4d9dd35806
"Division by invariant integers using multiplication" paper by Granlund and Montgomery contains a method for directly computing divisibility (x%c == 0 for c constant) by means of the modular inverse. The method is further elaborated in "Hacker's Delight" by Warren Section 10-17 This general rule can compute divisibilty by one multiplication, and add and a compare for odd divisors and an additional rotate for even divisors. To apply the divisibility rule, we must take into account the rules to rewrite x%c = x-((x/c)*c) and (x/c) for c constant on the first optimization pass "opt". This complicates the matching as we want to match only in the cases where the result of (x/c) is not also needed. So, we must match on the expanded form of (x/c) in the expression x == c*(x/c) in the "late opt" pass after common subexpresion elimination. Note, that if there is an intermediate opt pass introduced in the future we could simplify these rules by delaying the magic division rewrite to "late opt" and matching directly on (x/c) in the intermediate opt pass. On amd64, the divisibility check is 30-45% faster. name old time/op new time/op delta` DivisiblePow2constI64-4 0.83ns ± 1% 0.82ns ± 0% ~ (p=0.079 n=5+4) DivisibleconstI64-4 2.68ns ± 1% 1.87ns ± 0% -30.33% (p=0.000 n=5+4) DivisibleWDivconstI64-4 2.69ns ± 1% 2.71ns ± 3% ~ (p=1.000 n=5+5) DivisiblePow2constI32-4 1.15ns ± 1% 1.15ns ± 0% ~ (p=0.238 n=5+4) DivisibleconstI32-4 2.24ns ± 1% 1.20ns ± 0% -46.48% (p=0.016 n=5+4) DivisibleWDivconstI32-4 2.27ns ± 1% 2.27ns ± 1% ~ (p=0.683 n=5+5) DivisiblePow2constI16-4 0.81ns ± 1% 0.82ns ± 1% ~ (p=0.135 n=5+5) DivisibleconstI16-4 2.11ns ± 2% 1.20ns ± 1% -42.99% (p=0.008 n=5+5) DivisibleWDivconstI16-4 2.23ns ± 0% 2.27ns ± 2% +1.79% (p=0.029 n=4+4) DivisiblePow2constI8-4 0.81ns ± 1% 0.81ns ± 1% ~ (p=0.286 n=5+5) DivisibleconstI8-4 2.13ns ± 3% 1.19ns ± 1% -43.84% (p=0.008 n=5+5) DivisibleWDivconstI8-4 2.23ns ± 1% 2.25ns ± 1% ~ (p=0.183 n=5+5) Fixes #30282 Fixes #15806 Change-Id: Id20d78263a4fdfe0509229ae4dfa2fede83fc1d0 Reviewed-on: https://go-review.googlesource.com/c/go/+/173998 Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Keith Randall <khr@golang.org> |
||
|---|---|---|
| .github | ||
| api | ||
| doc | ||
| lib/time | ||
| misc | ||
| src | ||
| test | ||
| .gitattributes | ||
| .gitignore | ||
| AUTHORS | ||
| CONTRIBUTING.md | ||
| CONTRIBUTORS | ||
| favicon.ico | ||
| LICENSE | ||
| PATENTS | ||
| README.md | ||
| robots.txt | ||
The Go Programming Language
Go is an open source programming language that makes it easy to build simple, reliable, and efficient software.
Gopher image by Renee French, licensed under Creative Commons 3.0 Attributions license.
Our canonical Git repository is located at https://go.googlesource.com/go. There is a mirror of the repository at https://github.com/golang/go.
Unless otherwise noted, the Go source files are distributed under the BSD-style license found in the LICENSE file.
Download and Install
Binary Distributions
Official binary distributions are available at https://golang.org/dl/.
After downloading a binary release, visit https://golang.org/doc/install or load doc/install.html in your web browser for installation instructions.
Install From Source
If a binary distribution is not available for your combination of operating system and architecture, visit https://golang.org/doc/install/source or load doc/install-source.html in your web browser for source installation instructions.
Contributing
Go is the work of thousands of contributors. We appreciate your help!
To contribute, please read the contribution guidelines: https://golang.org/doc/contribute.html
Note that the Go project uses the issue tracker for bug reports and proposals only. See https://golang.org/wiki/Questions for a list of places to ask questions about the Go language.