) c3h88 GOARCH=amd64 c3h88 perf gomote (newer Intel, Google Cloud) s7 GOARCH=amd64 rsc basement server (AMD Ryzen 9 7950X) c4as16 GOARCH=arm64 c4as16 perf gomote (Google Cloud) mac GOARCH=arm64 Apple M3 Pro in MacBook Pro 386 GOARCH=386 gotip-linux-386 gomote arm GOARCH=arm gotip-linux-arm gomote loong64 GOARCH=loong64 gotip-linux-loong64 gomote ppc64le GOARCH=ppc64le gotip-linux-ppc64le gomote riscv64 GOARCH=riscv64 gotip-linux-riscv64 gomote benchmark \ system c2s16 c3h88 s7 c4as16 mac 386 arm loong64 ppc64le riscv64 AddVW/words=1/data=random -1.15% -1.74% -5.89% -9.80% -11.54% +23.71% -12.74% -14.25% +14.67% +10.27% AddVW/words=2/data=random -2.59% ~ -4.38% -19.31% -15.41% +24.80% ~ -19.99% +13.73% +19.71% AddVW/words=3/data=random -3.75% -19.10% -3.79% -23.15% -17.04% +20.04% -10.07% -23.20% ~ +15.39% AddVW/words=4/data=random -2.84% +7.05% -8.77% -22.64% -15.77% +16.01% -7.36% -28.22% ~ +23.00% AddVW/words=5/data=random -10.97% +2.16% -12.09% -20.89% -17.14% +9.42% -4.69% -32.60% ~ +10.07% AddVW/words=6/data=random -9.87% ~ -7.54% -19.08% -6.46% ~ -3.44% -34.61% ~ +12.19% AddVW/words=7/data=random -14.36% ~ -10.09% -19.10% -10.47% -6.20% -5.06% -38.14% -11.54% +6.79% AddVW/words=8/data=random -17.50% ~ -11.06% -25.14% -12.88% -8.35% -5.11% -41.39% -14.04% +11.87% AddVW/words=9/data=random -19.76% -4.05% -15.47% -24.08% -16.50% -12.34% -21.56% -44.25% -14.82% ~ AddVW/words=10/data=random -13.89% ~ -9.69% -23.06% -8.04% -12.58% -19.25% -32.80% -11.68% ~ AddVW/words=16/data=random -29.36% -15.35% -21.86% -25.04% -19.89% -32.26% -16.29% -42.66% -25.92% -3.01% AddVW/words=32/data=random -39.02% -28.76% -39.87% -11.22% -2.85% -55.40% -31.17% -55.37% -37.92% -16.28% AddVW/words=64/data=random -25.94% -19.09% -20.60% -6.90% +8.91% -51.00% -43.72% -62.27% -44.11% -28.74% AddVW/words=100/data=random -22.79% -18.13% -18.25% ~ +33.89% -67.40% -51.77% -63.54% -53.75% -30.97% AddVW/words=1000/data=random -8.98% -3.84% ~ -3.15% ~ -93.35% -63.92% -65.66% -68.67% -42.30% AddVW/words=10000/data=random -1.38% -0.38% ~ ~ ~ -89.16% -65.18% -44.65% -70.35% -20.08% AddVW/words=100000/data=random ~ ~ ~ ~ ~ -87.03% -64.51% -36.08% -61.40% -16.53% SubVW/words=1/data=random -3.67% ~ -8.38% -10.26% -3.07% +45.78% -6.06% -11.17% ~ ~ SubVW/words=2/data=random -3.48% -10.07% -5.76% -20.14% -8.45% +44.28% ~ -19.09% ~ +16.98% SubVW/words=3/data=random -7.11% -26.64% -4.48% -22.07% -9.21% +35.61% ~ -23.93% -18.20% ~ SubVW/words=4/data=random -4.23% +7.19% -8.95% -22.62% -13.89% +33.20% -8.96% -29.96% ~ +22.23% SubVW/words=5/data=random -11.49% +1.92% -10.86% -22.27% -17.53% +24.48% -2.88% -35.19% -19.55% ~ SubVW/words=6/data=random -7.67% ~ -7.72% -18.44% -6.24% +12.03% -2.00% -39.68% -10.73% ~ SubVW/words=7/data=random -13.69% -18.32% -11.82% -18.92% -11.57% +6.63% ~ -43.54% -30.81% ~ SubVW/words=8/data=random -16.02% ~ -11.07% -24.50% -11.92% +4.32% -3.01% -46.95% -24.14% ~ SubVW/words=9/data=random -18.76% -3.34% -14.84% -23.79% -17.50% ~ -21.80% -49.98% -29.62% ~ SubVW/words=10/data=random -13.23% ~ -9.25% -21.26% -11.63% ~ -18.58% -39.19% -20.09% ~ SubVW/words=16/data=random -28.25% -13.24% -22.66% -27.18% -19.13% -23.38% -20.24% -51.01% -28.06% -3.05% SubVW/words=32/data=random -38.41% -28.88% -40.12% -11.20% -2.80% -49.17% -34.67% -63.29% -39.25% -15.20% SubVW/words=64/data=random -25.51% -19.24% -22.20% -6.57% +9.98% -48.52% -48.14% -69.50% -49.44% -27.92% SubVW/words=100/data=random -21.69% -18.51% ~ +1.92% +34.42% -65.88% -54.67% -71.24% -58.88% -30.71% SubVW/words=1000/data=random -9.81% -4.05% -2.14% -3.06% ~ -93.37% -67.33% -74.12% -68.36% -42.17% SubVW/words=10000/data=random ~ -0.52% ~ ~ ~ -88.87% -68.54% -44.94% -70.63% -19.95% SubVW/words=100000/data=random ~ ~ ~ ~ ~ -86.69% -68.09% -48.36% -62.42% -19.32% AddVW/words=1/data=shortcut -29.38% -25.38% -27.37% -23.15% -25.41% +3.01% -33.60% -36.12% -15.76% ~ AddVW/words=2/data=shortcut -32.79% -34.72% -31.47% -24.47% -28.21% -3.75% -34.66% -43.89% -23.65% -21.56% AddVW/words=3/data=shortcut -38.50% -46.83% -35.67% -26.38% -30.29% -10.41% -44.89% -47.68% -30.93% -26.85% AddVW/words=4/data=shortcut -40.40% -28.85% -34.19% -29.83% -32.95% -16.09% -42.86% -51.02% -34.19% -26.69% AddVW/words=5/data=shortcut -43.87% -35.42% -36.46% -32.59% -37.72% -20.82% -45.14% -54.01% -35.49% -30.48% AddVW/words=6/data=shortcut -46.98% -39.34% -42.22% -35.43% -38.18% -27.46% -46.72% -56.61% -40.21% -34.07% AddVW/words=7/data=shortcut -49.63% -47.97% -46.61% -35.28% -41.93% -31.14% -49.29% -58.89% -41.10% -37.01% AddVW/words=8/data=shortcut -50.48% -42.33% -45.40% -40.24% -41.74% -32.92% -50.62% -60.98% -44.85% -38.10% AddVW/words=9/data=shortcut -54.27% -43.52% -49.06% -42.16% -45.22% -37.57% -51.84% -62.91% -46.04% -40.82% AddVW/words=10/data=shortcut -56.01% -45.40% -51.42% -43.29% -46.14% -38.65% -53.65% -64.62% -47.05% -43.21% AddVW/words=16/data=shortcut -62.73% -55.66% -59.31% -56.38% -54.31% -53.16% -61.03% -72.29% -58.24% -52.57% AddVW/words=32/data=shortcut -74.00% -69.42% -71.75% -33.65% -37.35% -71.73% -72.59% -82.44% -70.87% -67.69% AddVW/words=64/data=shortcut -56.69% -52.72% -52.09% -35.48% -36.87% -84.24% -83.10% -90.37% -82.56% -80.81% AddVW/words=100/data=shortcut -56.68% -53.18% -51.49% -33.49% -37.72% -89.95% -88.21% -93.37% -88.47% -86.52% AddVW/words=1000/data=shortcut -56.68% -52.45% -51.66% -35.31% -36.65% -98.88% -98.62% -99.24% -98.78% -98.41% AddVW/words=10000/data=shortcut -56.70% -52.40% -51.92% -33.49% -36.98% -99.89% -99.86% -99.92% -99.87% -99.91% AddVW/words=100000/data=shortcut -56.67% -52.46% -52.38% -35.31% -37.20% -99.99% -99.99% -99.99% -99.99% -99.99% SubVW/words=1/data=shortcut -29.80% -20.71% -26.94% -23.24% -25.33% +26.97% -32.02% -37.85% -40.20% -12.67% SubVW/words=2/data=shortcut -35.47% -36.38% -31.93% -25.43% -30.18% +18.96% -33.48% -46.48% -39.38% -18.65% SubVW/words=3/data=shortcut -39.22% -49.96% -36.90% -25.82% -30.96% +12.53% -40.67% -51.07% -43.71% -23.78% SubVW/words=4/data=shortcut -40.46% -24.90% -34.66% -29.87% -33.97% +4.60% -42.32% -54.92% -42.83% -22.45% SubVW/words=5/data=shortcut -43.84% -34.17% -38.00% -32.55% -37.27% -2.46% -43.09% -58.18% -45.70% -26.45% SubVW/words=6/data=shortcut -47.69% -37.49% -42.73% -35.90% -37.73% -8.52% -46.55% -61.01% -44.00% -30.14% SubVW/words=7/data=shortcut -49.45% -50.66% -46.88% -34.77% -41.64% -14.46% -48.92% -63.46% -50.47% -33.39% SubVW/words=8/data=shortcut -50.45% -39.31% -47.14% -40.47% -41.70% -15.77% -50.21% -65.64% -47.71% -34.01% SubVW/words=9/data=shortcut -54.28% -43.07% -49.42% -41.34% -44.99% -19.39% -51.55% -67.61% -56.92% -36.82% SubVW/words=10/data=shortcut -56.85% -47.88% -50.92% -42.76% -45.67% -23.60% -53.04% -69.34% -60.18% -39.43% SubVW/words=16/data=shortcut -62.36% -54.83% -58.80% -55.83% -53.74% -41.04% -60.16% -76.75% -60.56% -48.63% SubVW/words=32/data=shortcut -73.68% -68.64% -71.57% -33.52% -37.34% -64.73% -72.67% -85.89% -71.87% -64.56% SubVW/words=64/data=shortcut -56.68% -51.66% -52.56% -34.75% -37.54% -80.30% -83.58% -92.39% -83.41% -78.70% SubVW/words=100/data=shortcut -56.68% -50.97% -51.57% -33.68% -36.78% -87.42% -88.53% -94.84% -88.87% -84.96% SubVW/words=1000/data=shortcut -56.68% -50.89% -52.10% -34.94% -37.77% -98.59% -98.71% -99.43% -98.80% -98.20% SubVW/words=10000/data=shortcut -56.68% -51.00% -52.44% -33.65% -37.27% -99.86% -99.87% -99.94% -99.88% -99.90% SubVW/words=100000/data=shortcut -56.68% -50.80% -52.20% -34.79% -37.46% -99.99% -99.99% -99.99% -99.99% -99.99% AddVW/words=1/data=carry -0.51% -5.29% -24.03% -26.48% ~ ~ -33.14% -30.23% ~ -20.74% AddVW/words=2/data=carry -6.36% ~ -21.05% -39.40% ~ +10.72% -29.12% -31.34% ~ -17.29% AddVW/words=3/data=carry ~ ~ -17.46% -19.53% +17.58% ~ -26.23% -23.61% +7.80% -14.34% AddVW/words=4/data=carry +19.02% +16.80% ~ ~ +28.25% ~ -27.90% -20.31% +19.16% ~ AddVW/words=5/data=carry +3.97% +53.02% ~ ~ +11.31% ~ -19.05% -17.47% +16.81% ~ AddVW/words=6/data=carry +2.98% +19.83% ~ ~ +14.84% ~ -18.48% -14.92% +18.25% ~ AddVW/words=7/data=carry ~ ~ ~ ~ +27.17% ~ -15.50% -12.74% +13.00% ~ AddVW/words=8/data=carry +0.58% +22.32% ~ +6.10% +29.63% ~ -13.04% ~ +28.46% +2.95% AddVW/words=9/data=carry ~ +31.53% ~ ~ +14.42% ~ -11.32% ~ +18.37% +3.28% AddVW/words=10/data=carry +3.94% +22.36% ~ +6.29% +19.22% ~ -11.27% ~ +20.10% +3.91% AddVW/words=16/data=carry +2.82% +14.23% ~ +10.06% +25.91% -16.12% ~ ~ +52.28% +10.40% AddVW/words=32/data=carry ~ +25.35% +13.66% ~ +34.89% -34.39% +6.51% -18.71% +41.06% +19.42% AddVW/words=64/data=carry -42.03% ~ -39.70% +6.65% +32.29% -39.94% +14.34% ~ +19.68% +20.86% AddVW/words=100/data=carry -33.95% -34.28% -39.65% ~ +27.72% -26.80% +17.40% ~ +26.39% +23.32% AddVW/words=1000/data=carry -42.49% -47.87% -47.44% +1.25% +4.25% -41.76% +23.40% ~ +25.48% +27.99% AddVW/words=10000/data=carry -41.85% -48.49% -49.43% ~ ~ -42.09% +24.61% -10.32% +40.55% +18.35% AddVW/words=100000/data=carry -28.18% -48.13% -48.24% +1.35% ~ -42.90% +24.73% -9.79% +22.55% +17.16% SubVW/words=1/data=carry -10.32% -17.16% -24.14% -26.24% ~ +18.43% -34.10% -29.54% -9.57% ~ SubVW/words=2/data=carry -19.45% -23.31% -20.74% -39.73% ~ +15.74% -28.13% -30.21% ~ -18.74% SubVW/words=3/data=carry ~ -16.18% -15.34% -19.54% +17.62% +12.39% -27.64% -27.09% ~ -14.97% SubVW/words=4/data=carry +11.67% +24.42% ~ ~ +25.11% +14.07% -28.08% -26.18% ~ ~ SubVW/words=5/data=carry +8.08% +25.64% ~ ~ +10.35% +8.12% -21.75% -25.50% ~ -4.86% SubVW/words=6/data=carry ~ +13.82% ~ ~ +12.92% +6.79% -20.25% -24.70% ~ -2.74% SubVW/words=7/data=carry ~ ~ +8.29% +4.51% +26.59% +4.62% -18.01% -24.09% ~ -1.26% SubVW/words=8/data=carry ~ +23.16% +16.19% +6.16% +25.46% +6.74% -15.57% -22.74% ~ +1.44% SubVW/words=9/data=carry ~ +30.71% +20.81% ~ +12.36% ~ -12.99% ~ ~ +3.13% SubVW/words=10/data=carry +5.03% +19.53% +14.84% +14.16% +16.12% ~ -11.64% -16.00% +15.45% +3.29% SubVW/words=16/data=carry +14.42% +15.58% +33.07% +11.43% +24.65% ~ ~ -21.90% +25.59% +9.40% SubVW/words=32/data=carry ~ +27.57% +46.58% ~ +35.35% -8.49% ~ -24.04% +11.86% +18.40% SubVW/words=64/data=carry -24.34% -27.83% -20.90% +13.34% +37.17% -14.90% ~ -8.81% +12.88% +18.92% SubVW/words=100/data=carry -25.19% -34.70% -27.45% +12.86% +28.42% -14.48% ~ ~ +25.71% +21.93% SubVW/words=1000/data=carry -24.93% -47.86% -47.26% +2.66% ~ -23.88% ~ ~ +25.99% +27.81% SubVW/words=10000/data=carry -24.17% -36.48% -49.41% +1.06% ~ -25.06% ~ -26.50% +27.94% +18.36% SubVW/words=100000/data=carry -22.51% -35.86% -49.46% +3.96% ~ -25.18% ~ -22.15% +26.86% +15.44% Change-Id: I8f252073040e674780ac6ec9912082fb205329dd Reviewed-on: https://go-review.googlesource.com/c/go/+/664898 Reviewed-by: Alan Donovan <adonovan@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> |
||
|
Russ Cox
|
b44b360dd4 |
math/big: add more complete tests and benchmarks of assembly
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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|
Keith Randall
|
f4803ddc2c |
math/big: fix loong64 assembly for vet
Vet is failing on this code because some arguments of mulAddVWW got renamed in the go decl (CL 664895) but not the assembly accessors. Looks like the assembly got written before that CL but checked in after that CL. Change-Id: I270e8db5f8327aa2029c21a126fab1231a3506a1 Reviewed-on: https://go-review.googlesource.com/c/go/+/665717 Reviewed-by: Dmitri Shuralyov <dmitshur@google.com> Reviewed-by: Keith Randall <khr@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Dmitri Shuralyov <dmitshur@golang.org> Auto-Submit: Dmitri Shuralyov <dmitshur@golang.org> |
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|
Huang Qiqi
|
396a48bea6 |
math/big: optimize subVV function for loong64
Benchmark results on Loongson 3C5000 (which is an LA464 implementation):
goos: linux
goarch: loong64
pkg: math/big
cpu: Loongson-3C5000 @ 2200.00MHz
│ test/old_3c5000_subvv.log │ test/new_3c5000_subvv.log │
│ sec/op │ sec/op vs base │
SubVV/1 10.920n ± 0% 7.657n ± 0% -29.88% (p=0.000 n=20)
SubVV/2 14.100n ± 0% 8.841n ± 0% -37.30% (p=0.000 n=20)
SubVV/3 16.38n ± 0% 11.06n ± 0% -32.48% (p=0.000 n=20)
SubVV/4 18.65n ± 0% 12.85n ± 0% -31.10% (p=0.000 n=20)
SubVV/5 20.93n ± 0% 14.79n ± 0% -29.34% (p=0.000 n=20)
SubVV/10 32.30n ± 0% 22.29n ± 0% -30.99% (p=0.000 n=20)
SubVV/100 244.3n ± 0% 149.2n ± 0% -38.93% (p=0.000 n=20)
SubVV/1000 2.292µ ± 0% 1.378µ ± 0% -39.88% (p=0.000 n=20)
SubVV/10000 26.26µ ± 0% 25.64µ ± 0% -2.33% (p=0.000 n=20)
SubVV/100000 341.3µ ± 0% 238.0µ ± 0% -30.26% (p=0.000 n=20)
geomean 209.1n 144.5n -30.86%
Change-Id: I3863c2c6728f1b0f8fecbf77de13254299c5b1cb
Reviewed-on: https://go-review.googlesource.com/c/go/+/659877
Reviewed-by: abner chenc <chenguoqi@loongson.cn>
Reviewed-by: Carlos Amedee <carlos@golang.org>
Reviewed-by: Dmitri Shuralyov <dmitshur@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
|
||
|
Huang Qiqi
|
72fa8adbdc |
math/big: optimize mulAddVWW function for loong64
Benchmark results on Loongson 3A5000 (which is an LA464 implementation):
goos: linux
goarch: loong64
pkg: math/big
cpu: Loongson-3A5000-HV @ 2500.00MHz
│ test/old_3a5000_muladdvww.log │ test/new_3a5000_muladdvww.log │
│ sec/op │ sec/op vs base │
MulAddVWW/1 7.606n ± 0% 6.987n ± 0% -8.14% (p=0.000 n=20)
MulAddVWW/2 9.207n ± 0% 8.567n ± 0% -6.95% (p=0.000 n=20)
MulAddVWW/3 10.810n ± 0% 9.223n ± 0% -14.68% (p=0.000 n=20)
MulAddVWW/4 13.01n ± 0% 12.41n ± 0% -4.61% (p=0.000 n=20)
MulAddVWW/5 15.79n ± 0% 12.99n ± 0% -17.73% (p=0.000 n=20)
MulAddVWW/10 25.62n ± 0% 20.02n ± 0% -21.86% (p=0.000 n=20)
MulAddVWW/100 217.0n ± 0% 170.9n ± 0% -21.24% (p=0.000 n=20)
MulAddVWW/1000 2.064µ ± 0% 1.612µ ± 0% -21.90% (p=0.000 n=20)
MulAddVWW/10000 24.50µ ± 0% 16.74µ ± 0% -31.66% (p=0.000 n=20)
MulAddVWW/100000 239.1µ ± 0% 171.1µ ± 0% -28.45% (p=0.000 n=20)
geomean 159.2n 130.3n -18.18%
Change-Id: I063434bc382f4f1234f879172ab671a3d6f2eb80
Reviewed-on: https://go-review.googlesource.com/c/go/+/659881
Reviewed-by: Dmitri Shuralyov <dmitshur@google.com>
Reviewed-by: abner chenc <chenguoqi@loongson.cn>
Reviewed-by: Carlos Amedee <carlos@golang.org>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
|
||
|
Huang Qiqi
|
24daaeea09 |
math/big: optimize subVW function for loong64
Benchmark results on Loongson 3C5000 (which is an LA464 implementation):
goos: linux
goarch: loong64
pkg: math/big
cpu: Loongson-3C5000 @ 2200.00MHz
│ test/old_3c5000_subvw.log │ test/new_3c5000_subvw.log │
│ sec/op │ sec/op vs base │
SubVW/1 8.564n ± 0% 5.915n ± 0% -30.93% (p=0.000 n=20)
SubVW/2 11.675n ± 0% 6.825n ± 0% -41.54% (p=0.000 n=20)
SubVW/3 13.410n ± 0% 7.969n ± 0% -40.57% (p=0.000 n=20)
SubVW/4 15.300n ± 0% 9.740n ± 0% -36.34% (p=0.000 n=20)
SubVW/5 17.34n ± 1% 10.66n ± 0% -38.55% (p=0.000 n=20)
SubVW/10 26.55n ± 0% 15.21n ± 0% -42.70% (p=0.000 n=20)
SubVW/100 199.2n ± 0% 102.5n ± 0% -48.52% (p=0.000 n=20)
SubVW/1000 1866.5n ± 1% 924.6n ± 0% -50.46% (p=0.000 n=20)
SubVW/10000 17.67µ ± 2% 12.04µ ± 2% -31.83% (p=0.000 n=20)
SubVW/100000 186.4µ ± 0% 132.0µ ± 0% -29.17% (p=0.000 n=20)
SubVWext/1 8.616n ± 0% 5.949n ± 0% -30.95% (p=0.000 n=20)
SubVWext/2 11.410n ± 0% 7.008n ± 1% -38.58% (p=0.000 n=20)
SubVWext/3 13.255n ± 1% 8.073n ± 0% -39.09% (p=0.000 n=20)
SubVWext/4 15.095n ± 0% 9.893n ± 0% -34.47% (p=0.000 n=20)
SubVWext/5 16.87n ± 0% 10.86n ± 0% -35.63% (p=0.000 n=20)
SubVWext/10 26.00n ± 0% 15.54n ± 0% -40.22% (p=0.000 n=20)
SubVWext/100 196.0n ± 0% 104.3n ± 1% -46.76% (p=0.000 n=20)
SubVWext/1000 1847.0n ± 0% 923.7n ± 0% -49.99% (p=0.000 n=20)
SubVWext/10000 17.30µ ± 1% 11.71µ ± 1% -32.31% (p=0.000 n=20)
SubVWext/100000 187.5µ ± 0% 131.6µ ± 0% -29.82% (p=0.000 n=20)
geomean 159.7n 97.79n -38.79%
Change-Id: I21a6903e79b02cb22282e80c9bfe2ae9f1a87589
Reviewed-on: https://go-review.googlesource.com/c/go/+/659878
Reviewed-by: Carlos Amedee <carlos@golang.org>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Dmitri Shuralyov <dmitshur@google.com>
Reviewed-by: abner chenc <chenguoqi@loongson.cn>
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Huang Qiqi
|
2fe0330cd7 |
math/big: optimize addVW function for loong64
Benchmark results on Loongson 3C5000 (which is an LA464 implementation):
goos: linux
goarch: loong64
pkg: math/big
cpu: Loongson-3C5000 @ 2200.00MHz
│ test/old_3c5000_addvw.log │ test/new_3c5000_addvw.log │
│ sec/op │ sec/op vs base │
AddVW/1 9.555n ± 0% 5.915n ± 0% -38.09% (p=0.000 n=20)
AddVW/2 11.370n ± 0% 6.825n ± 0% -39.97% (p=0.000 n=20)
AddVW/3 12.485n ± 0% 7.970n ± 0% -36.16% (p=0.000 n=20)
AddVW/4 14.980n ± 0% 9.718n ± 0% -35.13% (p=0.000 n=20)
AddVW/5 16.73n ± 0% 10.63n ± 0% -36.46% (p=0.000 n=20)
AddVW/10 24.57n ± 0% 15.18n ± 0% -38.23% (p=0.000 n=20)
AddVW/100 184.9n ± 0% 102.4n ± 0% -44.62% (p=0.000 n=20)
AddVW/1000 1721.0n ± 0% 921.4n ± 0% -46.46% (p=0.000 n=20)
AddVW/10000 16.83µ ± 0% 11.68µ ± 0% -30.58% (p=0.000 n=20)
AddVW/100000 184.7µ ± 0% 131.3µ ± 0% -28.93% (p=0.000 n=20)
AddVWext/1 9.554n ± 0% 5.915n ± 0% -38.09% (p=0.000 n=20)
AddVWext/2 11.370n ± 0% 6.825n ± 0% -39.97% (p=0.000 n=20)
AddVWext/3 12.505n ± 0% 7.969n ± 0% -36.27% (p=0.000 n=20)
AddVWext/4 14.980n ± 0% 9.718n ± 0% -35.13% (p=0.000 n=20)
AddVWext/5 16.70n ± 0% 10.63n ± 0% -36.33% (p=0.000 n=20)
AddVWext/10 24.54n ± 0% 15.18n ± 0% -38.13% (p=0.000 n=20)
AddVWext/100 185.0n ± 0% 102.4n ± 0% -44.65% (p=0.000 n=20)
AddVWext/1000 1721.0n ± 0% 921.4n ± 0% -46.46% (p=0.000 n=20)
AddVWext/10000 16.83µ ± 0% 11.68µ ± 0% -30.60% (p=0.000 n=20)
AddVWext/100000 184.9µ ± 0% 130.4µ ± 0% -29.51% (p=0.000 n=20)
geomean 155.5n 96.87n -37.70%
Change-Id: I824a90cb365e09d7d0d4a2c53ff4b30cf057a75e
Reviewed-on: https://go-review.googlesource.com/c/go/+/659876
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: abner chenc <chenguoqi@loongson.cn>
Reviewed-by: Dmitri Shuralyov <dmitshur@google.com>
Reviewed-by: Carlos Amedee <carlos@golang.org>
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Russ Cox
|
432fd9c60f |
math/big: remove copy responsibility from, rename shlVU, shrVU
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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|
Russ Cox
|
4dffdd797b |
math/big: replace addMulVVW with addMulVVWW
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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|
Vishwanatha HD
|
4ae6ab2bdf |
cmd/asm: add LCDBR instruction on s390x
