Google Git
Sign in
go / go / ea0491b70a82a207a951f869c7c1e5a52dbf410f
commitea0491b70a82a207a951f869c7c1e5a52dbf410f[log] [tgz]
authorDavid Leon Gil <coruus@gmail.com>Fri Jun 26 10:29:45 2015 -0700
committerAdam Langley <agl@golang.org>Sat Aug 29 19:11:03 2015 +0000
treead18e5005258ccd1075a0cc2f2786cbdc1d417c7
parentfac1039615b7f252c38317ce5069d35b45da3cef [diff]
math/big: use optimized formula in ModSqrt for 3 mod 4 primes

For primes which are 3 mod 4, using Tonelli-Shanks is slower
and more complicated than using the identity

     a**((p+1)/4) mod p == sqrt(a)

For 2^450-2^225-1 and 2^10860-2^5430-1, which are 3 mod 4:

BenchmarkModSqrt225_TonelliTri      1000     1135375 ns/op
BenchmarkModSqrt225_3Mod4          10000      156009 ns/op
BenchmarkModSqrt5430_Tonelli           1  3448851386 ns/op
BenchmarkModSqrt5430_3Mod4             2   914616710 ns/op

~2.6x to 7x faster.

Fixes #11437 (which is a prime choice of issues to fix)

Change-Id: I813fb29454160483ec29825469e0370d517850c2
Reviewed-on: https://go-review.googlesource.com/11522
Reviewed-by: Adam Langley <agl@golang.org>
2 files changed
tree: ad18e5005258ccd1075a0cc2f2786cbdc1d417c7
  1. api/
  2. doc/
  3. lib/
  4. misc/
  5. src/
  6. test/
  7. .gitattributes
  8. .gitignore
  9. AUTHORS
  10. CONTRIBUTING.md
  11. CONTRIBUTORS
  12. favicon.ico
  13. LICENSE
  14. PATENTS
  15. README.md
  16. robots.txt
README.md

The Go Programming Language

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

Gopher image

For documentation about how to install and use Go, visit https://golang.org/ or load doc/install-source.html in your web browser.

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.

Please report issues here: https://golang.org/issue/new

Go is the work of hundreds of contributors. We appreciate your help!

To contribute, please read the contribution guidelines: https://golang.org/doc/contribute.html

Please note that we do not use pull requests.

Unless otherwise noted, the Go source files are distributed under the BSD-style license found in the LICENSE file.

Binary Distribution Notes

If you have just untarred a binary Go distribution, you need to set the environment variable $GOROOT to the full path of the go directory (the one containing this file). You can omit the variable if you unpack it into /usr/local/go, or if you rebuild from sources by running all.bash (see doc/install-source.html). You should also add the Go binary directory $GOROOT/bin to your shell's path.

For example, if you extracted the tar file into $HOME/go, you might put the following in your .profile:

export GOROOT=$HOME/go
export PATH=$PATH:$GOROOT/bin

See https://golang.org/doc/install or doc/install.html for more details.