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#136: Start working on database persistence

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This commit is contained in:
TwinProduction
2021-07-12 00:56:30 -04:00
committed by Chris
parent e6335da94f
commit bd1eb7c61b
657 changed files with 2190821 additions and 82 deletions
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19
vendor/github.com/kballard/go-shellquote/LICENSE generated vendored Normal file
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Copyright (C) 2014 Kevin Ballard
Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the "Software"),
to deal in the Software without restriction, including without limitation
the rights to use, copy, modify, merge, publish, distribute, sublicense,
and/or sell copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE
OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

36
vendor/github.com/kballard/go-shellquote/README generated vendored Normal file
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PACKAGE
package shellquote
import "github.com/kballard/go-shellquote"
Shellquote provides utilities for joining/splitting strings using sh's
word-splitting rules.
VARIABLES
var (
UnterminatedSingleQuoteError = errors.New("Unterminated single-quoted string")
UnterminatedDoubleQuoteError = errors.New("Unterminated double-quoted string")
UnterminatedEscapeError = errors.New("Unterminated backslash-escape")
)
FUNCTIONS
func Join(args ...string) string
Join quotes each argument and joins them with a space. If passed to
/bin/sh, the resulting string will be split back into the original
arguments.
func Split(input string) (words []string, err error)
Split splits a string according to /bin/sh's word-splitting rules. It
supports backslash-escapes, single-quotes, and double-quotes. Notably it
does not support the $'' style of quoting. It also doesn't attempt to
perform any other sort of expansion, including brace expansion, shell
expansion, or pathname expansion.
If the given input has an unterminated quoted string or ends in a
backslash-escape, one of UnterminatedSingleQuoteError,
UnterminatedDoubleQuoteError, or UnterminatedEscapeError is returned.

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vendor/github.com/kballard/go-shellquote/doc.go generated vendored Normal file
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// Shellquote provides utilities for joining/splitting strings using sh's
// word-splitting rules.
package shellquote

102
vendor/github.com/kballard/go-shellquote/quote.go generated vendored Normal file
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package shellquote
import (
"bytes"
"strings"
"unicode/utf8"
)
// Join quotes each argument and joins them with a space.
// If passed to /bin/sh, the resulting string will be split back into the
// original arguments.
func Join(args ...string) string {
var buf bytes.Buffer
for i, arg := range args {
if i != 0 {
buf.WriteByte(' ')
}
quote(arg, &buf)
}
return buf.String()
}
const (
specialChars = "\\'\"`${[|&;<>()*?!"
extraSpecialChars = " \t\n"
prefixChars = "~"
)
func quote(word string, buf *bytes.Buffer) {
// We want to try to produce a "nice" output. As such, we will
// backslash-escape most characters, but if we encounter a space, or if we
// encounter an extra-special char (which doesn't work with
// backslash-escaping) we switch over to quoting the whole word. We do this
// with a space because it's typically easier for people to read multi-word
// arguments when quoted with a space rather than with ugly backslashes
// everywhere.
origLen := buf.Len()
if len(word) == 0 {
// oops, no content
buf.WriteString("''")
return
}
cur, prev := word, word
atStart := true
for len(cur) > 0 {
c, l := utf8.DecodeRuneInString(cur)
cur = cur[l:]
if strings.ContainsRune(specialChars, c) || (atStart && strings.ContainsRune(prefixChars, c)) {
// copy the non-special chars up to this point
if len(cur) < len(prev) {
buf.WriteString(prev[0 : len(prev)-len(cur)-l])
}
buf.WriteByte('\\')
buf.WriteRune(c)
prev = cur
} else if strings.ContainsRune(extraSpecialChars, c) {
// start over in quote mode
buf.Truncate(origLen)
goto quote
}
atStart = false
}
if len(prev) > 0 {
buf.WriteString(prev)
}
return
quote:
// quote mode
// Use single-quotes, but if we find a single-quote in the word, we need
// to terminate the string, emit an escaped quote, and start the string up
// again
inQuote := false
for len(word) > 0 {
i := strings.IndexRune(word, '\'')
if i == -1 {
break
}
if i > 0 {
if !inQuote {
buf.WriteByte('\'')
inQuote = true
}
buf.WriteString(word[0:i])
}
word = word[i+1:]
if inQuote {
buf.WriteByte('\'')
inQuote = false
}
buf.WriteString("\\'")
}
if len(word) > 0 {
if !inQuote {
buf.WriteByte('\'')
}
buf.WriteString(word)
buf.WriteByte('\'')
}
}

156
vendor/github.com/kballard/go-shellquote/unquote.go generated vendored Normal file
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package shellquote
import (
"bytes"
"errors"
"strings"
"unicode/utf8"
)
var (
UnterminatedSingleQuoteError = errors.New("Unterminated single-quoted string")
UnterminatedDoubleQuoteError = errors.New("Unterminated double-quoted string")
UnterminatedEscapeError = errors.New("Unterminated backslash-escape")
)
var (
splitChars = " \n\t"
singleChar = '\''
doubleChar = '"'
escapeChar = '\\'
doubleEscapeChars = "$`\"\n\\"
)
// Split splits a string according to /bin/sh's word-splitting rules. It
// supports backslash-escapes, single-quotes, and double-quotes. Notably it does
// not support the $'' style of quoting. It also doesn't attempt to perform any
// other sort of expansion, including brace expansion, shell expansion, or
// pathname expansion.
//
// If the given input has an unterminated quoted string or ends in a
// backslash-escape, one of UnterminatedSingleQuoteError,
// UnterminatedDoubleQuoteError, or UnterminatedEscapeError is returned.
func Split(input string) (words []string, err error) {
var buf bytes.Buffer
words = make([]string, 0)
for len(input) > 0 {
// skip any splitChars at the start
c, l := utf8.DecodeRuneInString(input)
if strings.ContainsRune(splitChars, c) {
input = input[l:]
continue
} else if c == escapeChar {
// Look ahead for escaped newline so we can skip over it
next := input[l:]
if len(next) == 0 {
err = UnterminatedEscapeError
return
}
c2, l2 := utf8.DecodeRuneInString(next)
if c2 == '\n' {
input = next[l2:]
continue
}
}
var word string
word, input, err = splitWord(input, &buf)
if err != nil {
return
}
words = append(words, word)
}
return
}
func splitWord(input string, buf *bytes.Buffer) (word string, remainder string, err error) {
buf.Reset()
raw:
{
cur := input
for len(cur) > 0 {
c, l := utf8.DecodeRuneInString(cur)
cur = cur[l:]
if c == singleChar {
buf.WriteString(input[0 : len(input)-len(cur)-l])
input = cur
goto single
} else if c == doubleChar {
buf.WriteString(input[0 : len(input)-len(cur)-l])
input = cur
goto double
} else if c == escapeChar {
buf.WriteString(input[0 : len(input)-len(cur)-l])
input = cur
goto escape
} else if strings.ContainsRune(splitChars, c) {
buf.WriteString(input[0 : len(input)-len(cur)-l])
return buf.String(), cur, nil
}
}
if len(input) > 0 {
buf.WriteString(input)
input = ""
}
goto done
}
escape:
{
if len(input) == 0 {
return "", "", UnterminatedEscapeError
}
c, l := utf8.DecodeRuneInString(input)
if c == '\n' {
// a backslash-escaped newline is elided from the output entirely
} else {
buf.WriteString(input[:l])
}
input = input[l:]
}
goto raw
single:
{
i := strings.IndexRune(input, singleChar)
if i == -1 {
return "", "", UnterminatedSingleQuoteError
}
buf.WriteString(input[0:i])
input = input[i+1:]
goto raw
}
double:
{
cur := input
for len(cur) > 0 {
c, l := utf8.DecodeRuneInString(cur)
cur = cur[l:]
if c == doubleChar {
buf.WriteString(input[0 : len(input)-len(cur)-l])
input = cur
goto raw
} else if c == escapeChar {
// bash only supports certain escapes in double-quoted strings
c2, l2 := utf8.DecodeRuneInString(cur)
cur = cur[l2:]
if strings.ContainsRune(doubleEscapeChars, c2) {
buf.WriteString(input[0 : len(input)-len(cur)-l-l2])
if c2 == '\n' {
// newline is special, skip the backslash entirely
} else {
buf.WriteRune(c2)
}
input = cur
}
}
}
return "", "", UnterminatedDoubleQuoteError
}
done:
return buf.String(), input, nil
}