This CL is to add LCDBR assembly instruction mnemonics, mainly used in math package. The LCDBR instruction has the same effect as the FNEG pseudo-instructions, just that it sets the flag. Change-Id: I3f00f1ed19148d074c3b6c5f64af0772289f2802 Reviewed-on: https://go-review.googlesource.com/c/go/+/648036 Reviewed-by: Srinivas Pokala <Pokala.Srinivas@ibm.com> Reviewed-by: Cherry Mui <cherryyz@google.com> Reviewed-by: Michael Munday <mike.munday@lowrisc.org> Reviewed-by: Michael Pratt <mpratt@google.com> Run-TryBot: Michael Munday <mike.munday@lowrisc.org> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> TryBot-Result: Gopher Robot <gobot@golang.org> |
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|
Russ Cox
|
a812e5f3c3 |
math/big: update calibration tests and recalibrate
Refactor calibration tests to use the same logic for all. Choosing thresholds that are broadly appropriate for all systems is part science but also part guesswork and judgement. We could instead set per-GOOS/GOARCH thresholds, but that seems like too much work, and even then there would be variation between different chips within a GOOS/GOARCH. (For example see the three linux/amd64 systems benchmarked below.) The thresholds chosen in this CL are: karatsubaThreshold = 40 // unchanged basicSqrThreshold = 12 // was 20 karatsubaSqrThreshold = 80 // was 260 divRecursiveThreshold = 40 // was 100 The new file calibrate.md explains the calibration process and links to graphs justifying those values. (The graphs are hosted on swtch.com to avoid adding a megabyte of extra data to the Go repo and Go distributions.) A rendered copy of calibrate.md is at https://swtch.com/math/big/calibrate.html. goos: linux goarch: amd64 pkg: math/big cpu: Intel(R) Xeon(R) Platinum 8481C CPU @ 2.70GHz │ old │ new │ │ sec/op │ sec/op vs base │ Div/20/10-88 13.13n ± 2% 13.14n ± 2% ~ (p=0.494 n=15) Div/40/20-88 13.13n ± 2% 13.14n ± 2% ~ (p=0.137 n=15) Div/100/50-88 25.50n ± 0% 25.51n ± 0% ~ (p=0.038 n=15) Div/200/100-88 113.1n ± 1% 116.0n ± 3% +2.56% (p=0.000 n=15) Div/400/200-88 135.3n ± 0% 137.1n ± 1% ~ (p=0.004 n=15) Div/1000/500-88 259.9n ± 1% 259.0n ± 2% ~ (p=0.182 n=15) Div/2000/1000-88 568.8n ± 1% 564.7n ± 3% ~ (p=0.927 n=15) Div/20000/10000-88 25.79µ ± 1% 22.11µ ± 2% -14.26% (p=0.000 n=15) Div/200000/100000-88 755.1µ ± 1% 737.6µ ± 1% -2.32% (p=0.000 n=15) Div/2000000/1000000-88 31.30m ± 0% 31.20m ± 1% ~ (p=0.081 n=15) Div/20000000/10000000-88 1.268 ± 0% 1.265 ± 0% ~ (p=0.011 n=15) NatMul/10-88 142.6n ± 0% 142.9n ± 7% ~ (p=0.145 n=15) NatMul/100-88 4.347µ ± 0% 4.350µ ± 3% ~ (p=0.430 n=15) NatMul/1000-88 187.6µ ± 0% 188.4µ ± 2% ~ (p=0.004 n=15) NatMul/10000-88 8.052m ± 0% 8.057m ± 1% ~ (p=0.148 n=15) NatMul/100000-88 260.6m ± 0% 260.7m ± 0% ~ (p=0.512 n=15) NatSqr/1-88 26.58n ± 5% 27.96n ± 8% ~ (p=0.574 n=15) NatSqr/2-88 42.35n ± 7% 44.87n ± 6% ~ (p=0.690 n=15) NatSqr/3-88 53.28n ± 4% 55.62n ± 5% ~ (p=0.151 n=15) NatSqr/5-88 76.26n ± 6% 81.43n ± 6% +6.78% (p=0.000 n=15) NatSqr/8-88 110.8n ± 5% 116.4n ± 6% ~ (p=0.040 n=15) NatSqr/10-88 141.4n ± 4% 147.8n ± 4% ~ (p=0.011 n=15) NatSqr/20-88 325.8n ± 3% 341.7n ± 4% +4.88% (p=0.000 n=15) NatSqr/30-88 536.8n ± 3% 556.1n ± 4% ~ (p=0.027 n=15) NatSqr/50-88 1.168µ ± 3% 1.197µ ± 3% ~ (p=0.442 n=15) NatSqr/80-88 2.527µ ± 2% 2.480µ ± 2% -1.86% (p=0.000 n=15) NatSqr/100-88 3.771µ ± 2% 3.535µ ± 2% -6.26% (p=0.000 n=15) NatSqr/200-88 14.03µ ± 2% 10.57µ ± 3% -24.68% (p=0.000 n=15) NatSqr/300-88 24.06µ ± 2% 20.57µ ± 2% -14.52% (p=0.000 n=15) NatSqr/500-88 65.43µ ± 1% 45.45µ ± 1% -30.55% (p=0.000 n=15) NatSqr/800-88 126.41µ ± 1% 94.13µ ± 2% -25.54% (p=0.000 n=15) NatSqr/1000-88 196.4µ ± 1% 135.1µ ± 1% -31.18% (p=0.000 n=15) NatSqr/10000-88 6.404m ± 0% 5.326m ± 1% -16.84% (p=0.000 n=15) NatSqr/100000-88 267.2m ± 0% 198.7m ± 0% -25.64% (p=0.000 n=15) geomean 7.318µ 6.948µ -5.06% goos: linux goarch: amd64 pkg: math/big cpu: Intel(R) Xeon(R) CPU @ 3.10GHz │ old │ new │ │ sec/op │ sec/op vs base │ Div/20/10-16 22.23n ± 0% 22.23n ± 0% ~ (p=0.973 n=15) Div/40/20-16 22.23n ± 0% 22.23n ± 0% ~ (p=0.226 n=15) Div/100/50-16 55.27n ± 1% 55.59n ± 0% ~ (p=0.004 n=15) Div/200/100-16 174.7n ± 3% 175.9n ± 2% ~ (p=0.645 n=15) Div/400/200-16 208.8n ± 1% 209.5n ± 2% ~ (p=0.169 n=15) Div/1000/500-16 378.7n ± 2% 380.5n ± 2% ~ (p=0.091 n=15) Div/2000/1000-16 778.4n ± 1% 781.1n ± 2% ~ (p=0.104 n=15) Div/20000/10000-16 25.16µ ± 1% 24.93µ ± 1% -0.91% (p=0.000 n=15) Div/200000/100000-16 926.4µ ± 0% 927.7µ ± 1% ~ (p=0.436 n=15) Div/2000000/1000000-16 35.58m ± 0% 35.53m ± 0% ~ (p=0.267 n=15) Div/20000000/10000000-16 1.333 ± 0% 1.330 ± 0% ~ (p=0.126 n=15) NatMul/10-16 172.6n ± 0% 165.4n ± 0% -4.17% (p=0.000 n=15) NatMul/100-16 5.706µ ± 0% 5.503µ ± 0% -3.56% (p=0.000 n=15) NatMul/1000-16 220.8µ ± 0% 219.1µ ± 0% -0.76% (p=0.000 n=15) NatMul/10000-16 8.688m ± 0% 8.621m ± 0% -0.77% (p=0.000 n=15) NatMul/100000-16 333.3m ± 0% 333.5m ± 0% ~ (p=0.512 n=15) NatSqr/1-16 28.66n ± 1% 28.42n ± 3% -0.84% (p=0.000 n=15) NatSqr/2-16 48.29n ± 2% 48.19n ± 2% ~ (p=0.042 n=15) NatSqr/3-16 59.93n ± 0% 59.64n ± 2% -0.48% (p=0.000 n=15) NatSqr/5-16 88.05n ± 0% 87.89n ± 3% ~ (p=0.066 n=15) NatSqr/8-16 127.7n ± 0% 126.9n ± 3% -0.63% (p=0.000 n=15) NatSqr/10-16 170.4n ± 0% 169.7n ± 3% ~ (p=0.004 n=15) NatSqr/20-16 388.8n ± 0% 392.9n ± 3% ~ (p=0.123 n=15) NatSqr/30-16 635.2n ± 0% 641.7n ± 3% ~ (p=0.123 n=15) NatSqr/50-16 1.304µ ± 1% 1.314µ ± 3% ~ (p=0.927 n=15) NatSqr/80-16 2.709µ ± 1% 2.899µ ± 4% +7.01% (p=0.000 n=15) NatSqr/100-16 3.885µ ± 0% 3.981µ ± 4% ~ (p=0.123 n=15) NatSqr/200-16 13.29µ ± 2% 12.14µ ± 4% -8.67% (p=0.000 n=15) NatSqr/300-16 23.39µ ± 0% 22.51µ ± 3% -3.78% (p=0.000 n=15) NatSqr/500-16 58.13µ ± 1% 50.56µ ± 2% -13.02% (p=0.000 n=15) NatSqr/800-16 118.4µ ± 1% 107.6µ ± 2% -9.11% (p=0.000 n=15) NatSqr/1000-16 172.7µ ± 1% 151.8µ ± 2% -12.11% (p=0.000 n=15) NatSqr/10000-16 6.065m ± 1% 5.757m ± 1% -5.08% (p=0.000 n=15) NatSqr/100000-16 240.9m ± 0% 228.1m ± 0% -5.32% (p=0.000 n=15) geomean 8.601µ 8.453µ -1.71% goos: linux goarch: amd64 pkg: math/big cpu: AMD Ryzen 9 7950X 16-Core Processor │ old │ new │ │ sec/op │ sec/op vs base │ Div/20/10-32 11.11n ± 0% 11.11n ± 1% ~ (p=0.532 n=15) Div/40/20-32 11.08n ± 1% 11.11n ± 0% ~ (p=0.815 n=15) Div/100/50-32 16.81n ± 0% 16.84n ± 29% ~ (p=0.020 n=15) Div/200/100-32 73.91n ± 0% 76.85n ± 11% +3.98% (p=0.000 n=15) Div/400/200-32 87.35n ± 0% 88.91n ± 34% +1.79% (p=0.000 n=15) Div/1000/500-32 169.3n ± 1% 168.9n ± 1% ~ (p=0.049 n=15) Div/2000/1000-32 369.3n ± 0% 369.0n ± 0% ~ (p=0.108 n=15) Div/20000/10000-32 15.92µ ± 0% 13.55µ ± 2% -14.91% (p=0.000 n=15) Div/200000/100000-32 491.4µ ± 0% 482.4µ ± 1% -1.84% (p=0.000 n=15) Div/2000000/1000000-32 20.09m ± 0% 19.96m ± 0% -0.69% (p=0.000 n=15) Div/20000000/10000000-32 756.5m ± 0% 755.5m ± 0% ~ (p=0.089 n=15) NatMul/10-32 125.4n ± 5% 124.8n ± 1% ~ (p=0.588 n=15) NatMul/100-32 2.952µ ± 3% 2.969µ ± 0% ~ (p=0.237 n=15) NatMul/1000-32 120.7µ ± 0% 121.1µ ± 0% +0.30% (p=0.000 n=15) NatMul/10000-32 4.845m ± 0% 4.839m ± 1% ~ (p=0.653 n=15) NatMul/100000-32 173.3m ± 0% 173.3m ± 0% ~ (p=0.838 n=15) NatSqr/1-32 31.18n ± 23% 32.08n ± 2% ~ (p=0.015 n=15) NatSqr/2-32 57.22n ± 28% 58.88n ± 2% ~ (p=0.054 n=15) NatSqr/3-32 61.34n ± 18% 64.33n ± 2% ~ (p=0.237 n=15) NatSqr/5-32 72.47n ± 17% 79.81n ± 3% ~ (p=0.067 n=15) NatSqr/8-32 83.26n ± 26% 100.10n ± 3% ~ (p=0.016 n=15) NatSqr/10-32 87.31n ± 43% 125.50n ± 2% ~ (p=0.003 n=15) NatSqr/20-32 193.5n ± 25% 244.4n ± 13% ~ (p=0.002 n=15) NatSqr/30-32 323.9n ± 17% 380.9n ± 6% ~ (p=0.003 n=15) NatSqr/50-32 713.4n ± 9% 761.7n ± 8% ~ (p=0.419 n=15) NatSqr/80-32 1.486µ ± 7% 1.609µ ± 5% +8.28% (p=0.000 n=15) NatSqr/100-32 2.115µ ± 9% 2.253µ ± 1% ~ (p=0.104 n=15) NatSqr/200-32 7.201µ ± 4% 6.610µ ± 1% -8.21% (p=0.000 n=15) NatSqr/300-32 13.08µ ± 2% 12.37µ ± 1% -5.41% (p=0.000 n=15) NatSqr/500-32 32.56µ ± 2% 27.83µ ± 2% -14.52% (p=0.000 n=15) NatSqr/800-32 66.83µ ± 3% 59.59µ ± 1% -10.83% (p=0.000 n=15) NatSqr/1000-32 98.09µ ± 1% 83.59µ ± 1% -14.78% (p=0.000 n=15) NatSqr/10000-32 3.445m ± 1% 3.245m ± 0% -5.81% (p=0.000 n=15) NatSqr/100000-32 137.3m ± 0% 127.0m ± 0% -7.54% (p=0.000 n=15) geomean 4.897µ 4.972µ +1.52% goos: linux goarch: arm64 pkg: math/big │ old │ new │ │ sec/op │ sec/op vs base │ Div/20/10-16 15.26n ± 2% 15.14n ± 1% ~ (p=0.212 n=15) Div/40/20-16 15.22n ± 1% 15.16n ± 0% ~ (p=0.190 n=15) Div/100/50-16 26.53n ± 2% 26.42n ± 0% -0.41% (p=0.000 n=15) Div/200/100-16 124.3n ± 0% 124.0n ± 0% ~ (p=0.704 n=15) Div/400/200-16 142.4n ± 0% 141.8n ± 0% ~ (p=0.074 n=15) Div/1000/500-16 262.0n ± 1% 261.3n ± 1% ~ (p=0.046 n=15) Div/2000/1000-16 532.6n ± 0% 532.5n ± 1% ~ (p=0.798 n=15) Div/20000/10000-16 22.27µ ± 0% 22.88µ ± 0% +2.73% (p=0.000 n=15) Div/200000/100000-16 890.4µ ± 0% 902.8µ ± 0% +1.39% (p=0.000 n=15) Div/2000000/1000000-16 35.03m ± 0% 35.10m ± 0% ~ (p=0.305 n=15) Div/20000000/10000000-16 1.380 ± 0% 1.385 ± 0% ~ (p=0.019 n=15) NatMul/10-16 177.6n ± 1% 175.6n ± 3% ~ (p=0.480 n=15) NatMul/100-16 5.675µ ± 0% 5.669µ ± 1% ~ (p=0.705 n=15) NatMul/1000-16 224.3µ ± 0% 224.6µ ± 0% ~ (p=0.653 n=15) NatMul/10000-16 8.735m ± 0% 8.739m ± 0% ~ (p=0.567 n=15) NatMul/100000-16 331.6m ± 0% 331.6m ± 1% ~ (p=0.412 n=15) NatSqr/1-16 43.69n ± 2% 42.77n ± 6% ~ (p=0.383 n=15) NatSqr/2-16 65.26n ± 2% 63.91n ± 5% ~ (p=0.285 n=15) NatSqr/3-16 73.95n ± 1% 72.25n ± 6% ~ (p=0.198 n=15) NatSqr/5-16 95.06n ± 1% 94.21n ± 3% ~ (p=0.721 n=15) NatSqr/8-16 155.5n ± 1% 153.4n ± 4% ~ (p=0.170 n=15) NatSqr/10-16 175.4n ± 1% 174.0n ± 2% ~ (p=0.271 n=15) NatSqr/20-16 360.8n ± 0% 358.5n ± 2% ~ (p=0.170 n=15) NatSqr/30-16 584.7n ± 0% 582.9n ± 1% ~ (p=0.170 n=15) NatSqr/50-16 1.323µ ± 0% 1.322µ ± 0% ~ (p=0.627 n=15) NatSqr/80-16 2.916µ ± 0% 2.674µ ± 0% -8.30% (p=0.000 n=15) NatSqr/100-16 4.365µ ± 0% 3.802µ ± 0% -12.90% (p=0.000 n=15) NatSqr/200-16 16.42µ ± 0% 11.29µ ± 0% -31.26% (p=0.000 n=15) NatSqr/300-16 28.07µ ± 0% 22.83µ ± 0% -18.68% (p=0.000 n=15) NatSqr/500-16 76.30µ ± 0% 50.06µ ± 0% -34.39% (p=0.000 n=15) NatSqr/800-16 147.5µ ± 0% 101.2µ ± 1% -31.41% (p=0.000 n=15) NatSqr/1000-16 228.6µ ± 0% 149.5µ ± 0% -34.61% (p=0.000 n=15) NatSqr/10000-16 7.417m ± 0% 6.025m ± 0% -18.76% (p=0.000 n=15) NatSqr/100000-16 309.2m ± 0% 214.9m ± 0% -30.50% (p=0.000 n=15) geomean 8.559µ 7.906µ -7.63% goos: darwin goarch: arm64 pkg: math/big cpu: Apple M3 Pro │ old │ new │ │ sec/op │ sec/op vs base │ Div/20/10-12 9.577n ± 6% 9.473n ± 5% ~ (p=0.384 n=15) Div/40/20-12 9.480n ± 1% 9.430n ± 1% ~ (p=0.019 n=15) Div/100/50-12 14.82n ± 0% 14.82n ± 0% ~ (p=0.845 n=15) Div/200/100-12 83.94n ± 1% 84.35n ± 4% ~ (p=0.512 n=15) Div/400/200-12 102.7n ± 1% 102.9n ± 0% ~ (p=0.845 n=15) Div/1000/500-12 185.3n ± 1% 181.9n ± 1% -1.83% (p=0.000 n=15) Div/2000/1000-12 397.0n ± 1% 396.7n ± 0% ~ (p=0.959 n=15) Div/20000/10000-12 14.05µ ± 0% 13.70µ ± 1% ~ (p=0.002 n=15) Div/200000/100000-12 529.4µ ± 3% 526.7µ ± 2% ~ (p=0.967 n=15) Div/2000000/1000000-12 20.05m ± 0% 20.05m ± 0% ~ (p=0.653 n=15) Div/20000000/10000000-12 788.2m ± 1% 789.0m ± 1% ~ (p=0.412 n=15) NatMul/10-12 79.95n ± 1% 80.87n ± 1% +1.15% (p=0.000 n=15) NatMul/100-12 2.973µ ± 0% 2.986µ ± 2% ~ (p=0.051 n=15) NatMul/1000-12 122.6µ ± 5% 123.0µ ± 1% ~ (p=0.783 n=15) NatMul/10000-12 4.990m ± 1% 5.000m ± 1% ~ (p=0.653 n=15) NatMul/100000-12 185.3m ± 3% 190.3m ± 1% ~ (p=0.089 n=15) NatSqr/1-12 11.84n ± 1% 11.88n ± 1% ~ (p=0.735 n=15) NatSqr/2-12 21.01n ± 1% 21.44n ± 6% ~ (p=0.039 n=15) NatSqr/3-12 25.59n ± 0% 26.74n ± 9% +4.49% (p=0.000 n=15) NatSqr/5-12 36.78n ± 0% 37.04n ± 1% +0.71% (p=0.000 n=15) NatSqr/8-12 63.09n ± 3% 63.22n ± 1% ~ (p=0.846 n=15) NatSqr/10-12 79.98n ± 0% 79.78n ± 0% ~ (p=0.100 n=15) NatSqr/20-12 174.0n ± 0% 175.5n ± 1% ~ (p=0.361 n=15) NatSqr/30-12 290.0n ± 0% 291.4n ± 0% ~ (p=0.002 n=15) NatSqr/50-12 655.2n ± 4% 658.1n ± 0% ~ (p=0.060 n=15) NatSqr/80-12 1.506µ ± 0% 1.397µ ± 5% -7.24% (p=0.000 n=15) NatSqr/100-12 2.273µ ± 0% 2.005µ ± 5% -11.79% (p=0.000 n=15) NatSqr/200-12 8.833µ ± 6% 6.109µ ± 0% -30.84% (p=0.000 n=15) NatSqr/300-12 15.15µ ± 4% 12.37µ ± 0% -18.34% (p=0.000 n=15) NatSqr/500-12 41.89µ ± 0% 27.70µ ± 1% -33.88% (p=0.000 n=15) NatSqr/800-12 80.72µ ± 0% 56.40µ ± 0% -30.12% (p=0.000 n=15) NatSqr/1000-12 127.06µ ± 1% 84.06µ ± 1% -33.84% (p=0.000 n=15) NatSqr/10000-12 4.130m ± 0% 3.390m ± 0% -17.91% (p=0.000 n=15) NatSqr/100000-12 173.2m ± 0% 131.2m ± 6% -24.25% (p=0.000 n=15) geomean 4.489µ 4.189µ -6.68% Change-Id: Iaf65fd85457b003ebf07a787c875cda321b40cc9 Reviewed-on: https://go-review.googlesource.com/c/go/+/652058 LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Robert Griesemer <gri@google.com> Reviewed-by: Alan Donovan <adonovan@google.com> Auto-Submit: Russ Cox <rsc@golang.org> |
||
|
Russ Cox
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d037ed62bc |
math/big: simplify, speed up Karatsuba multiplication
The old Karatsuba implementation only operated on lengths that are
a power of two times a number smaller than karatsubaThreshold.
For example, when karatsubaThreshold = 40, multiplying a pair
of 99-word numbers runs karatsuba on the low 96 (= 39<<2) words
and then has to fix up the answer to include the high 3 words of each.
I suspect this requirement was needed to make the analysis of
how many temporary words to reserve easier, back when the
answer was 3*n and depended on exactly halving the size at
each Karatsuba step.
Now that we have the more flexible temporary allocation stack,
we can change Karatsuba to accept operands of odd length.
Doing so avoids most of the fixup that the old approach required.
For example, multiplying a pair of 99-word numbers runs
karatsuba on all 99 words now.
This is simpler and about the same speed or, for large cases, faster.
goos: linux
goarch: amd64
pkg: math/big
cpu: Intel(R) Xeon(R) CPU @ 3.10GHz
│ old │ new │
│ sec/op │ sec/op vs base │
GCD10x10/WithoutXY-16 99.62n ± 3% 99.10n ± 3% ~ (p=0.009 n=15)
GCD10x10/WithXY-16 243.4n ± 1% 245.2n ± 1% ~ (p=0.009 n=15)
GCD100x100/WithoutXY-16 921.9n ± 1% 919.2n ± 1% ~ (p=0.076 n=15)
GCD100x100/WithXY-16 1.527µ ± 1% 1.526µ ± 0% ~ (p=0.813 n=15)
GCD1000x1000/WithoutXY-16 9.704µ ± 1% 9.696µ ± 0% ~ (p=0.532 n=15)
GCD1000x1000/WithXY-16 14.03µ ± 1% 13.96µ ± 0% ~ (p=0.014 n=15)
GCD10000x10000/WithoutXY-16 206.5µ ± 2% 206.5µ ± 0% ~ (p=0.967 n=15)
GCD10000x10000/WithXY-16 398.0µ ± 1% 397.4µ ± 0% ~ (p=0.683 n=15)
Div/20/10-16 22.22n ± 0% 22.23n ± 0% ~ (p=0.105 n=15)
Div/40/20-16 22.23n ± 0% 22.23n ± 0% ~ (p=0.307 n=15)
Div/100/50-16 55.47n ± 0% 55.47n ± 0% ~ (p=0.573 n=15)
Div/200/100-16 174.9n ± 1% 174.6n ± 1% ~ (p=0.814 n=15)
Div/400/200-16 209.5n ± 1% 210.5n ± 1% ~ (p=0.454 n=15)
Div/1000/500-16 379.9n ± 0% 383.5n ± 2% ~ (p=0.123 n=15)
Div/2000/1000-16 780.1n ± 0% 784.6n ± 1% +0.58% (p=0.000 n=15)
Div/20000/10000-16 25.22µ ± 1% 25.15µ ± 0% ~ (p=0.213 n=15)
Div/200000/100000-16 921.8µ ± 1% 926.1µ ± 0% ~ (p=0.009 n=15)
Div/2000000/1000000-16 37.91m ± 0% 35.63m ± 0% -6.02% (p=0.000 n=15)
Div/20000000/10000000-16 1.378 ± 0% 1.336 ± 0% -3.03% (p=0.000 n=15)
NatMul/10-16 166.8n ± 4% 168.9n ± 3% ~ (p=0.008 n=15)
NatMul/100-16 5.519µ ± 2% 5.548µ ± 4% ~ (p=0.032 n=15)
NatMul/1000-16 230.4µ ± 1% 220.2µ ± 1% -4.43% (p=0.000 n=15)
NatMul/10000-16 8.569m ± 1% 8.640m ± 1% ~ (p=0.005 n=15)
NatMul/100000-16 376.5m ± 1% 334.1m ± 0% -11.26% (p=0.000 n=15)
NatSqr/1-16 27.85n ± 5% 28.60n ± 2% ~ (p=0.123 n=15)
NatSqr/2-16 47.99n ± 2% 48.84n ± 1% ~ (p=0.008 n=15)
NatSqr/3-16 59.41n ± 2% 60.87n ± 2% +2.46% (p=0.001 n=15)
NatSqr/5-16 87.27n ± 2% 89.31n ± 3% ~ (p=0.087 n=15)
NatSqr/8-16 124.6n ± 3% 128.9n ± 3% ~ (p=0.006 n=15)
NatSqr/10-16 166.3n ± 3% 172.7n ± 3% ~ (p=0.002 n=15)
NatSqr/20-16 385.2n ± 2% 394.7n ± 3% ~ (p=0.036 n=15)
NatSqr/30-16 622.7n ± 3% 642.9n ± 3% ~ (p=0.032 n=15)
NatSqr/50-16 1.274µ ± 3% 1.323µ ± 4% ~ (p=0.003 n=15)
NatSqr/80-16 2.606µ ± 4% 2.714µ ± 4% ~ (p=0.044 n=15)
NatSqr/100-16 3.731µ ± 4% 3.871µ ± 4% ~ (p=0.038 n=15)
NatSqr/200-16 12.99µ ± 2% 13.09µ ± 3% ~ (p=0.838 n=15)
NatSqr/300-16 22.87µ ± 2% 23.25µ ± 2% ~ (p=0.285 n=15)
NatSqr/500-16 58.43µ ± 1% 58.25µ ± 2% ~ (p=0.345 n=15)
NatSqr/800-16 115.3µ ± 3% 116.2µ ± 3% ~ (p=0.126 n=15)
NatSqr/1000-16 173.9µ ± 1% 174.3µ ± 1% ~ (p=0.935 n=15)
NatSqr/10000-16 6.133m ± 2% 6.034m ± 1% -1.62% (p=0.000 n=15)
NatSqr/100000-16 253.8m ± 1% 241.5m ± 0% -4.87% (p=0.000 n=15)
geomean 7.745µ 7.760µ +0.19%
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 │
GCD10x10/WithoutXY-88 62.17n ± 4% 61.44n ± 0% -1.17% (p=0.000 n=15)
GCD10x10/WithXY-88 173.4n ± 2% 172.4n ± 4% ~ (p=0.615 n=15)
GCD100x100/WithoutXY-88 584.0n ± 1% 582.9n ± 0% ~ (p=0.009 n=15)
GCD100x100/WithXY-88 1.098µ ± 1% 1.091µ ± 2% ~ (p=0.002 n=15)
GCD1000x1000/WithoutXY-88 6.055µ ± 0% 6.049µ ± 0% ~ (p=0.007 n=15)
GCD1000x1000/WithXY-88 9.430µ ± 0% 9.417µ ± 1% ~ (p=0.123 n=15)
GCD10000x10000/WithoutXY-88 153.4µ ± 2% 149.0µ ± 2% -2.85% (p=0.000 n=15)
GCD10000x10000/WithXY-88 350.6µ ± 3% 349.0µ ± 2% ~ (p=0.126 n=15)
Div/20/10-88 13.12n ± 0% 13.12n ± 1% 0.00% (p=0.042 n=15)
Div/40/20-88 13.12n ± 0% 13.13n ± 0% ~ (p=0.004 n=15)
Div/100/50-88 25.49n ± 0% 25.49n ± 0% ~ (p=0.452 n=15)
Div/200/100-88 115.7n ± 2% 113.8n ± 2% ~ (p=0.212 n=15)
Div/400/200-88 135.0n ± 1% 136.1n ± 1% ~ (p=0.005 n=15)
Div/1000/500-88 257.5n ± 1% 259.9n ± 1% ~ (p=0.004 n=15)
Div/2000/1000-88 567.5n ± 1% 572.4n ± 2% ~ (p=0.616 n=15)
Div/20000/10000-88 25.65µ ± 0% 25.77µ ± 1% ~ (p=0.032 n=15)
Div/200000/100000-88 777.4µ ± 1% 754.3µ ± 1% -2.97% (p=0.000 n=15)
Div/2000000/1000000-88 33.66m ± 0% 31.37m ± 0% -6.81% (p=0.000 n=15)
Div/20000000/10000000-88 1.320 ± 0% 1.266 ± 0% -4.04% (p=0.000 n=15)
NatMul/10-88 151.9n ± 7% 143.3n ± 7% ~ (p=0.878 n=15)
NatMul/100-88 4.418µ ± 2% 4.337µ ± 3% ~ (p=0.512 n=15)
NatMul/1000-88 206.8µ ± 1% 189.8µ ± 1% -8.25% (p=0.000 n=15)
NatMul/10000-88 8.531m ± 1% 8.095m ± 0% -5.12% (p=0.000 n=15)
NatMul/100000-88 298.9m ± 0% 260.5m ± 1% -12.85% (p=0.000 n=15)
NatSqr/1-88 27.55n ± 6% 28.25n ± 7% ~ (p=0.024 n=15)
NatSqr/2-88 44.71n ± 6% 46.21n ± 9% ~ (p=0.024 n=15)
NatSqr/3-88 55.44n ± 4% 58.41n ± 10% ~ (p=0.126 n=15)
NatSqr/5-88 80.71n ± 5% 81.41n ± 5% ~ (p=0.032 n=15)
NatSqr/8-88 115.7n ± 4% 115.4n ± 5% ~ (p=0.814 n=15)
NatSqr/10-88 147.4n ± 4% 147.3n ± 4% ~ (p=0.505 n=15)
NatSqr/20-88 337.8n ± 3% 337.3n ± 4% ~ (p=0.814 n=15)
NatSqr/30-88 556.9n ± 3% 557.6n ± 4% ~ (p=0.814 n=15)
NatSqr/50-88 1.208µ ± 4% 1.208µ ± 3% ~ (p=0.910 n=15)
NatSqr/80-88 2.591µ ± 3% 2.581µ ± 3% ~ (p=0.705 n=15)
NatSqr/100-88 3.870µ ± 3% 3.858µ ± 3% ~ (p=0.846 n=15)
NatSqr/200-88 14.43µ ± 3% 14.28µ ± 2% ~ (p=0.383 n=15)
NatSqr/300-88 24.68µ ± 2% 24.49µ ± 2% ~ (p=0.624 n=15)
NatSqr/500-88 66.27µ ± 1% 66.18µ ± 1% ~ (p=0.735 n=15)
NatSqr/800-88 128.7µ ± 1% 127.4µ ± 1% ~ (p=0.050 n=15)
NatSqr/1000-88 198.7µ ± 1% 197.7µ ± 1% ~ (p=0.229 n=15)