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vendor/github.com/mattn/go-isatty/.travis.yml generated vendored Normal file
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language: go
sudo: false
go:
- 1.13.x
- tip
before_install:
- go get -t -v ./...
script:
- ./go.test.sh
after_success:
- bash <(curl -s https://codecov.io/bash)

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vendor/github.com/mattn/go-isatty/LICENSE generated vendored Normal file
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Copyright (c) Yasuhiro MATSUMOTO <mattn.jp@gmail.com>
MIT License (Expat)
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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vendor/github.com/mattn/go-isatty/README.md generated vendored Normal file
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# go-isatty
[![Godoc Reference](https://godoc.org/github.com/mattn/go-isatty?status.svg)](http://godoc.org/github.com/mattn/go-isatty)
[![Codecov](https://codecov.io/gh/mattn/go-isatty/branch/master/graph/badge.svg)](https://codecov.io/gh/mattn/go-isatty)
[![Coverage Status](https://coveralls.io/repos/github/mattn/go-isatty/badge.svg?branch=master)](https://coveralls.io/github/mattn/go-isatty?branch=master)
[![Go Report Card](https://goreportcard.com/badge/mattn/go-isatty)](https://goreportcard.com/report/mattn/go-isatty)
isatty for golang
## Usage
```go
package main
import (
"fmt"
"github.com/mattn/go-isatty"
"os"
)
func main() {
if isatty.IsTerminal(os.Stdout.Fd()) {
fmt.Println("Is Terminal")
} else if isatty.IsCygwinTerminal(os.Stdout.Fd()) {
fmt.Println("Is Cygwin/MSYS2 Terminal")
} else {
fmt.Println("Is Not Terminal")
}
}
```
## Installation
```
$ go get github.com/mattn/go-isatty
```
## License
MIT
## Author
Yasuhiro Matsumoto (a.k.a mattn)
## Thanks
* k-takata: base idea for IsCygwinTerminal
https://github.com/k-takata/go-iscygpty

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vendor/github.com/mattn/go-isatty/doc.go generated vendored Normal file
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// Package isatty implements interface to isatty
package isatty

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vendor/github.com/mattn/go-isatty/go.mod generated vendored Normal file
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module github.com/mattn/go-isatty
go 1.12
require golang.org/x/sys v0.0.0-20200116001909-b77594299b42

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vendor/github.com/mattn/go-isatty/go.sum generated vendored Normal file
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golang.org/x/sys v0.0.0-20200116001909-b77594299b42 h1:vEOn+mP2zCOVzKckCZy6YsCtDblrpj/w7B9nxGNELpg=
golang.org/x/sys v0.0.0-20200116001909-b77594299b42/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=

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vendor/github.com/mattn/go-isatty/go.test.sh generated vendored Normal file
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#!/usr/bin/env bash
set -e
echo "" > coverage.txt
for d in $(go list ./... | grep -v vendor); do
go test -race -coverprofile=profile.out -covermode=atomic "$d"
if [ -f profile.out ]; then
cat profile.out >> coverage.txt
rm profile.out
fi
done

18
vendor/github.com/mattn/go-isatty/isatty_bsd.go generated vendored Normal file
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// +build darwin freebsd openbsd netbsd dragonfly
// +build !appengine
package isatty
import "golang.org/x/sys/unix"
// IsTerminal return true if the file descriptor is terminal.
func IsTerminal(fd uintptr) bool {
_, err := unix.IoctlGetTermios(int(fd), unix.TIOCGETA)
return err == nil
}
// IsCygwinTerminal return true if the file descriptor is a cygwin or msys2
// terminal. This is also always false on this environment.
func IsCygwinTerminal(fd uintptr) bool {
return false
}

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vendor/github.com/mattn/go-isatty/isatty_others.go generated vendored Normal file
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// +build appengine js nacl
package isatty
// IsTerminal returns true if the file descriptor is terminal which
// is always false on js and appengine classic which is a sandboxed PaaS.
func IsTerminal(fd uintptr) bool {
return false
}
// IsCygwinTerminal() return true if the file descriptor is a cygwin or msys2
// terminal. This is also always false on this environment.
func IsCygwinTerminal(fd uintptr) bool {
return false
}

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vendor/github.com/mattn/go-isatty/isatty_plan9.go generated vendored Normal file
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// +build plan9
package isatty
import (
"syscall"
)
// IsTerminal returns true if the given file descriptor is a terminal.
func IsTerminal(fd uintptr) bool {
path, err := syscall.Fd2path(int(fd))
if err != nil {
return false
}
return path == "/dev/cons" || path == "/mnt/term/dev/cons"
}
// IsCygwinTerminal return true if the file descriptor is a cygwin or msys2
// terminal. This is also always false on this environment.
func IsCygwinTerminal(fd uintptr) bool {
return false
}

22
vendor/github.com/mattn/go-isatty/isatty_solaris.go generated vendored Normal file
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// +build solaris
// +build !appengine
package isatty
import (
"golang.org/x/sys/unix"
)
// IsTerminal returns true if the given file descriptor is a terminal.
// see: http://src.illumos.org/source/xref/illumos-gate/usr/src/lib/libbc/libc/gen/common/isatty.c
func IsTerminal(fd uintptr) bool {
var termio unix.Termio
err := unix.IoctlSetTermio(int(fd), unix.TCGETA, &termio)
return err == nil
}
// IsCygwinTerminal return true if the file descriptor is a cygwin or msys2
// terminal. This is also always false on this environment.
func IsCygwinTerminal(fd uintptr) bool {
return false
}

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vendor/github.com/mattn/go-isatty/isatty_tcgets.go generated vendored Normal file
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// +build linux aix
// +build !appengine
package isatty
import "golang.org/x/sys/unix"
// IsTerminal return true if the file descriptor is terminal.
func IsTerminal(fd uintptr) bool {
_, err := unix.IoctlGetTermios(int(fd), unix.TCGETS)
return err == nil
}
// IsCygwinTerminal return true if the file descriptor is a cygwin or msys2
// terminal. This is also always false on this environment.
func IsCygwinTerminal(fd uintptr) bool {
return false
}

125
vendor/github.com/mattn/go-isatty/isatty_windows.go generated vendored Normal file
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// +build windows
// +build !appengine
package isatty
import (
"errors"
"strings"
"syscall"
"unicode/utf16"
"unsafe"
)
const (
objectNameInfo uintptr = 1
fileNameInfo = 2
fileTypePipe = 3
)
var (
kernel32 = syscall.NewLazyDLL("kernel32.dll")
ntdll = syscall.NewLazyDLL("ntdll.dll")
procGetConsoleMode = kernel32.NewProc("GetConsoleMode")
procGetFileInformationByHandleEx = kernel32.NewProc("GetFileInformationByHandleEx")
procGetFileType = kernel32.NewProc("GetFileType")
procNtQueryObject = ntdll.NewProc("NtQueryObject")
)
func init() {
// Check if GetFileInformationByHandleEx is available.
if procGetFileInformationByHandleEx.Find() != nil {
procGetFileInformationByHandleEx = nil
}
}
// IsTerminal return true if the file descriptor is terminal.
func IsTerminal(fd uintptr) bool {
var st uint32
r, _, e := syscall.Syscall(procGetConsoleMode.Addr(), 2, fd, uintptr(unsafe.Pointer(&st)), 0)
return r != 0 && e == 0
}
// Check pipe name is used for cygwin/msys2 pty.
// Cygwin/MSYS2 PTY has a name like:
// \{cygwin,msys}-XXXXXXXXXXXXXXXX-ptyN-{from,to}-master
func isCygwinPipeName(name string) bool {
token := strings.Split(name, "-")
if len(token) < 5 {
return false
}
if token[0] != `\msys` &&
token[0] != `\cygwin` &&
token[0] != `\Device\NamedPipe\msys` &&
token[0] != `\Device\NamedPipe\cygwin` {
return false
}
if token[1] == "" {
return false
}
if !strings.HasPrefix(token[2], "pty") {
return false
}
if token[3] != `from` && token[3] != `to` {
return false
}
if token[4] != "master" {
return false
}
return true
}
// getFileNameByHandle use the undocomented ntdll NtQueryObject to get file full name from file handler
// since GetFileInformationByHandleEx is not avilable under windows Vista and still some old fashion
// guys are using Windows XP, this is a workaround for those guys, it will also work on system from
// Windows vista to 10
// see https://stackoverflow.com/a/18792477 for details
func getFileNameByHandle(fd uintptr) (string, error) {
if procNtQueryObject == nil {
return "", errors.New("ntdll.dll: NtQueryObject not supported")
}
var buf [4 + syscall.MAX_PATH]uint16
var result int
r, _, e := syscall.Syscall6(procNtQueryObject.Addr(), 5,
fd, objectNameInfo, uintptr(unsafe.Pointer(&buf)), uintptr(2*len(buf)), uintptr(unsafe.Pointer(&result)), 0)
if r != 0 {
return "", e
}
return string(utf16.Decode(buf[4 : 4+buf[0]/2])), nil
}
// IsCygwinTerminal() return true if the file descriptor is a cygwin or msys2
// terminal.
func IsCygwinTerminal(fd uintptr) bool {
if procGetFileInformationByHandleEx == nil {
name, err := getFileNameByHandle(fd)
if err != nil {
return false
}
return isCygwinPipeName(name)
}
// Cygwin/msys's pty is a pipe.
ft, _, e := syscall.Syscall(procGetFileType.Addr(), 1, fd, 0, 0)
if ft != fileTypePipe || e != 0 {
return false
}
var buf [2 + syscall.MAX_PATH]uint16
r, _, e := syscall.Syscall6(procGetFileInformationByHandleEx.Addr(),
4, fd, fileNameInfo, uintptr(unsafe.Pointer(&buf)),
uintptr(len(buf)*2), 0, 0)
if r == 0 || e != 0 {
return false
}
l := *(*uint32)(unsafe.Pointer(&buf))
return isCygwinPipeName(string(utf16.Decode(buf[2 : 2+l/2])))
}

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vendor/github.com/mattn/go-isatty/renovate.json generated vendored Normal file
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{
"extends": [
"config:base"
],
"postUpdateOptions": [
"gomodTidy"
]
}

27
vendor/github.com/remyoudompheng/bigfft/LICENSE generated vendored Normal file
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Copyright (c) 2012 The Go Authors. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following disclaimer
in the documentation and/or other materials provided with the
distribution.
* Neither the name of Google Inc. nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