NatSqr/10000-88 6.582m ± 1% 6.426m ± 1% -2.37% (p=0.000 n=15)
NatSqr/100000-88 274.3m ± 0% 267.3m ± 0% -2.57% (p=0.000 n=15)
geomean 6.518µ 6.438µ -1.22%
goos: linux
goarch: arm64
pkg: math/big
│ old │ new │
│ sec/op │ sec/op vs base │
GCD10x10/WithoutXY-16 61.70n ± 1% 61.32n ± 1% ~ (p=0.361 n=15)
GCD10x10/WithXY-16 217.3n ± 1% 217.0n ± 1% ~ (p=0.395 n=15)
GCD100x100/WithoutXY-16 569.7n ± 0% 572.6n ± 2% ~ (p=0.213 n=15)
GCD100x100/WithXY-16 1.241µ ± 1% 1.236µ ± 1% ~ (p=0.157 n=15)
GCD1000x1000/WithoutXY-16 5.558µ ± 0% 5.566µ ± 0% ~ (p=0.228 n=15)
GCD1000x1000/WithXY-16 9.319µ ± 0% 9.326µ ± 0% ~ (p=0.233 n=15)
GCD10000x10000/WithoutXY-16 126.4µ ± 2% 128.7µ ± 3% ~ (p=0.081 n=15)
GCD10000x10000/WithXY-16 279.3µ ± 0% 278.3µ ± 5% ~ (p=0.187 n=15)
Div/20/10-16 15.12n ± 1% 15.21n ± 1% ~ (p=0.490 n=15)
Div/40/20-16 15.11n ± 0% 15.23n ± 1% ~ (p=0.107 n=15)
Div/100/50-16 26.53n ± 0% 26.50n ± 0% ~ (p=0.299 n=15)
Div/200/100-16 123.7n ± 0% 124.0n ± 0% ~ (p=0.086 n=15)
Div/400/200-16 142.5n ± 0% 142.4n ± 0% ~ (p=0.039 n=15)
Div/1000/500-16 259.9n ± 1% 261.2n ± 1% ~ (p=0.044 n=15)
Div/2000/1000-16 539.4n ± 1% 532.3n ± 1% -1.32% (p=0.001 n=15)
Div/20000/10000-16 22.43µ ± 0% 22.32µ ± 0% -0.49% (p=0.000 n=15)
Div/200000/100000-16 898.3µ ± 0% 889.6µ ± 0% -0.96% (p=0.000 n=15)
Div/2000000/1000000-16 38.37m ± 0% 35.11m ± 0% -8.49% (p=0.000 n=15)
Div/20000000/10000000-16 1.449 ± 0% 1.384 ± 0% -4.48% (p=0.000 n=15)
NatMul/10-16 182.0n ± 1% 177.8n ± 1% -2.31% (p=0.000 n=15)
NatMul/100-16 5.537µ ± 0% 5.693µ ± 0% +2.82% (p=0.000 n=15)
NatMul/1000-16 229.9µ ± 0% 224.8µ ± 0% -2.24% (p=0.000 n=15)
NatMul/10000-16 8.985m ± 0% 8.751m ± 0% -2.61% (p=0.000 n=15)
NatMul/100000-16 371.1m ± 0% 331.5m ± 0% -10.66% (p=0.000 n=15)
NatSqr/1-16 46.77n ± 6% 42.76n ± 1% -8.57% (p=0.000 n=15)
NatSqr/2-16 66.99n ± 4% 63.62n ± 1% -5.03% (p=0.000 n=15)
NatSqr/3-16 76.79n ± 4% 73.42n ± 1% ~ (p=0.007 n=15)
NatSqr/5-16 99.00n ± 3% 95.35n ± 1% -3.69% (p=0.000 n=15)
NatSqr/8-16 160.0n ± 3% 155.1n ± 1% -3.06% (p=0.001 n=15)
NatSqr/10-16 178.4n ± 2% 175.9n ± 0% -1.40% (p=0.001 n=15)
NatSqr/20-16 361.9n ± 2% 361.3n ± 0% ~ (p=0.083 n=15)
NatSqr/30-16 584.7n ± 0% 586.8n ± 0% +0.36% (p=0.000 n=15)
NatSqr/50-16 1.327µ ± 0% 1.329µ ± 0% ~ (p=0.349 n=15)
NatSqr/80-16 2.893µ ± 1% 2.925µ ± 0% +1.11% (p=0.000 n=15)
NatSqr/100-16 4.330µ ± 1% 4.381µ ± 0% +1.18% (p=0.000 n=15)
NatSqr/200-16 16.25µ ± 1% 16.43µ ± 0% +1.07% (p=0.000 n=15)
NatSqr/300-16 27.85µ ± 1% 28.06µ ± 0% +0.77% (p=0.000 n=15)
NatSqr/500-16 76.01µ ± 0% 76.34µ ± 0% ~ (p=0.002 n=15)
NatSqr/800-16 146.8µ ± 0% 148.1µ ± 0% +0.83% (p=0.000 n=15)
NatSqr/1000-16 228.2µ ± 0% 228.6µ ± 0% ~ (p=0.123 n=15)
NatSqr/10000-16 7.524m ± 0% 7.426m ± 0% -1.31% (p=0.000 n=15)
NatSqr/100000-16 316.7m ± 0% 309.2m ± 0% -2.36% (p=0.000 n=15)
geomean 7.264µ 7.172µ -1.27%
goos: darwin
goarch: arm64
pkg: math/big
cpu: Apple M3 Pro
│ old │ new │
│ sec/op │ sec/op vs base │
GCD10x10/WithoutXY-12 32.61n ± 1% 32.42n ± 1% ~ (p=0.021 n=15)
GCD10x10/WithXY-12 87.70n ± 1% 88.42n ± 1% ~ (p=0.010 n=15)
GCD100x100/WithoutXY-12 305.9n ± 0% 306.4n ± 0% ~ (p=0.003 n=15)
GCD100x100/WithXY-12 560.3n ± 2% 556.6n ± 1% ~ (p=0.018 n=15)
GCD1000x1000/WithoutXY-12 3.509µ ± 2% 3.464µ ± 1% ~ (p=0.145 n=15)
GCD1000x1000/WithXY-12 5.347µ ± 2% 5.372µ ± 1% ~ (p=0.046 n=15)
GCD10000x10000/WithoutXY-12 73.75µ ± 1% 73.99µ ± 1% ~ (p=0.004 n=15)
GCD10000x10000/WithXY-12 148.4µ ± 0% 147.8µ ± 1% ~ (p=0.076 n=15)
Div/20/10-12 9.481n ± 0% 9.462n ± 1% ~ (p=0.631 n=15)
Div/40/20-12 9.457n ± 0% 9.462n ± 1% ~ (p=0.798 n=15)
Div/100/50-12 14.91n ± 0% 14.79n ± 1% -0.80% (p=0.000 n=15)
Div/200/100-12 84.56n ± 1% 84.60n ± 1% ~ (p=0.271 n=15)
Div/400/200-12 103.8n ± 0% 102.8n ± 0% -0.96% (p=0.000 n=15)
Div/1000/500-12 181.3n ± 1% 184.2n ± 2% ~ (p=0.091 n=15)
Div/2000/1000-12 397.5n ± 0% 397.4n ± 0% ~ (p=0.299 n=15)
Div/20000/10000-12 14.04µ ± 1% 13.99µ ± 0% ~ (p=0.221 n=15)
Div/200000/100000-12 523.1µ ± 0% 514.0µ ± 3% ~ (p=0.775 n=15)
Div/2000000/1000000-12 21.58m ± 0% 20.01m ± 1% -7.29% (p=0.000 n=15)
Div/20000000/10000000-12 813.5m ± 0% 796.2m ± 1% -2.13% (p=0.000 n=15)
NatMul/10-12 80.46n ± 1% 80.02n ± 1% ~ (p=0.063 n=15)
NatMul/100-12 2.904µ ± 0% 2.979µ ± 1% +2.58% (p=0.000 n=15)
NatMul/1000-12 127.8µ ± 0% 122.3µ ± 0% -4.28% (p=0.000 n=15)
NatMul/10000-12 5.141m ± 0% 4.975m ± 1% -3.23% (p=0.000 n=15)
NatMul/100000-12 208.8m ± 0% 189.6m ± 3% -9.21% (p=0.000 n=15)
NatSqr/1-12 11.90n ± 1% 11.76n ± 1% ~ (p=0.059 n=15)
NatSqr/2-12 21.33n ± 1% 21.12n ± 0% ~ (p=0.063 n=15)
NatSqr/3-12 26.05n ± 1% 25.79n ± 0% ~ (p=0.002 n=15)
NatSqr/5-12 37.31n ± 0% 36.98n ± 1% ~ (p=0.008 n=15)
NatSqr/8-12 63.07n ± 0% 62.75n ± 1% ~ (p=0.061 n=15)
NatSqr/10-12 79.48n ± 0% 79.59n ± 0% ~ (p=0.455 n=15)
NatSqr/20-12 173.1n ± 0% 173.2n ± 1% ~ (p=0.518 n=15)
NatSqr/30-12 288.6n ± 1% 289.2n ± 0% ~ (p=0.030 n=15)
NatSqr/50-12 653.3n ± 0% 653.3n ± 0% ~ (p=0.361 n=15)
NatSqr/80-12 1.492µ ± 0% 1.496µ ± 0% ~ (p=0.018 n=15)
NatSqr/100-12 2.270µ ± 1% 2.270µ ± 0% ~ (p=0.326 n=15)
NatSqr/200-12 8.776µ ± 1% 8.784µ ± 1% ~ (p=0.083 n=15)
NatSqr/300-12 15.07µ ± 0% 15.09µ ± 0% ~ (p=0.455 n=15)
NatSqr/500-12 41.71µ ± 0% 41.77µ ± 1% ~ (p=0.305 n=15)
NatSqr/800-12 80.77µ ± 1% 80.59µ ± 0% ~ (p=0.113 n=15)
NatSqr/1000-12 126.4µ ± 1% 126.5µ ± 0% ~ (p=0.683 n=15)
NatSqr/10000-12 4.204m ± 0% 4.119m ± 0% -2.02% (p=0.000 n=15)
NatSqr/100000-12 177.0m ± 0% 172.9m ± 0% -2.31% (p=0.000 n=15)
geomean 3.790µ 3.757µ -0.87%
Change-Id: Ifc7a9b61f678df216690511ac8bb9143189a795e
Reviewed-on: https://go-review.googlesource.com/c/go/+/652057
Auto-Submit: Russ Cox <rsc@golang.org>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Robert Griesemer <gri@google.com>
|
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Russ Cox
|
70dcc78871 |
math/big: avoid negative slice size in nat.rem
In a division, normally the answer to N digits / D digits has N-D digits, but not when N-D is negative. Fix the calculation of the number of digits for the temporary in nat.rem not to be negative. Fixes #72043. Change-Id: Ib9faa430aeb6c5f4c4a730f1ec631d2bf3f7472c Reviewed-on: https://go-review.googlesource.com/c/go/+/655156 Reviewed-by: Robert Griesemer <gri@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> |
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Xiaolin Zhao
|
6ba91df153 |
math: implement func archExp and archExp2 in assembly on loong64
goos: linux
goarch: loong64
pkg: math
cpu: Loongson-3A6000 @ 2500.00MHz
| bench.old | bench.new |
| sec/op | sec/op vs base |
Exp 26.30n ± 0% 12.93n ± 0% -50.85% (p=0.000 n=10)
ExpGo 26.86n ± 0% 26.92n ± 0% +0.22% (p=0.000 n=10)
Expm1 16.76n ± 0% 16.75n ± 0% ~ (p=0.060 n=10)
Exp2 23.05n ± 0% 12.12n ± 0% -47.42% (p=0.000 n=10)
Exp2Go 23.41n ± 0% 23.47n ± 0% +0.28% (p=0.000 n=10)
geomean 22.97n 17.54n -23.64%
goos: linux
goarch: loong64
pkg: math/cmplx
cpu: Loongson-3A6000 @ 2500.00MHz
| bench.old | bench.new |
| sec/op | sec/op vs base |
Exp 51.32n ± 0% 35.41n ± 0% -30.99% (p=0.000 n=10)
goos: linux
goarch: loong64
pkg: math
cpu: Loongson-3A5000 @ 2500.00MHz
| bench.old | bench.new |
| sec/op | sec/op vs base |
Exp 50.27n ± 0% 48.75n ± 1% -3.01% (p=0.000 n=10)
ExpGo 50.72n ± 0% 50.44n ± 0% -0.55% (p=0.000 n=10)
Expm1 28.40n ± 0% 28.32n ± 0% ~ (p=0.360 n=10)
Exp2 50.09n ± 0% 21.49n ± 1% -57.10% (p=0.000 n=10)
Exp2Go 50.05n ± 0% 49.69n ± 0% -0.72% (p=0.000 n=10)
geomean 44.85n 37.52n -16.35%
goos: linux
goarch: loong64
pkg: math/cmplx
cpu: Loongson-3A5000 @ 2500.00MHz
| bench.old | bench.new |
| sec/op | sec/op vs base |
Exp 88.56n ± 0% 67.29n ± 0% -24.03% (p=0.000 n=10)
Change-Id: I89e456d26fc075d83335ee4a31227d2aface5714
Reviewed-on: https://go-review.googlesource.com/c/go/+/653935
Reviewed-by: Junyang Shao <shaojunyang@google.com>
Reviewed-by: abner chenc <chenguoqi@loongson.cn>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Michael Pratt <mpratt@google.com>
|
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Russ Cox
|
2b73707358 |
math/big: add tests for allocation during multiply
Test that big.Int.Mul reusing the same target is not allocating temporary garbage during its computation. That code is going to be modified in an upcoming CL. Change-Id: I3ed55c06da030282233c29cd7af2a04f395dc7a2 Reviewed-on: https://go-review.googlesource.com/c/go/+/652056 LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Alan Donovan <adonovan@google.com> Auto-Submit: Russ Cox <rsc@golang.org> |
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Russ Cox
|
0ab2253ce1 |
math/big: move multiplication to natmul.go
No code changes. This CL moves the multiplication (and squaring) code into natmul.go, in preparation for cleaning up Karatsuba and then adding Toom-Cook and FFT-based multiplication. Change-Id: I7f84328284cc4e1ca4da0ebb9f666a5535e8d7f2 Reviewed-on: https://go-review.googlesource.com/c/go/+/652055 LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Auto-Submit: Russ Cox <rsc@golang.org> Reviewed-by: Alan Donovan <adonovan@google.com> |
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Russ Cox
|
1f7e28acdf |
math/big: optimize atoi of base 2, 4, 16