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vendor/github.com/remyoudompheng/bigfft/README generated vendored Normal file
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Benchmarking math/big vs. bigfft
Number size old ns/op new ns/op delta
1kb 1599 1640 +2.56%
10kb 61533 62170 +1.04%
50kb 833693 831051 -0.32%
100kb 2567995 2693864 +4.90%
1Mb 105237800 28446400 -72.97%
5Mb 1272947000 168554600 -86.76%
10Mb 3834354000 405120200 -89.43%
20Mb 11514488000 845081600 -92.66%
50Mb 49199945000 2893950000 -94.12%
100Mb 147599836000 5921594000 -95.99%
Benchmarking GMP vs bigfft
Number size GMP ns/op Go ns/op delta
1kb 536 1500 +179.85%
10kb 26669 50777 +90.40%
50kb 252270 658534 +161.04%
100kb 686813 2127534 +209.77%
1Mb 12100000 22391830 +85.06%
5Mb 111731843 133550600 +19.53%
10Mb 212314000 318595800 +50.06%
20Mb 490196000 671512800 +36.99%
50Mb 1280000000 2451476000 +91.52%
100Mb 2673000000 5228991000 +95.62%
Benchmarks were run on a Core 2 Quad Q8200 (2.33GHz).
FFT is enabled when input numbers are over 200kbits.
Scanning large decimal number from strings.
(math/big [n^2 complexity] vs bigfft [n^1.6 complexity], Core i5-4590)
Digits old ns/op new ns/op delta
1e3 9995 10876 +8.81%
1e4 175356 243806 +39.03%
1e5 9427422 6780545 -28.08%
1e6 1776707489 144867502 -91.85%
2e6 6865499995 346540778 -94.95%
5e6 42641034189 1069878799 -97.49%
10e6 151975273589 2693328580 -98.23%

36
vendor/github.com/remyoudompheng/bigfft/arith_386.s generated vendored Normal file
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// Trampolines to math/big assembly implementations.
#include "textflag.h"
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
JMP math∕big·addVV(SB)
// func subVV(z, x, y []Word) (c Word)
TEXT ·subVV(SB),NOSPLIT,$0
JMP math∕big·subVV(SB)
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),NOSPLIT,$0
JMP math∕big·addVW(SB)
// func subVW(z, x []Word, y Word) (c Word)
TEXT ·subVW(SB),NOSPLIT,$0
JMP math∕big·subVW(SB)
// func shlVU(z, x []Word, s uint) (c Word)
TEXT ·shlVU(SB),NOSPLIT,$0
JMP math∕big·shlVU(SB)
// func shrVU(z, x []Word, s uint) (c Word)
TEXT ·shrVU(SB),NOSPLIT,$0
JMP math∕big·shrVU(SB)
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
TEXT ·mulAddVWW(SB),NOSPLIT,$0
JMP math∕big·mulAddVWW(SB)
// func addMulVVW(z, x []Word, y Word) (c Word)
TEXT ·addMulVVW(SB),NOSPLIT,$0
JMP math∕big·addMulVVW(SB)

38
vendor/github.com/remyoudompheng/bigfft/arith_amd64.s generated vendored Normal file
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// Trampolines to math/big assembly implementations.
#include "textflag.h"
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
JMP math∕big·addVV(SB)
// func subVV(z, x, y []Word) (c Word)
// (same as addVV except for SBBQ instead of ADCQ and label names)
TEXT ·subVV(SB),NOSPLIT,$0
JMP math∕big·subVV(SB)
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),NOSPLIT,$0
JMP math∕big·addVW(SB)
// func subVW(z, x []Word, y Word) (c Word)
// (same as addVW except for SUBQ/SBBQ instead of ADDQ/ADCQ and label names)
TEXT ·subVW(SB),NOSPLIT,$0
JMP math∕big·subVW(SB)
// func shlVU(z, x []Word, s uint) (c Word)
TEXT ·shlVU(SB),NOSPLIT,$0
JMP math∕big·shlVU(SB)
// func shrVU(z, x []Word, s uint) (c Word)
TEXT ·shrVU(SB),NOSPLIT,$0
JMP math∕big·shrVU(SB)
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
TEXT ·mulAddVWW(SB),NOSPLIT,$0
JMP math∕big·mulAddVWW(SB)
// func addMulVVW(z, x []Word, y Word) (c Word)
TEXT ·addMulVVW(SB),NOSPLIT,$0
JMP math∕big·addMulVVW(SB)

36
vendor/github.com/remyoudompheng/bigfft/arith_arm.s generated vendored Normal file
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// Trampolines to math/big assembly implementations.
#include "textflag.h"
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
B math∕big·addVV(SB)
// func subVV(z, x, y []Word) (c Word)
TEXT ·subVV(SB),NOSPLIT,$0
B math∕big·subVV(SB)
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),NOSPLIT,$0
B math∕big·addVW(SB)
// func subVW(z, x []Word, y Word) (c Word)
TEXT ·subVW(SB),NOSPLIT,$0
B math∕big·subVW(SB)
// func shlVU(z, x []Word, s uint) (c Word)
TEXT ·shlVU(SB),NOSPLIT,$0
B math∕big·shlVU(SB)
// func shrVU(z, x []Word, s uint) (c Word)
TEXT ·shrVU(SB),NOSPLIT,$0
B math∕big·shrVU(SB)
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
TEXT ·mulAddVWW(SB),NOSPLIT,$0
B math∕big·mulAddVWW(SB)
// func addMulVVW(z, x []Word, y Word) (c Word)
TEXT ·addMulVVW(SB),NOSPLIT,$0
B math∕big·addMulVVW(SB)

36
vendor/github.com/remyoudompheng/bigfft/arith_arm64.s generated vendored Normal file
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// Trampolines to math/big assembly implementations.
#include "textflag.h"
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
B math∕big·addVV(SB)
// func subVV(z, x, y []Word) (c Word)
TEXT ·subVV(SB),NOSPLIT,$0
B math∕big·subVV(SB)
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),NOSPLIT,$0
B math∕big·addVW(SB)
// func subVW(z, x []Word, y Word) (c Word)
TEXT ·subVW(SB),NOSPLIT,$0
B math∕big·subVW(SB)
// func shlVU(z, x []Word, s uint) (c Word)
TEXT ·shlVU(SB),NOSPLIT,$0
B math∕big·shlVU(SB)
// func shrVU(z, x []Word, s uint) (c Word)
TEXT ·shrVU(SB),NOSPLIT,$0
B math∕big·shrVU(SB)
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
TEXT ·mulAddVWW(SB),NOSPLIT,$0
B math∕big·mulAddVWW(SB)
// func addMulVVW(z, x []Word, y Word) (c Word)
TEXT ·addMulVVW(SB),NOSPLIT,$0
B math∕big·addMulVVW(SB)

16
vendor/github.com/remyoudompheng/bigfft/arith_decl.go generated vendored Normal file
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// Copyright 2010 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package bigfft
import . "math/big"
// implemented in arith_$GOARCH.s
func addVV(z, x, y []Word) (c Word)
func subVV(z, x, y []Word) (c Word)
func addVW(z, x []Word, y Word) (c Word)
func subVW(z, x []Word, y Word) (c Word)
func shlVU(z, x []Word, s uint) (c Word)
func mulAddVWW(z, x []Word, y, r Word) (c Word)
func addMulVVW(z, x []Word, y Word) (c Word)

40
vendor/github.com/remyoudompheng/bigfft/arith_mips64x.s generated vendored Normal file
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// Trampolines to math/big assembly implementations.
// +build mips64 mips64le
#include "textflag.h"
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
JMP math∕big·addVV(SB)
// func subVV(z, x, y []Word) (c Word)
// (same as addVV except for SBBQ instead of ADCQ and label names)
TEXT ·subVV(SB),NOSPLIT,$0
JMP math∕big·subVV(SB)
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),NOSPLIT,$0
JMP math∕big·addVW(SB)
// func subVW(z, x []Word, y Word) (c Word)
// (same as addVW except for SUBQ/SBBQ instead of ADDQ/ADCQ and label names)
TEXT ·subVW(SB),NOSPLIT,$0
JMP math∕big·subVW(SB)
// func shlVU(z, x []Word, s uint) (c Word)
TEXT ·shlVU(SB),NOSPLIT,$0
JMP math∕big·shlVU(SB)
// func shrVU(z, x []Word, s uint) (c Word)
TEXT ·shrVU(SB),NOSPLIT,$0
JMP math∕big·shrVU(SB)
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
TEXT ·mulAddVWW(SB),NOSPLIT,$0
JMP math∕big·mulAddVWW(SB)
// func addMulVVW(z, x []Word, y Word) (c Word)
TEXT ·addMulVVW(SB),NOSPLIT,$0
JMP math∕big·addMulVVW(SB)

40
vendor/github.com/remyoudompheng/bigfft/arith_mipsx.s generated vendored Normal file
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// Trampolines to math/big assembly implementations.
// +build mips mipsle
#include "textflag.h"
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
JMP math∕big·addVV(SB)
// func subVV(z, x, y []Word) (c Word)
// (same as addVV except for SBBQ instead of ADCQ and label names)
TEXT ·subVV(SB),NOSPLIT,$0
JMP math∕big·subVV(SB)
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),NOSPLIT,$0
JMP math∕big·addVW(SB)
// func subVW(z, x []Word, y Word) (c Word)
// (same as addVW except for SUBQ/SBBQ instead of ADDQ/ADCQ and label names)
TEXT ·subVW(SB),NOSPLIT,$0
JMP math∕big·subVW(SB)
// func shlVU(z, x []Word, s uint) (c Word)
TEXT ·shlVU(SB),NOSPLIT,$0
JMP math∕big·shlVU(SB)
// func shrVU(z, x []Word, s uint) (c Word)
TEXT ·shrVU(SB),NOSPLIT,$0
JMP math∕big·shrVU(SB)
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
TEXT ·mulAddVWW(SB),NOSPLIT,$0
JMP math∕big·mulAddVWW(SB)
// func addMulVVW(z, x []Word, y Word) (c Word)
TEXT ·addMulVVW(SB),NOSPLIT,$0
JMP math∕big·addMulVVW(SB)

38
vendor/github.com/remyoudompheng/bigfft/arith_ppc64x.s generated vendored Normal file
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// Trampolines to math/big assembly implementations.
// +build ppc64 ppc64le
#include "textflag.h"
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
BR math∕big·addVV(SB)
// func subVV(z, x, y []Word) (c Word)
TEXT ·subVV(SB),NOSPLIT,$0
BR math∕big·subVV(SB)
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),NOSPLIT,$0
BR math∕big·addVW(SB)
// func subVW(z, x []Word, y Word) (c Word)
TEXT ·subVW(SB),NOSPLIT,$0
BR math∕big·subVW(SB)
// func shlVU(z, x []Word, s uint) (c Word)
TEXT ·shlVU(SB),NOSPLIT,$0
BR math∕big·shlVU(SB)
// func shrVU(z, x []Word, s uint) (c Word)
TEXT ·shrVU(SB),NOSPLIT,$0
BR math∕big·shrVU(SB)
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
TEXT ·mulAddVWW(SB),NOSPLIT,$0
BR math∕big·mulAddVWW(SB)
// func addMulVVW(z, x []Word, y Word) (c Word)
TEXT ·addMulVVW(SB),NOSPLIT,$0
BR math∕big·addMulVVW(SB)

37
vendor/github.com/remyoudompheng/bigfft/arith_s390x.s generated vendored Normal file
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// Trampolines to math/big assembly implementations.
#include "textflag.h"
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
BR math∕big·addVV(SB)
// func subVV(z, x, y []Word) (c Word)
TEXT ·subVV(SB),NOSPLIT,$0
BR math∕big·subVV(SB)
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),NOSPLIT,$0
BR math∕big·addVW(SB)
// func subVW(z, x []Word, y Word) (c Word)
TEXT ·subVW(SB),NOSPLIT,$0
BR math∕big·subVW(SB)
// func shlVU(z, x []Word, s uint) (c Word)
TEXT ·shlVU(SB),NOSPLIT,$0
BR math∕big·shlVU(SB)
// func shrVU(z, x []Word, s uint) (c Word)
TEXT ·shrVU(SB),NOSPLIT,$0
BR math∕big·shrVU(SB)
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
TEXT ·mulAddVWW(SB),NOSPLIT,$0
BR math∕big·mulAddVWW(SB)
// func addMulVVW(z, x []Word, y Word) (c Word)
TEXT ·addMulVVW(SB),NOSPLIT,$0
BR math∕big·addMulVVW(SB)