Avoid multiplies when converting base 2, 4, 16 inputs, reducing conversion time from O(N²) to O(N). The Base8 and Base10 code paths should be unmodified, but the base-2,4,16 changes tickle the compiler to generate better (amd64) or worse (arm64) when really it should not. This is described in detail in #71868 and should be ignored for the purposes of this CL. goos: linux goarch: amd64 pkg: math/big cpu: Intel(R) Xeon(R) CPU @ 3.10GHz │ old │ new │ │ sec/op │ sec/op vs base │ Scan/10/Base2-16 324.4n ± 0% 258.7n ± 0% -20.25% (p=0.000 n=15) Scan/100/Base2-16 2.376µ ± 0% 1.968µ ± 0% -17.17% (p=0.000 n=15) Scan/1000/Base2-16 23.89µ ± 0% 19.16µ ± 0% -19.80% (p=0.000 n=15) Scan/10000/Base2-16 311.5µ ± 0% 190.4µ ± 0% -38.86% (p=0.000 n=15) Scan/100000/Base2-16 10.508m ± 0% 1.904m ± 0% -81.88% (p=0.000 n=15) Scan/10/Base8-16 138.3n ± 0% 127.9n ± 0% -7.52% (p=0.000 n=15) Scan/100/Base8-16 886.1n ± 0% 790.2n ± 0% -10.82% (p=0.000 n=15) Scan/1000/Base8-16 9.227µ ± 0% 8.234µ ± 0% -10.76% (p=0.000 n=15) Scan/10000/Base8-16 165.8µ ± 0% 155.6µ ± 0% -6.19% (p=0.000 n=15) Scan/100000/Base8-16 9.044m ± 0% 8.935m ± 0% -1.20% (p=0.000 n=15) Scan/10/Base10-16 129.9n ± 0% 120.0n ± 0% -7.62% (p=0.000 n=15) Scan/100/Base10-16 816.3n ± 0% 730.0n ± 0% -10.57% (p=0.000 n=15) Scan/1000/Base10-16 8.518µ ± 0% 7.628µ ± 0% -10.45% (p=0.000 n=15) Scan/10000/Base10-16 158.6µ ± 0% 149.4µ ± 0% -5.80% (p=0.000 n=15) Scan/100000/Base10-16 8.962m ± 0% 8.855m ± 0% -1.20% (p=0.000 n=15) Scan/10/Base16-16 114.5n ± 0% 108.6n ± 0% -5.15% (p=0.000 n=15) Scan/100/Base16-16 648.3n ± 0% 525.0n ± 0% -19.02% (p=0.000 n=15) Scan/1000/Base16-16 7.375µ ± 0% 5.636µ ± 0% -23.58% (p=0.000 n=15) Scan/10000/Base16-16 171.18µ ± 0% 66.99µ ± 0% -60.87% (p=0.000 n=15) Scan/100000/Base16-16 9490.9µ ± 0% 682.8µ ± 0% -92.81% (p=0.000 n=15) geomean 20.11µ 13.69µ -31.94% 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 │ Scan/10/Base2-88 275.4n ± 0% 215.0n ± 0% -21.93% (p=0.000 n=15) Scan/100/Base2-88 1.869µ ± 0% 1.629µ ± 0% -12.84% (p=0.000 n=15) Scan/1000/Base2-88 18.56µ ± 0% 15.81µ ± 0% -14.82% (p=0.000 n=15) Scan/10000/Base2-88 270.0µ ± 0% 157.2µ ± 0% -41.77% (p=0.000 n=15) Scan/100000/Base2-88 11.518m ± 0% 1.571m ± 0% -86.36% (p=0.000 n=15) Scan/10/Base8-88 108.9n ± 0% 106.0n ± 0% -2.66% (p=0.000 n=15) Scan/100/Base8-88 655.2n ± 0% 594.9n ± 0% -9.20% (p=0.000 n=15) Scan/1000/Base8-88 6.467µ ± 0% 5.966µ ± 0% -7.75% (p=0.000 n=15) Scan/10000/Base8-88 151.2µ ± 0% 147.4µ ± 0% -2.53% (p=0.000 n=15) Scan/100000/Base8-88 10.33m ± 0% 10.30m ± 0% -0.25% (p=0.000 n=15) Scan/10/Base10-88 100.20n ± 0% 98.53n ± 0% -1.67% (p=0.000 n=15) Scan/100/Base10-88 596.9n ± 0% 543.3n ± 0% -8.98% (p=0.000 n=15) Scan/1000/Base10-88 5.904µ ± 0% 5.485µ ± 0% -7.10% (p=0.000 n=15) Scan/10000/Base10-88 145.7µ ± 0% 142.0µ ± 0% -2.55% (p=0.000 n=15) Scan/100000/Base10-88 10.26m ± 0% 10.24m ± 0% -0.18% (p=0.000 n=15) Scan/10/Base16-88 90.33n ± 0% 87.60n ± 0% -3.02% (p=0.000 n=15) Scan/100/Base16-88 506.4n ± 0% 437.7n ± 0% -13.57% (p=0.000 n=15) Scan/1000/Base16-88 5.056µ ± 0% 4.007µ ± 0% -20.75% (p=0.000 n=15) Scan/10000/Base16-88 163.35µ ± 0% 65.37µ ± 0% -59.98% (p=0.000 n=15) Scan/100000/Base16-88 11027.2µ ± 0% 735.1µ ± 0% -93.33% (p=0.000 n=15) geomean 17.13µ 11.74µ -31.46% goos: linux goarch: arm64 pkg: math/big │ old │ new │ │ sec/op │ sec/op vs base │ Scan/10/Base2-16 324.7n ± 0% 348.4n ± 0% +7.30% (p=0.000 n=15) Scan/100/Base2-16 2.604µ ± 0% 3.031µ ± 0% +16.40% (p=0.000 n=15) Scan/1000/Base2-16 26.15µ ± 0% 29.94µ ± 0% +14.52% (p=0.000 n=15) Scan/10000/Base2-16 334.3µ ± 0% 298.8µ ± 0% -10.64% (p=0.000 n=15) Scan/100000/Base2-16 10.664m ± 0% 2.991m ± 0% -71.95% (p=0.000 n=15) Scan/10/Base8-16 144.4n ± 1% 162.2n ± 1% +12.33% (p=0.000 n=15) Scan/100/Base8-16 917.2n ± 0% 1084.0n ± 0% +18.19% (p=0.000 n=15) Scan/1000/Base8-16 9.367µ ± 0% 10.901µ ± 0% +16.38% (p=0.000 n=15) Scan/10000/Base8-16 164.2µ ± 0% 181.2µ ± 0% +10.34% (p=0.000 n=15) Scan/100000/Base8-16 8.871m ± 1% 9.140m ± 0% +3.04% (p=0.000 n=15) Scan/10/Base10-16 134.6n ± 1% 148.3n ± 1% +10.18% (p=0.000 n=15) Scan/100/Base10-16 837.1n ± 0% 986.6n ± 0% +17.86% (p=0.000 n=15) Scan/1000/Base10-16 8.563µ ± 0% 9.936µ ± 0% +16.03% (p=0.000 n=15) Scan/10000/Base10-16 156.5µ ± 1% 171.3µ ± 0% +9.41% (p=0.000 n=15) Scan/100000/Base10-16 8.863m ± 1% 9.011m ± 0% +1.66% (p=0.000 n=15) Scan/10/Base16-16 115.7n ± 2% 129.1n ± 1% +11.58% (p=0.000 n=15) Scan/100/Base16-16 708.6n ± 0% 796.8n ± 0% +12.45% (p=0.000 n=15) Scan/1000/Base16-16 7.314µ ± 0% 7.554µ ± 0% +3.28% (p=0.000 n=15) Scan/10000/Base16-16 149.05µ ± 0% 74.60µ ± 0% -49.95% (p=0.000 n=15) Scan/100000/Base16-16 9091.6µ ± 0% 741.5µ ± 0% -91.84% (p=0.000 n=15) geomean 20.39µ 17.65µ -13.44% goos: darwin goarch: arm64 pkg: math/big cpu: Apple M3 Pro │ old │ new │ │ sec/op │ sec/op vs base │ Scan/10/Base2-12 193.8n ± 2% 157.3n ± 1% -18.83% (p=0.000 n=15) Scan/100/Base2-12 1.445µ ± 2% 1.362µ ± 1% -5.74% (p=0.000 n=15) Scan/1000/Base2-12 14.28µ ± 0% 13.51µ ± 0% -5.42% (p=0.000 n=15) Scan/10000/Base2-12 177.1µ ± 0% 134.6µ ± 0% -24.04% (p=0.000 n=15) Scan/100000/Base2-12 5.429m ± 1% 1.333m ± 0% -75.45% (p=0.000 n=15) Scan/10/Base8-12 75.52n ± 2% 76.09n ± 1% ~ (p=0.010 n=15) Scan/100/Base8-12 528.4n ± 1% 532.1n ± 1% ~ (p=0.003 n=15) Scan/1000/Base8-12 5.423µ ± 1% 5.427µ ± 0% ~ (p=0.183 n=15) Scan/10000/Base8-12 89.26µ ± 1% 89.37µ ± 0% ~ (p=0.237 n=15) Scan/100000/Base8-12 4.543m ± 2% 4.560m ± 1% ~ (p=0.595 n=15) Scan/10/Base10-12 69.87n ± 1% 70.51n ± 0% ~ (p=0.002 n=15) Scan/100/Base10-12 488.4n ± 1% 491.2n ± 0% ~ (p=0.060 n=15) Scan/1000/Base10-12 5.014µ ± 1% 5.008µ ± 0% ~ (p=0.783 n=15) Scan/10000/Base10-12 84.90µ ± 0% 85.10µ ± 0% ~ (p=0.109 n=15) Scan/100000/Base10-12 4.516m ± 1% 4.521m ± 1% ~ (p=0.713 n=15) Scan/10/Base16-12 59.21n ± 1% 57.70n ± 1% -2.55% (p=0.000 n=15) Scan/100/Base16-12 380.0n ± 1% 360.7n ± 1% -5.08% (p=0.000 n=15) Scan/1000/Base16-12 3.775µ ± 0% 3.421µ ± 0% -9.38% (p=0.000 n=15) Scan/10000/Base16-12 80.62µ ± 0% 34.44µ ± 1% -57.28% (p=0.000 n=15) Scan/100000/Base16-12 4826.4µ ± 2% 450.9µ ± 2% -90.66% (p=0.000 n=15) geomean 11.05µ 8.448µ -23.52% Change-Id: Ifdb2049545f34072aa75cdbb72bed4cf465f0ad7 Reviewed-on: https://go-review.googlesource.com/c/go/+/650640 Auto-Submit: Russ Cox <rsc@golang.org> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Robert Griesemer <gri@google.com> |
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|
Russ Cox
|
f8f08bfd7c |
math/big: improve scan test and benchmark
Add a few more test cases for scanning (integer conversion),
which were helpful in debugging some upcoming changes.
BenchmarkScan currently times converting the value 10**N
represented in base B back into []Word form.
When B = 10, the text is 1 followed by many zeros, which
could hit a "multiply by zero" special case when processing
many digit chunks, misrepresenting the actual time required
depending on whether that case is optimized.
Change the benchmark to use 9**N, which is about as big and
will not cause runs of zeros in any of the tested bases.
The benchmark comparison below is not showing faster code,
since of course the code is not changing at all here. Instead,
it is showing that the new benchmark work is roughly the same
size as the old benchmark work.
goos: darwin
goarch: arm64
pkg: math/big
cpu: Apple M3 Pro
│ old │ new │
│ sec/op │ sec/op vs base │
ScanPi-12 43.35µ ± 1% 43.59µ ± 1% ~ (p=0.069 n=15)
Scan/10/Base2-12 202.3n ± 2% 193.7n ± 1% -4.25% (p=0.000 n=15)
Scan/100/Base2-12 1.512µ ± 3% 1.447µ ± 1% -4.30% (p=0.000 n=15)
Scan/1000/Base2-12 15.06µ ± 2% 14.33µ ± 0% -4.83% (p=0.000 n=15)
Scan/10000/Base2-12 188.0µ ± 5% 177.3µ ± 1% -5.65% (p=0.000 n=15)
Scan/100000/Base2-12 5.814m ± 3% 5.382m ± 1% -7.43% (p=0.000 n=15)
Scan/10/Base8-12 78.57n ± 2% 75.02n ± 1% -4.52% (p=0.000 n=15)
Scan/100/Base8-12 548.2n ± 2% 526.8n ± 1% -3.90% (p=0.000 n=15)
Scan/1000/Base8-12 5.674µ ± 2% 5.421µ ± 0% -4.46% (p=0.000 n=15)
Scan/10000/Base8-12 94.42µ ± 1% 88.61µ ± 1% -6.15% (p=0.000 n=15)
Scan/100000/Base8-12 4.906m ± 2% 4.498m ± 3% -8.31% (p=0.000 n=15)
Scan/10/Base10-12 73.42n ± 1% 69.56n ± 0% -5.26% (p=0.000 n=15)
Scan/100/Base10-12 511.9n ± 1% 488.2n ± 0% -4.63% (p=0.000 n=15)
Scan/1000/Base10-12 5.254µ ± 2% 5.009µ ± 0% -4.66% (p=0.000 n=15)
Scan/10000/Base10-12 90.22µ ± 2% 84.52µ ± 0% -6.32% (p=0.000 n=15)
Scan/100000/Base10-12 4.842m ± 3% 4.471m ± 3% -7.65% (p=0.000 n=15)
Scan/10/Base16-12 62.28n ± 1% 58.70n ± 1% -5.75% (p=0.000 n=15)
Scan/100/Base16-12 398.6n ± 0% 377.9n ± 1% -5.19% (p=0.000 n=15)
Scan/1000/Base16-12 4.108µ ± 1% 3.782µ ± 0% -7.94% (p=0.000 n=15)
Scan/10000/Base16-12 83.78µ ± 2% 80.51µ ± 1% -3.90% (p=0.000 n=15)
Scan/100000/Base16-12 5.080m ± 3% 4.698m ± 3% -7.53% (p=0.000 n=15)
geomean 12.41µ 11.74µ -5.36%
Change-Id: If3ce290ecc7f38672f11b42fd811afb53dee665d
Reviewed-on: https://go-review.googlesource.com/c/go/+/650639
Reviewed-by: Alan Donovan <adonovan@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Auto-Submit: Russ Cox <rsc@golang.org>
|
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|
Russ Cox
|
872496da2b |
math/big: replace nat pool with Word stack
In the early days of math/big, algorithms that needed more space
grew the result larger than it needed to be and then used the
high words as extra space. This made results their own temporary
space caches, at the cost that saving a result in a data structure
might hold significantly more memory than necessary.