216
vendor/github.com/remyoudompheng/bigfft/fermat.go generated vendored Normal file
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package bigfft
import (
"math/big"
)
// Arithmetic modulo 2^n+1.
// A fermat of length w+1 represents a number modulo 2^(w*_W) + 1. The last
// word is zero or one. A number has at most two representatives satisfying the
// 0-1 last word constraint.
type fermat nat
func (n fermat) String() string { return nat(n).String() }
func (z fermat) norm() {
n := len(z) - 1
c := z[n]
if c == 0 {
return
}
if z[0] >= c {
z[n] = 0
z[0] -= c
return
}
// z[0] < z[n].
subVW(z, z, c) // Substract c
if c > 1 {
z[n] -= c - 1
c = 1
}
// Add back c.
if z[n] == 1 {
z[n] = 0
return
} else {
addVW(z, z, 1)
}
}
// Shift computes (x << k) mod (2^n+1).
func (z fermat) Shift(x fermat, k int) {
if len(z) != len(x) {
panic("len(z) != len(x) in Shift")
}
n := len(x) - 1
// Shift by n*_W is taking the opposite.
k %= 2 * n * _W
if k < 0 {
k += 2 * n * _W
}
neg := false
if k >= n*_W {
k -= n * _W
neg = true
}
kw, kb := k/_W, k%_W
z[n] = 1 // Add (-1)
if !neg {
for i := 0; i < kw; i++ {
z[i] = 0
}
// Shift left by kw words.
// x = a·2^(n-k) + b
// x<<k = (b<<k) - a
copy(z[kw:], x[:n-kw])
b := subVV(z[:kw+1], z[:kw+1], x[n-kw:])
if z[kw+1] > 0 {
z[kw+1] -= b
} else {
subVW(z[kw+1:], z[kw+1:], b)
}
} else {
for i := kw + 1; i < n; i++ {
z[i] = 0
}
// Shift left and negate, by kw words.
copy(z[:kw+1], x[n-kw:n+1]) // z_low = x_high
b := subVV(z[kw:n], z[kw:n], x[:n-kw]) // z_high -= x_low
z[n] -= b
}
// Add back 1.
if z[n] > 0 {
z[n]--
} else if z[0] < ^big.Word(0) {
z[0]++
} else {
addVW(z, z, 1)
}
// Shift left by kb bits
shlVU(z, z, uint(kb))
z.norm()
}
// ShiftHalf shifts x by k/2 bits the left. Shifting by 1/2 bit
// is multiplication by sqrt(2) mod 2^n+1 which is 2^(3n/4) - 2^(n/4).
// A temporary buffer must be provided in tmp.
func (z fermat) ShiftHalf(x fermat, k int, tmp fermat) {
n := len(z) - 1
if k%2 == 0 {
z.Shift(x, k/2)
return
}
u := (k - 1) / 2
a := u + (3*_W/4)*n
b := u + (_W/4)*n
z.Shift(x, a)
tmp.Shift(x, b)
z.Sub(z, tmp)
}
// Add computes addition mod 2^n+1.
func (z fermat) Add(x, y fermat) fermat {
if len(z) != len(x) {
panic("Add: len(z) != len(x)")
}
addVV(z, x, y) // there cannot be a carry here.
z.norm()
return z
}
// Sub computes substraction mod 2^n+1.
func (z fermat) Sub(x, y fermat) fermat {
if len(z) != len(x) {
panic("Add: len(z) != len(x)")
}
n := len(y) - 1
b := subVV(z[:n], x[:n], y[:n])
b += y[n]
// If b > 0, we need to subtract b<<n, which is the same as adding b.
z[n] = x[n]
if z[0] <= ^big.Word(0)-b {
z[0] += b
} else {
addVW(z, z, b)
}
z.norm()
return z
}
func (z fermat) Mul(x, y fermat) fermat {
if len(x) != len(y) {
panic("Mul: len(x) != len(y)")
}
n := len(x) - 1
if n < 30 {
z = z[:2*n+2]
basicMul(z, x, y)
z = z[:2*n+1]
} else {
var xi, yi, zi big.Int
xi.SetBits(x)
yi.SetBits(y)
zi.SetBits(z)
zb := zi.Mul(&xi, &yi).Bits()
if len(zb) <= n {
// Short product.
copy(z, zb)
for i := len(zb); i < len(z); i++ {
z[i] = 0
}
return z
}
z = zb
}
// len(z) is at most 2n+1.
if len(z) > 2*n+1 {
panic("len(z) > 2n+1")
}
// We now have
// z = z[:n] + 1<<(n*W) * z[n:2n+1]
// which normalizes to:
// z = z[:n] - z[n:2n] + z[2n]
c1 := big.Word(0)
if len(z) > 2*n {
c1 = addVW(z[:n], z[:n], z[2*n])
}
c2 := big.Word(0)
if len(z) >= 2*n {
c2 = subVV(z[:n], z[:n], z[n:2*n])
} else {
m := len(z) - n
c2 = subVV(z[:m], z[:m], z[n:])
c2 = subVW(z[m:n], z[m:n], c2)
}
// Restore carries.
// Substracting z[n] -= c2 is the same
// as z[0] += c2
z = z[:n+1]
z[n] = c1
c := addVW(z, z, c2)
if c != 0 {
panic("impossible")
}
z.norm()
return z
}
// copied from math/big
//
// basicMul multiplies x and y and leaves the result in z.
// The (non-normalized) result is placed in z[0 : len(x) + len(y)].
func basicMul(z, x, y fermat) {
// initialize z
for i := 0; i < len(z); i++ {
z[i] = 0
}
for i, d := range y {
if d != 0 {
z[len(x)+i] = addMulVVW(z[i:i+len(x)], x, d)
}
}
}

370
vendor/github.com/remyoudompheng/bigfft/fft.go generated vendored Normal file
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// Package bigfft implements multiplication of big.Int using FFT.
//
// The implementation is based on the Schönhage-Strassen method
// using integer FFT modulo 2^n+1.
package bigfft
import (
"math/big"
"unsafe"
)
const _W = int(unsafe.Sizeof(big.Word(0)) * 8)
type nat []big.Word
func (n nat) String() string {
v := new(big.Int)
v.SetBits(n)
return v.String()
}
// fftThreshold is the size (in words) above which FFT is used over
// Karatsuba from math/big.
//
// TestCalibrate seems to indicate a threshold of 60kbits on 32-bit
// arches and 110kbits on 64-bit arches.
var fftThreshold = 1800
// Mul computes the product x*y and returns z.
// It can be used instead of the Mul method of
// *big.Int from math/big package.
func Mul(x, y *big.Int) *big.Int {
xwords := len(x.Bits())
ywords := len(y.Bits())
if xwords > fftThreshold && ywords > fftThreshold {
return mulFFT(x, y)
}
return new(big.Int).Mul(x, y)
}
func mulFFT(x, y *big.Int) *big.Int {
var xb, yb nat = x.Bits(), y.Bits()
zb := fftmul(xb, yb)
z := new(big.Int)
z.SetBits(zb)
if x.Sign()*y.Sign() < 0 {
z.Neg(z)
}
return z
}
// A FFT size of K=1<<k is adequate when K is about 2*sqrt(N) where
// N = x.Bitlen() + y.Bitlen().
func fftmul(x, y nat) nat {
k, m := fftSize(x, y)
xp := polyFromNat(x, k, m)
yp := polyFromNat(y, k, m)
rp := xp.Mul(&yp)
return rp.Int()
}
// fftSizeThreshold[i] is the maximal size (in bits) where we should use
// fft size i.
var fftSizeThreshold = [...]int64{0, 0, 0,
4 << 10, 8 << 10, 16 << 10, // 5
32 << 10, 64 << 10, 1 << 18, 1 << 20, 3 << 20, // 10
8 << 20, 30 << 20, 100 << 20, 300 << 20, 600 << 20,
}
// returns the FFT length k, m the number of words per chunk
// such that m << k is larger than the number of words
// in x*y.
func fftSize(x, y nat) (k uint, m int) {
words := len(x) + len(y)
bits := int64(words) * int64(_W)
k = uint(len(fftSizeThreshold))
for i := range fftSizeThreshold {
if fftSizeThreshold[i] > bits {
k = uint(i)
break
}
}
// The 1<<k chunks of m words must have N bits so that
// 2^N-1 is larger than x*y. That is, m<<k > words
m = words>>k + 1
return
}
// valueSize returns the length (in words) to use for polynomial
// coefficients, to compute a correct product of polynomials P*Q
// where deg(P*Q) < K (== 1<<k) and where coefficients of P and Q are
// less than b^m (== 1 << (m*_W)).
// The chosen length (in bits) must be a multiple of 1 << (k-extra).
func valueSize(k uint, m int, extra uint) int {
// The coefficients of P*Q are less than b^(2m)*K
// so we need W * valueSize >= 2*m*W+K
n := 2*m*_W + int(k) // necessary bits
K := 1 << (k - extra)
if K < _W {
K = _W
}
n = ((n / K) + 1) * K // round to a multiple of K
return n / _W
}
// poly represents an integer via a polynomial in Z[x]/(x^K+1)
// where K is the FFT length and b^m is the computation basis 1<<(m*_W).
// If P = a[0] + a[1] x + ... a[n] x^(K-1), the associated natural number
// is P(b^m).
type poly struct {
k uint // k is such that K = 1<<k.
m int // the m such that P(b^m) is the original number.
a []nat // a slice of at most K m-word coefficients.
}
// polyFromNat slices the number x into a polynomial
// with 1<<k coefficients made of m words.
func polyFromNat(x nat, k uint, m int) poly {
p := poly{k: k, m: m}
length := len(x)/m + 1
p.a = make([]nat, length)
for i := range p.a {
if len(x) < m {
p.a[i] = make(nat, m)
copy(p.a[i], x)
break
}
p.a[i] = x[:m]
x = x[m:]
}
return p
}
// Int evaluates back a poly to its integer value.
func (p *poly) Int() nat {
length := len(p.a)*p.m + 1
if na := len(p.a); na > 0 {
length += len(p.a[na-1])
}
n := make(nat, length)
m := p.m
np := n
for i := range p.a {
l := len(p.a[i])
c := addVV(np[:l], np[:l], p.a[i])
if np[l] < ^big.Word(0) {
np[l] += c
} else {
addVW(np[l:], np[l:], c)
}
np = np[m:]
}
n = trim(n)
return n
}
func trim(n nat) nat {
for i := range n {
if n[len(n)-1-i] != 0 {
return n[:len(n)-i]
}
}
return nil
}
// Mul multiplies p and q modulo X^K-1, where K = 1<<p.k.
// The product is done via a Fourier transform.
func (p *poly) Mul(q *poly) poly {
// extra=2 because:
// * some power of 2 is a K-th root of unity when n is a multiple of K/2.
// * 2 itself is a square (see fermat.ShiftHalf)
n := valueSize(p.k, p.m, 2)
pv, qv := p.Transform(n), q.Transform(n)
rv := pv.Mul(&qv)
r := rv.InvTransform()
r.m = p.m
return r
}
// A polValues represents the value of a poly at the powers of a
// K-th root of unity θ=2^(l/2) in Z/(b^n+1)Z, where b^n = 2^(K/4*l).
type polValues struct {
k uint // k is such that K = 1<<k.
n int // the length of coefficients, n*_W a multiple of K/4.
values []fermat // a slice of K (n+1)-word values
}
// Transform evaluates p at θ^i for i = 0...K-1, where
// θ is a K-th primitive root of unity in Z/(b^n+1)Z.
func (p *poly) Transform(n int) polValues {
k := p.k
inputbits := make([]big.Word, (n+1)<<k)
input := make([]fermat, 1<<k)
// Now computed q(ω^i) for i = 0 ... K-1
valbits := make([]big.Word, (n+1)<<k)
values := make([]fermat, 1<<k)
for i := range values {
input[i] = inputbits[i*(n+1) : (i+1)*(n+1)]
if i < len(p.a) {
copy(input[i], p.a[i])
}
values[i] = fermat(valbits[i*(n+1) : (i+1)*(n+1)])
}
fourier(values, input, false, n, k)
return polValues{k, n, values}
}
// InvTransform reconstructs p (modulo X^K - 1) from its
// values at θ^i for i = 0..K-1.
func (v *polValues) InvTransform() poly {
k, n := v.k, v.n
// Perform an inverse Fourier transform to recover p.
pbits := make([]big.Word, (n+1)<<k)
p := make([]fermat, 1<<k)
for i := range p {
p[i] = fermat(pbits[i*(n+1) : (i+1)*(n+1)])
}
fourier(p, v.values, true, n, k)
// Divide by K, and untwist q to recover p.
u := make(fermat, n+1)
a := make([]nat, 1<<k)
for i := range p {
u.Shift(p[i], -int(k))
copy(p[i], u)
a[i] = nat(p[i])
}
return poly{k: k, m: 0, a: a}
}
// NTransform evaluates p at θω^i for i = 0...K-1, where
// θ is a (2K)-th primitive root of unity in Z/(b^n+1)Z
// and ω = θ².
func (p *poly) NTransform(n int) polValues {
k := p.k
if len(p.a) >= 1<<k {
panic("Transform: len(p.a) >= 1<<k")
}
// θ is represented as a shift.
θshift := (n * _W) >> k
// p(x) = a_0 + a_1 x + ... + a_{K-1} x^(K-1)
// p(θx) = q(x) where
// q(x) = a_0 + θa_1 x + ... + θ^(K-1) a_{K-1} x^(K-1)
//
// Twist p by θ to obtain q.
tbits := make([]big.Word, (n+1)<<k)
twisted := make([]fermat, 1<<k)
src := make(fermat, n+1)
for i := range twisted {
twisted[i] = fermat(tbits[i*(n+1) : (i+1)*(n+1)])
if i < len(p.a) {
for i := range src {
src[i] = 0
}
copy(src, p.a[i])
twisted[i].Shift(src, θshift*i)
}
}
// Now computed q(ω^i) for i = 0 ... K-1
valbits := make([]big.Word, (n+1)<<k)
values := make([]fermat, 1<<k)
for i := range values {
values[i] = fermat(valbits[i*(n+1) : (i+1)*(n+1)])
}
fourier(values, twisted, false, n, k)
return polValues{k, n, values}
}
// InvTransform reconstructs a polynomial from its values at
// roots of x^K+1. The m field of the returned polynomial
// is unspecified.
func (v *polValues) InvNTransform() poly {
k := v.k
n := v.n
θshift := (n * _W) >> k
// Perform an inverse Fourier transform to recover q.
qbits := make([]big.Word, (n+1)<<k)
q := make([]fermat, 1<<k)
for i := range q {
q[i] = fermat(qbits[i*(n+1) : (i+1)*(n+1)])
}
fourier(q, v.values, true, n, k)
// Divide by K, and untwist q to recover p.
u := make(fermat, n+1)
a := make([]nat, 1<<k)
for i := range q {
u.Shift(q[i], -int(k)-i*θshift)
copy(q[i], u)
a[i] = nat(q[i])
}
return poly{k: k, m: 0, a: a}
}
// fourier performs an unnormalized Fourier transform
// of src, a length 1<<k vector of numbers modulo b^n+1
// where b = 1<<_W.
func fourier(dst []fermat, src []fermat, backward bool, n int, k uint) {
var rec func(dst, src []fermat, size uint)
tmp := make(fermat, n+1) // pre-allocate temporary variables.
tmp2 := make(fermat, n+1) // pre-allocate temporary variables.
// The recursion function of the FFT.
// The root of unity used in the transform is ω=1<<(ω2shift/2).
// The source array may use shifted indices (i.e. the i-th
// element is src[i << idxShift]).
rec = func(dst, src []fermat, size uint) {
idxShift := k - size
ω2shift := (4 * n * _W) >> size
if backward {
ω2shift = -ω2shift
}
// Easy cases.
if len(src[0]) != n+1 || len(dst[0]) != n+1 {
panic("len(src[0]) != n+1 || len(dst[0]) != n+1")
}
switch size {
case 0:
copy(dst[0], src[0])
return
case 1:
dst[0].Add(src[0], src[1<<idxShift]) // dst[0] = src[0] + src[1]
dst[1].Sub(src[0], src[1<<idxShift]) // dst[1] = src[0] - src[1]
return
}
// Let P(x) = src[0] + src[1<<idxShift] * x + ... + src[K-1 << idxShift] * x^(K-1)
// The P(x) = Q1(x²) + x*Q2(x²)
// where Q1's coefficients are src with indices shifted by 1
// where Q2's coefficients are src[1<<idxShift:] with indices shifted by 1
// Split destination vectors in halves.
dst1 := dst[:1<<(size-1)]
dst2 := dst[1<<(size-1):]
// Transform Q1 and Q2 in the halves.
rec(dst1, src, size-1)
rec(dst2, src[1<<idxShift:], size-1)
// Reconstruct P's transform from transforms of Q1 and Q2.
// dst[i] is dst1[i] + ω^i * dst2[i]
// dst[i + 1<<(k-1)] is dst1[i] + ω^(i+K/2) * dst2[i]
//
for i := range dst1 {
tmp.ShiftHalf(dst2[i], i*ω2shift, tmp2) // ω^i * dst2[i]
dst2[i].Sub(dst1[i], tmp)
dst1[i].Add(dst1[i], tmp)
}
}
rec(dst, src, k)
}
// Mul returns the pointwise product of p and q.
func (p *polValues) Mul(q *polValues) (r polValues) {
n := p.n
r.k, r.n = p.k, p.n
r.values = make([]fermat, len(p.values))
bits := make([]big.Word, len(p.values)*(n+1))
buf := make(fermat, 8*n)
for i := range r.values {
r.values[i] = bits[i*(n+1) : (i+1)*(n+1)]
z := buf.Mul(p.values[i], q.values[i])
copy(r.values[i], z)
}
return
}