Specifically, new(big.Int).Mul(x, y) returned a big.Int with a
backing slice 3X as big as it strictly needed to be.
If you are storing many multiplication results, or even a single
large result, the 3X overhead can add up.
This approach to storage for temporaries also requires being able
to analyze the algorithms to predict the exact amount they need,
which can be difficult.
For both these reasons, the implementation of recursive long division,
which came later, introduced a “nat pool” where temporaries could be
stored and reused, or reclaimed by the GC when no longer used.
This avoids the storage and bookkeeping overheads but introduces a
per-temporary sync.Pool overhead. divRecursiveStep takes an array
of cached temporaries to remove some of that overhead.
The nat pool was better but is still not quite right.
This CL introduces something even better than the nat pool
(still probably not quite right, but the best I can see for now):
a sync.Pool holding stacks for allocating temporaries.
Now an operation can get one stack out of the pool and then
allocate as many temporaries as it needs during the operation,
eventually returning the stack back to the pool. The sync.Pool
operations are now per-exported-operation (like big.Int.Mul),
not per-temporary.
This CL converts both the pre-allocation in nat.mul and the
uses of the nat pool to use stack pools instead. This simplifies
some code and sets us up better for more complex algorithms
(such as Toom-Cook or FFT-based multiplication) that need
more temporaries. It is also a little bit faster.
goos: linux
goarch: amd64
pkg: math/big
cpu: Intel(R) Xeon(R) CPU @ 3.10GHz
│ old │ new │
│ sec/op │ sec/op vs base │
Div/20/10-16 23.68n ± 0% 22.21n ± 0% -6.21% (p=0.000 n=15)
Div/40/20-16 23.68n ± 0% 22.21n ± 0% -6.21% (p=0.000 n=15)
Div/100/50-16 56.65n ± 0% 55.53n ± 0% -1.98% (p=0.000 n=15)
Div/200/100-16 194.6n ± 1% 172.8n ± 0% -11.20% (p=0.000 n=15)
Div/400/200-16 232.1n ± 0% 206.7n ± 0% -10.94% (p=0.000 n=15)
Div/1000/500-16 405.3n ± 1% 383.8n ± 0% -5.30% (p=0.000 n=15)
Div/2000/1000-16 810.4n ± 1% 795.2n ± 0% -1.88% (p=0.000 n=15)
Div/20000/10000-16 25.88µ ± 0% 25.39µ ± 0% -1.89% (p=0.000 n=15)
Div/200000/100000-16 931.5µ ± 0% 924.3µ ± 0% -0.77% (p=0.000 n=15)
Div/2000000/1000000-16 37.77m ± 0% 37.75m ± 0% ~ (p=0.098 n=15)
Div/20000000/10000000-16 1.367 ± 0% 1.377 ± 0% +0.72% (p=0.003 n=15)
NatMul/10-16 168.5n ± 3% 164.0n ± 4% ~ (p=0.751 n=15)
NatMul/100-16 6.086µ ± 3% 5.380µ ± 3% -11.60% (p=0.000 n=15)
NatMul/1000-16 238.1µ ± 3% 228.3µ ± 1% -4.12% (p=0.000 n=15)
NatMul/10000-16 8.721m ± 2% 8.518m ± 1% -2.33% (p=0.000 n=15)
NatMul/100000-16 369.6m ± 0% 371.1m ± 0% +0.42% (p=0.000 n=15)
geomean 19.57µ 18.74µ -4.21%
│ old │ new │
│ B/op │ B/op vs base │
NatMul/10-16 192.0 ± 0% 192.0 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100-16 4.750Ki ± 0% 1.751Ki ± 0% -63.14% (p=0.000 n=15)
NatMul/1000-16 48.16Ki ± 0% 16.02Ki ± 0% -66.73% (p=0.000 n=15)
NatMul/10000-16 482.9Ki ± 1% 165.4Ki ± 3% -65.75% (p=0.000 n=15)
NatMul/100000-16 5.747Mi ± 7% 4.197Mi ± 0% -26.97% (p=0.000 n=15)
geomean 41.42Ki 20.63Ki -50.18%
¹ all samples are equal
│ old │ new │
│ allocs/op │ allocs/op vs base │
NatMul/10-16 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100-16 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/1000-16 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/10000-16 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100000-16 7.000 ± 14% 7.000 ± 14% ~ (p=0.668 n=15)
geomean 1.476 1.476 +0.00%
¹ all samples are equal
goos: linux
goarch: amd64
pkg: math/big
cpu: Intel(R) Xeon(R) Platinum 8481C CPU @ 2.70GHz
│ old │ new │
│ sec/op │ sec/op vs base │
Div/20/10-88 15.84n ± 1% 13.12n ± 0% -17.17% (p=0.000 n=15)
Div/40/20-88 15.88n ± 1% 13.12n ± 0% -17.38% (p=0.000 n=15)
Div/100/50-88 26.42n ± 0% 25.47n ± 0% -3.60% (p=0.000 n=15)
Div/200/100-88 132.4n ± 0% 114.9n ± 0% -13.22% (p=0.000 n=15)
Div/400/200-88 150.1n ± 0% 135.6n ± 0% -9.66% (p=0.000 n=15)
Div/1000/500-88 275.5n ± 0% 264.1n ± 0% -4.14% (p=0.000 n=15)
Div/2000/1000-88 586.5n ± 0% 581.1n ± 0% -0.92% (p=0.000 n=15)
Div/20000/10000-88 25.87µ ± 0% 25.72µ ± 0% -0.59% (p=0.000 n=15)
Div/200000/100000-88 772.2µ ± 0% 779.0µ ± 0% +0.88% (p=0.000 n=15)
Div/2000000/1000000-88 33.36m ± 0% 33.63m ± 0% +0.80% (p=0.000 n=15)
Div/20000000/10000000-88 1.307 ± 0% 1.320 ± 0% +1.03% (p=0.000 n=15)
NatMul/10-88 140.4n ± 0% 148.8n ± 4% +5.98% (p=0.000 n=15)
NatMul/100-88 4.663µ ± 1% 4.388µ ± 1% -5.90% (p=0.000 n=15)
NatMul/1000-88 207.7µ ± 0% 205.8µ ± 0% -0.89% (p=0.000 n=15)
NatMul/10000-88 8.456m ± 0% 8.468m ± 0% +0.14% (p=0.021 n=15)
NatMul/100000-88 295.1m ± 0% 297.9m ± 0% +0.94% (p=0.000 n=15)
geomean 14.96µ 14.33µ -4.23%
│ old │ new │
│ B/op │ B/op vs base │
NatMul/10-88 192.0 ± 0% 192.0 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100-88 4.750Ki ± 0% 1.758Ki ± 0% -62.99% (p=0.000 n=15)
NatMul/1000-88 48.44Ki ± 0% 16.08Ki ± 0% -66.80% (p=0.000 n=15)
NatMul/10000-88 489.7Ki ± 1% 166.1Ki ± 3% -66.08% (p=0.000 n=15)
NatMul/100000-88 5.546Mi ± 0% 3.819Mi ± 60% -31.15% (p=0.000 n=15)
geomean 41.29Ki 20.30Ki -50.85%
¹ all samples are equal
│ old │ new │
│ allocs/op │ allocs/op vs base │
NatMul/10-88 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100-88 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/1000-88 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/10000-88 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100000-88 5.000 ± 20% 6.000 ± 67% ~ (p=0.672 n=15)
geomean 1.380 1.431 +3.71%
¹ all samples are equal
goos: linux
goarch: arm64
pkg: math/big
│ old │ new │
│ sec/op │ sec/op vs base │
Div/20/10-16 15.85n ± 0% 15.23n ± 0% -3.91% (p=0.000 n=15)
Div/40/20-16 15.88n ± 0% 15.22n ± 0% -4.16% (p=0.000 n=15)
Div/100/50-16 29.69n ± 0% 26.39n ± 0% -11.11% (p=0.000 n=15)
Div/200/100-16 149.2n ± 0% 123.3n ± 0% -17.36% (p=0.000 n=15)
Div/400/200-16 160.3n ± 0% 139.2n ± 0% -13.16% (p=0.000 n=15)
Div/1000/500-16 271.0n ± 0% 256.1n ± 0% -5.50% (p=0.000 n=15)
Div/2000/1000-16 545.3n ± 0% 527.0n ± 0% -3.36% (p=0.000 n=15)
Div/20000/10000-16 22.60µ ± 0% 22.20µ ± 0% -1.77% (p=0.000 n=15)
Div/200000/100000-16 889.0µ ± 0% 892.2µ ± 0% +0.35% (p=0.000 n=15)
Div/2000000/1000000-16 38.01m ± 0% 38.12m ± 0% +0.30% (p=0.000 n=15)
Div/20000000/10000000-16 1.437 ± 0% 1.444 ± 0% +0.50% (p=0.000 n=15)
NatMul/10-16 166.4n ± 2% 169.5n ± 1% +1.86% (p=0.000 n=15)
NatMul/100-16 5.733µ ± 1% 5.570µ ± 1% -2.84% (p=0.000 n=15)
NatMul/1000-16 232.6µ ± 1% 229.8µ ± 0% -1.22% (p=0.000 n=15)
NatMul/10000-16 9.039m ± 1% 8.969m ± 0% -0.77% (p=0.000 n=15)
NatMul/100000-16 367.0m ± 0% 368.8m ± 0% +0.48% (p=0.000 n=15)
geomean 16.15µ 15.50µ -4.01%
│ old │ new │
│ B/op │ B/op vs base │
NatMul/10-16 192.0 ± 0% 192.0 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100-16 4.750Ki ± 0% 1.751Ki ± 0% -63.14% (p=0.000 n=15)
NatMul/1000-16 48.33Ki ± 0% 16.02Ki ± 0% -66.85% (p=0.000 n=15)
NatMul/10000-16 536.5Ki ± 1% 165.7Ki ± 3% -69.12% (p=0.000 n=15)
NatMul/100000-16 6.078Mi ± 6% 4.197Mi ± 0% -30.94% (p=0.000 n=15)
geomean 42.81Ki 20.64Ki -51.78%
¹ all samples are equal
│ old │ new │
│ allocs/op │ allocs/op vs base │
NatMul/10-16 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100-16 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/1000-16 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/10000-16 2.000 ± 50% 1.000 ± 0% -50.00% (p=0.001 n=15)
NatMul/100000-16 9.000 ± 11% 8.000 ± 12% -11.11% (p=0.001 n=15)
geomean 1.783 1.516 -14.97%
¹ all samples are equal
goos: darwin
goarch: arm64
pkg: math/big
cpu: Apple M3 Pro
│ old │ new │
│ sec/op │ sec/op vs base │
Div/20/10-12 9.850n ± 1% 9.405n ± 1% -4.52% (p=0.000 n=15)
Div/40/20-12 9.858n ± 0% 9.403n ± 1% -4.62% (p=0.000 n=15)
Div/100/50-12 16.40n ± 1% 14.81n ± 0% -9.70% (p=0.000 n=15)
Div/200/100-12 88.48n ± 2% 80.88n ± 0% -8.59% (p=0.000 n=15)
Div/400/200-12 107.90n ± 1% 99.28n ± 1% -7.99% (p=0.000 n=15)
Div/1000/500-12 188.8n ± 1% 178.6n ± 1% -5.40% (p=0.000 n=15)
Div/2000/1000-12 399.9n ± 0% 389.1n ± 0% -2.70% (p=0.000 n=15)
Div/20000/10000-12 13.94µ ± 2% 13.81µ ± 1% ~ (p=0.574 n=15)
Div/200000/100000-12 523.8µ ± 0% 521.7µ ± 0% -0.40% (p=0.000 n=15)
Div/2000000/1000000-12 21.46m ± 0% 21.48m ± 0% ~ (p=0.067 n=15)
Div/20000000/10000000-12 812.5m ± 0% 812.9m ± 0% ~ (p=0.061 n=15)
NatMul/10-12 77.14n ± 0% 78.35n ± 1% +1.57% (p=0.000 n=15)
NatMul/100-12 2.999µ ± 0% 2.871µ ± 1% -4.27% (p=0.000 n=15)
NatMul/1000-12 126.2µ ± 0% 126.8µ ± 0% +0.51% (p=0.011 n=15)
NatMul/10000-12 5.099m ± 0% 5.125m ± 0% +0.51% (p=0.000 n=15)
NatMul/100000-12 206.7m ± 0% 208.4m ± 0% +0.80% (p=0.000 n=15)
geomean 9.512µ 9.236µ -2.91%
│ old │ new │
│ B/op │ B/op vs base │
NatMul/10-12 192.0 ± 0% 192.0 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100-12 4.750Ki ± 0% 1.750Ki ± 0% -63.16% (p=0.000 n=15)
NatMul/1000-12 48.13Ki ± 0% 16.01Ki ± 0% -66.73% (p=0.000 n=15)
NatMul/10000-12 483.5Ki ± 1% 163.2Ki ± 2% -66.24% (p=0.000 n=15)
NatMul/100000-12 5.480Mi ± 4% 1.532Mi ± 104% -72.05% (p=0.000 n=15)
geomean 41.03Ki 16.82Ki -59.01%
¹ all samples are equal
│ old │ new │
│ allocs/op │ allocs/op vs base │
NatMul/10-12 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100-12 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/1000-12 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/10000-12 1.000 ± 0% 1.000 ± 0% ~ (p=1.000 n=15) ¹
NatMul/100000-12 5.000 ± 0% 1.000 ± 400% -80.00% (p=0.007 n=15)
geomean 1.380 1.000 -27.52%
¹ all samples are equal
Change-Id: I7efa6fe37971ed26ae120a32250fcb47ece0a011
Reviewed-on: https://go-review.googlesource.com/c/go/+/650638
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Auto-Submit: Russ Cox <rsc@golang.org>
Reviewed-by: Ian Lance Taylor <iant@google.com>
Reviewed-by: Alan Donovan <adonovan@google.com>
|
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|
Russ Cox
|
763766e9ab |
math/big: report allocs in BenchmarkNatMul, BenchmarkNatSqr
Change-Id: I112f55c0e3ee3b75e615a06b27552de164565c04 Reviewed-on: https://go-review.googlesource.com/c/go/+/650637 Reviewed-by: Robert Griesemer <gri@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Ian Lance Taylor <iant@google.com> Auto-Submit: Russ Cox <rsc@golang.org> |
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|
Russ Cox
|
b66d83ccea |
math/big: clean up GCD a little
The GCD code was setting one *Int to the value of another
by smashing one struct on top of the other, instead of using Set.