3
vendor/github.com/remyoudompheng/bigfft/go.mod generated vendored Normal file
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@ -0,0 +1,3 @@
module github.com/remyoudompheng/bigfft
go 1.12

70
vendor/github.com/remyoudompheng/bigfft/scan.go generated vendored Normal file
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package bigfft
import (
"math/big"
)
// FromDecimalString converts the base 10 string
// representation of a natural (non-negative) number
// into a *big.Int.
// Its asymptotic complexity is less than quadratic.
func FromDecimalString(s string) *big.Int {
var sc scanner
z := new(big.Int)
sc.scan(z, s)
return z
}
type scanner struct {
// powers[i] is 10^(2^i * quadraticScanThreshold).
powers []*big.Int
}
func (s *scanner) chunkSize(size int) (int, *big.Int) {
if size <= quadraticScanThreshold {
panic("size < quadraticScanThreshold")
}
pow := uint(0)
for n := size; n > quadraticScanThreshold; n /= 2 {
pow++
}
// threshold * 2^(pow-1) <= size < threshold * 2^pow
return quadraticScanThreshold << (pow - 1), s.power(pow - 1)
}
func (s *scanner) power(k uint) *big.Int {
for i := len(s.powers); i <= int(k); i++ {
z := new(big.Int)
if i == 0 {
if quadraticScanThreshold%14 != 0 {
panic("quadraticScanThreshold % 14 != 0")
}
z.Exp(big.NewInt(1e14), big.NewInt(quadraticScanThreshold/14), nil)
} else {
z.Mul(s.powers[i-1], s.powers[i-1])
}
s.powers = append(s.powers, z)
}
return s.powers[k]
}
func (s *scanner) scan(z *big.Int, str string) {
if len(str) <= quadraticScanThreshold {
z.SetString(str, 10)
return
}
sz, pow := s.chunkSize(len(str))
// Scan the left half.
s.scan(z, str[:len(str)-sz])
// FIXME: reuse temporaries.
left := Mul(z, pow)
// Scan the right half
s.scan(z, str[len(str)-sz:])
z.Add(z, left)
}
// quadraticScanThreshold is the number of digits
// below which big.Int.SetString is more efficient
// than subquadratic algorithms.
// 1232 digits fit in 4096 bits.
const quadraticScanThreshold = 1232