That was safe in this one case, but it's not idiomatic in math/big
nor safe in general, so rewrite the code not to do that.
(In one case, by swapping variables around; in another, by calling Set.)
The added Set call does slow down GCDs by a small amount,
since the answer has to be copied out. To compensate for that,
optimize a bit: remove the s, t temporaries entirely and handle
vector x word multiplication directly. The net result is that almost
all GCDs are faster, except for small ones, which are a few
nanoseconds slower.
goos: darwin
goarch: arm64
pkg: math/big
cpu: Apple M3 Pro
│ bench.before │ bench.after │
│ sec/op │ sec/op vs base │
GCD10x10/WithoutXY-12 23.80n ± 1% 31.71n ± 1% +33.24% (p=0.000 n=10)
GCD10x10/WithXY-12 100.40n ± 0% 92.14n ± 1% -8.22% (p=0.000 n=10)
GCD10x100/WithoutXY-12 63.70n ± 0% 70.73n ± 0% +11.05% (p=0.000 n=10)
GCD10x100/WithXY-12 278.6n ± 0% 233.1n ± 1% -16.35% (p=0.000 n=10)
GCD10x1000/WithoutXY-12 153.4n ± 0% 162.2n ± 1% +5.74% (p=0.000 n=10)
GCD10x1000/WithXY-12 456.0n ± 0% 411.8n ± 1% -9.69% (p=0.000 n=10)
GCD10x10000/WithoutXY-12 1.002µ ± 1% 1.036µ ± 0% +3.39% (p=0.000 n=10)
GCD10x10000/WithXY-12 2.330µ ± 1% 2.210µ ± 0% -5.13% (p=0.000 n=10)
GCD10x100000/WithoutXY-12 8.894µ ± 0% 8.889µ ± 1% ~ (p=0.754 n=10)
GCD10x100000/WithXY-12 20.84µ ± 0% 20.24µ ± 0% -2.84% (p=0.000 n=10)
GCD100x100/WithoutXY-12 373.3n ± 3% 314.4n ± 0% -15.76% (p=0.000 n=10)
GCD100x100/WithXY-12 662.5n ± 0% 572.4n ± 1% -13.59% (p=0.000 n=10)
GCD100x1000/WithoutXY-12 641.8n ± 0% 598.1n ± 1% -6.81% (p=0.000 n=10)
GCD100x1000/WithXY-12 1.123µ ± 0% 1.019µ ± 1% -9.26% (p=0.000 n=10)
GCD100x10000/WithoutXY-12 2.870µ ± 0% 2.831µ ± 0% -1.38% (p=0.000 n=10)
GCD100x10000/WithXY-12 4.930µ ± 1% 4.675µ ± 0% -5.16% (p=0.000 n=10)
GCD100x100000/WithoutXY-12 24.08µ ± 0% 23.97µ ± 0% -0.48% (p=0.007 n=10)
GCD100x100000/WithXY-12 43.66µ ± 0% 42.52µ ± 0% -2.61% (p=0.001 n=10)
GCD1000x1000/WithoutXY-12 3.999µ ± 0% 3.569µ ± 1% -10.75% (p=0.000 n=10)
GCD1000x1000/WithXY-12 6.397µ ± 0% 5.534µ ± 0% -13.49% (p=0.000 n=10)
GCD1000x10000/WithoutXY-12 6.875µ ± 0% 6.450µ ± 0% -6.18% (p=0.000 n=10)
GCD1000x10000/WithXY-12 20.75µ ± 1% 19.17µ ± 1% -7.64% (p=0.000 n=10)
GCD1000x100000/WithoutXY-12 36.38µ ± 0% 35.60µ ± 1% -2.13% (p=0.000 n=10)
GCD1000x100000/WithXY-12 172.1µ ± 0% 174.4µ ± 3% ~ (p=0.052 n=10)
GCD10000x10000/WithoutXY-12 79.89µ ± 1% 75.16µ ± 2% -5.92% (p=0.000 n=10)
GCD10000x10000/WithXY-12 160.1µ ± 0% 150.0µ ± 0% -6.33% (p=0.000 n=10)
GCD10000x100000/WithoutXY-12 213.2µ ± 1% 209.0µ ± 1% -1.98% (p=0.000 n=10)
GCD10000x100000/WithXY-12 1.399m ± 0% 1.342m ± 3% -4.08% (p=0.002 n=10)
GCD100000x100000/WithoutXY-12 5.463m ± 1% 5.504m ± 2% ~ (p=0.190 n=10)
GCD100000x100000/WithXY-12 11.36m ± 0% 11.46m ± 1% +0.86% (p=0.000 n=10)
geomean 6.953µ 6.695µ -3.71%
goos: linux
goarch: amd64
pkg: math/big
cpu: AMD Ryzen 9 7950X 16-Core Processor
│ bench.before │ bench.after │
│ sec/op │ sec/op vs base │
GCD10x10/WithoutXY-32 39.66n ± 4% 44.34n ± 4% +11.77% (p=0.000 n=10)
GCD10x10/WithXY-32 156.7n ± 12% 130.8n ± 2% -16.53% (p=0.000 n=10)
GCD10x100/WithoutXY-32 115.8n ± 5% 120.2n ± 2% +3.89% (p=0.000 n=10)
GCD10x100/WithXY-32 465.3n ± 3% 368.1n ± 2% -20.91% (p=0.000 n=10)
GCD10x1000/WithoutXY-32 201.1n ± 1% 210.8n ± 2% +4.82% (p=0.000 n=10)
GCD10x1000/WithXY-32 652.9n ± 4% 605.0n ± 1% -7.32% (p=0.002 n=10)
GCD10x10000/WithoutXY-32 1.046µ ± 2% 1.143µ ± 1% +9.33% (p=0.000 n=10)
GCD10x10000/WithXY-32 3.360µ ± 1% 3.258µ ± 1% -3.04% (p=0.000 n=10)
GCD10x100000/WithoutXY-32 9.391µ ± 3% 9.997µ ± 1% +6.46% (p=0.000 n=10)
GCD10x100000/WithXY-32 27.92µ ± 1% 28.21µ ± 0% +1.04% (p=0.043 n=10)
GCD100x100/WithoutXY-32 443.7n ± 5% 320.0n ± 2% -27.88% (p=0.000 n=10)
GCD100x100/WithXY-32 789.9n ± 2% 690.4n ± 1% -12.60% (p=0.000 n=10)
GCD100x1000/WithoutXY-32 718.4n ± 3% 600.0n ± 1% -16.48% (p=0.000 n=10)
GCD100x1000/WithXY-32 1.388µ ± 4% 1.175µ ± 1% -15.28% (p=0.000 n=10)
GCD100x10000/WithoutXY-32 2.750µ ± 1% 2.668µ ± 1% -2.96% (p=0.000 n=10)
GCD100x10000/WithXY-32 6.016µ ± 1% 5.590µ ± 1% -7.09% (p=0.000 n=10)
GCD100x100000/WithoutXY-32 21.40µ ± 1% 22.30µ ± 1% +4.21% (p=0.000 n=10)
GCD100x100000/WithXY-32 47.02µ ± 4% 48.80µ ± 0% +3.78% (p=0.015 n=10)
GCD1000x1000/WithoutXY-32 3.417µ ± 4% 3.020µ ± 1% -11.65% (p=0.000 n=10)
GCD1000x1000/WithXY-32 5.752µ ± 0% 5.418µ ± 2% -5.81% (p=0.000 n=10)
GCD1000x10000/WithoutXY-32 6.150µ ± 0% 6.246µ ± 1% +1.55% (p=0.000 n=10)
GCD1000x10000/WithXY-32 24.68µ ± 3% 25.07µ ± 1% ~ (p=0.051 n=10)
GCD1000x100000/WithoutXY-32 34.60µ ± 2% 36.85µ ± 1% +6.51% (p=0.000 n=10)
GCD1000x100000/WithXY-32 209.5µ ± 4% 227.4µ ± 0% +8.56% (p=0.000 n=10)
GCD10000x10000/WithoutXY-32 90.69µ ± 0% 88.48µ ± 0% -2.44% (p=0.000 n=10)
GCD10000x10000/WithXY-32 197.1µ ± 0% 200.5µ ± 0% +1.73% (p=0.000 n=10)
GCD10000x100000/WithoutXY-32 239.1µ ± 0% 242.5µ ± 0% +1.42% (p=0.000 n=10)
GCD10000x100000/WithXY-32 1.963m ± 3% 2.028m ± 0% +3.28% (p=0.000 n=10)
GCD100000x100000/WithoutXY-32 7.466m ± 0% 7.412m ± 0% -0.71% (p=0.000 n=10)
GCD100000x100000/WithXY-32 16.10m ± 2% 16.47m ± 0% +2.25% (p=0.000 n=10)
geomean 8.388µ 8.127µ -3.12%
Change-Id: I161dc409bad11bcc553bc8116449905ae5b06742
Reviewed-on: https://go-review.googlesource.com/c/go/+/650636
Reviewed-by: Robert Griesemer <gri@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Alan Donovan <adonovan@google.com>
Auto-Submit: Russ Cox <rsc@golang.org>
|
||
|
qmuntal
|
f707e53fd5 |
all: surround -test.run arguments with ^$
If the -test.run value is not surrounded by ^$ then any test that matches the -test.run value will be run. This is normally not the desired behavior, as it can lead to unexpected tests being run. Change-Id: I3447aaebad5156bbef7f263cdb9f6b8c32331324 Reviewed-on: https://go-review.googlesource.com/c/go/+/651956 Reviewed-by: Cherry Mui <cherryyz@google.com> Reviewed-by: Ian Lance Taylor <iant@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> |
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|
Eng Zer Jun
|
cc874072f3 |
math/big: use built-in max function
Change-Id: I65721039dab311762e55c6a60dd75b82f6b4622f Reviewed-on: https://go-review.googlesource.com/c/go/+/642335 Reviewed-by: Ian Lance Taylor <iant@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Reviewed-by: Robert Griesemer <gri@google.com> Auto-Submit: Ian Lance Taylor <iant@google.com> |
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|
Sean Liao
|
32ff485c7c |
math/bits: update reference to debruijn paper
The old link no longer works. Fixes #70684 Change-Id: I8711ef7d5721bf20ef83f5192dd0d1f73dda6ce1 Reviewed-on: https://go-review.googlesource.com/c/go/+/633775 Auto-Submit: Ian Lance Taylor <iant@golang.org> Reviewed-by: Keith Randall <khr@golang.org> Reviewed-by: Michael Knyszek <mknyszek@google.com> Reviewed-by: Keith Randall <khr@google.com> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> |
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|
Jorropo
|
4c3aa5d324 |
math/rand/v2: replace <= 0 with == 0 for Uint function docs
This harmonize the docs with (*Rand).Uint* functions. And it make it clearer, I wasn't sure if it would try to interpret the uint as a signed number somehow, it does not pull any surprises make that clear. Change-Id: I5a87a0a5563dbabfc31e536e40ee69b11f5cb6cf Reviewed-on: https://go-review.googlesource.com/c/go/+/633535 LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> Commit-Queue: Ian Lance Taylor <iant@google.com> Reviewed-by: Ian Lance Taylor <iant@google.com> Auto-Submit: Ian Lance Taylor <iant@google.com> Reviewed-by: Robert Griesemer <gri@google.com> |
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|
Russ Cox
|
a947912d8a |
internal/byteorder: use canonical Go casing in names
If Be and Le stand for big-endian and little-endian, then they should be BE and LE. Change-Id: I723e3962b8918da84791783d3c547638f1c9e8a9 Reviewed-on: https://go-review.googlesource.com/c/go/+/627376 Reviewed-by: Robert Griesemer <gri@google.com> Auto-Submit: Russ Cox <rsc@golang.org> LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com> |
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Adam
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f7a14ae0cd |
math/big: properly linkify a reference
Change-Id: Ie7649060db25f1573eeaadd534a600bb24d30572
GitHub-Last-Rev:
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Xiaolin Zhao
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b521ebb55a |
math: implement arch{Floor, Ceil, Trunc} in hardware on loong64
benchmark:
goos: linux
goarch: loong64
pkg: math
cpu: Loongson-3A6000 @ 2500.00MHz
│ bench.old │ bench.new │
│ sec/op │ sec/op vs base │
Ceil 10.810n ± 0% 2.578n ± 0% -76.15% (p=0.000 n=20)
Floor 10.810n ± 0% 2.531n ± 0% -76.59% (p=0.000 n=20)
Trunc 9.606n ± 0% 2.530n ± 0% -73.67% (p=0.000 n=20)
geomean 10.39n 2.546n -75.50%
goos: linux
goarch: loong64
pkg: math
cpu: Loongson-3A5000 @ 2500.00MHz
│ bench.old │ bench.new │
│ sec/op │ sec/op vs base │
Ceil 13.220n ± 0% 7.703n ± 8% -41.73% (p=0.000 n=20)
Floor 12.410n ± 0% 7.248n ± 2% -41.59% (p=0.000 n=20)
Trunc 11.210n ± 0% 7.757n ± 4% -30.80% (p=0.000 n=20)
geomean 12.25n 7.566n -38.25%
Change-Id: I3af51e9852e9cf5f965fed895d68945a2e8675f4
Reviewed-on: https://go-review.googlesource.com/c/go/+/612615
Reviewed-by: Michael Knyszek <mknyszek@google.com>
Reviewed-by: Cherry Mui <cherryyz@google.com>
Reviewed-by: abner chenc <chenguoqi@loongson.cn>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
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