syncthing/vendor/github.com/vitrun/qart/gf256/gf256.go
Jakob Borg 65aaa607ab Use Go 1.5 vendoring instead of Godeps
Change made by:

- running "gvt fetch" on each of the packages mentioned in
  Godeps/Godeps.json
- `rm -rf Godeps`
- tweaking the build scripts to not mention Godeps
- tweaking the build scripts to test `./lib/...`, `./cmd/...` explicitly
  (to avoid testing vendor)
- tweaking the build scripts to not juggle GOPATH for Godeps and instead
  set GO15VENDOREXPERIMENT.

This also results in some updated packages at the same time I bet.

Building with Go 1.3 and 1.4 still *works* but won't use our vendored
dependencies - the user needs to have the actual packages in their
GOPATH then, which they'll get with a normal "go get". Building with Go
1.6+ will get our vendored dependencies by default even when not using
our build script, which is nice.

By doing this we gain some freedom in that we can pick and choose
manually what to include in vendor, as it's not based on just dependency
analysis of our own code. This is also a risk as we might pick up
dependencies we are unaware of, as the build may work locally with those
packages present in GOPATH. On the other hand the build server will
detect this as it has no packages in it's GOPATH beyond what is included
in the repo.

Recommended tool to manage dependencies is github.com/FiloSottile/gvt.
2016-03-05 21:21:24 +01:00

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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 gf256 implements arithmetic over the Galois Field GF(256).
package gf256
import "strconv"
// A Field represents an instance of GF(256) defined by a specific polynomial.
type Field struct {
log [256]byte // log[0] is unused
exp [510]byte
}
// NewField returns a new field corresponding to the polynomial poly
// and generator α. The Reed-Solomon encoding in QR codes uses
// polynomial 0x11d with generator 2.
//
// The choice of generator α only affects the Exp and Log operations.
func NewField(poly, α int) *Field {
if poly < 0x100 || poly >= 0x200 || reducible(poly) {
panic("gf256: invalid polynomial: " + strconv.Itoa(poly))
}
var f Field
x := 1
for i := 0; i < 255; i++ {
if x == 1 && i != 0 {
panic("gf256: invalid generator " + strconv.Itoa(α) +
" for polynomial " + strconv.Itoa(poly))
}
f.exp[i] = byte(x)
f.exp[i+255] = byte(x)
f.log[x] = byte(i)
x = mul(x, α, poly)
}
f.log[0] = 255
for i := 0; i < 255; i++ {
if f.log[f.exp[i]] != byte(i) {
panic("bad log")
}
if f.log[f.exp[i+255]] != byte(i) {
panic("bad log")
}
}
for i := 1; i < 256; i++ {
if f.exp[f.log[i]] != byte(i) {
panic("bad log")
}
}
return &f
}
// nbit returns the number of significant in p.
func nbit(p int) uint {
n := uint(0)
for ; p > 0; p >>= 1 {
n++
}
return n
}
// polyDiv divides the polynomial p by q and returns the remainder.
func polyDiv(p, q int) int {
np := nbit(p)
nq := nbit(q)
for ; np >= nq; np-- {
if p&(1<<(np-1)) != 0 {
p ^= q << (np - nq)
}
}
return p
}
// mul returns the product x*y mod poly, a GF(256) multiplication.
func mul(x, y, poly int) int {
z := 0
for x > 0 {
if x&1 != 0 {
z ^= y
}
x >>= 1
y <<= 1
if y&0x100 != 0 {
y ^= poly
}
}
return z
}
// reducible reports whether p is reducible.
func reducible(p int) bool {
// Multiplying n-bit * n-bit produces (2n-1)-bit,
// so if p is reducible, one of its factors must be
// of np/2+1 bits or fewer.
np := nbit(p)
for q := 2; q < int(1<<(np/2+1)); q++ {
if polyDiv(p, q) == 0 {
return true
}
}
return false
}
// Add returns the sum of x and y in the field.
func (f *Field) Add(x, y byte) byte {
return x ^ y
}
// Exp returns the the base-α exponential of e in the field.
// If e < 0, Exp returns 0.
func (f *Field) Exp(e int) byte {
if e < 0 {
return 0
}
return f.exp[e%255]
}
// Log returns the base-α logarithm of x in the field.
// If x == 0, Log returns -1.
func (f *Field) Log(x byte) int {
if x == 0 {
return -1
}
return int(f.log[x])
}
// Inv returns the multiplicative inverse of x in the field.
// If x == 0, Inv returns 0.
func (f *Field) Inv(x byte) byte {
if x == 0 {
return 0
}
return f.exp[255-f.log[x]]
}
// Mul returns the product of x and y in the field.
func (f *Field) Mul(x, y byte) byte {
if x == 0 || y == 0 {
return 0
}
return f.exp[int(f.log[x])+int(f.log[y])]
}
// An RSEncoder implements Reed-Solomon encoding
// over a given field using a given number of error correction bytes.
type RSEncoder struct {
f *Field
c int
gen []byte
lgen []byte
p []byte
}
func (f *Field) gen(e int) (gen, lgen []byte) {
// p = 1
p := make([]byte, e+1)
p[e] = 1
for i := 0; i < e; i++ {
// p *= (x + Exp(i))
// p[j] = p[j]*Exp(i) + p[j+1].
c := f.Exp(i)
for j := 0; j < e; j++ {
p[j] = f.Mul(p[j], c) ^ p[j+1]
}
p[e] = f.Mul(p[e], c)
}
// lp = log p.
lp := make([]byte, e+1)
for i, c := range p {
if c == 0 {
lp[i] = 255
} else {
lp[i] = byte(f.Log(c))
}
}
return p, lp
}
// NewRSEncoder returns a new Reed-Solomon encoder
// over the given field and number of error correction bytes.
func NewRSEncoder(f *Field, c int) *RSEncoder {
gen, lgen := f.gen(c)
return &RSEncoder{f: f, c: c, gen: gen, lgen: lgen}
}
// ECC writes to check the error correcting code bytes
// for data using the given Reed-Solomon parameters.
func (rs *RSEncoder) ECC(data []byte, check []byte) {
if len(check) < rs.c {
panic("gf256: invalid check byte length")
}
if rs.c == 0 {
return
}
// The check bytes are the remainder after dividing
// data padded with c zeros by the generator polynomial.
// p = data padded with c zeros.
var p []byte
n := len(data) + rs.c
if len(rs.p) >= n {
p = rs.p
} else {
p = make([]byte, n)
}
copy(p, data)
for i := len(data); i < len(p); i++ {
p[i] = 0
}
// Divide p by gen, leaving the remainder in p[len(data):].
// p[0] is the most significant term in p, and
// gen[0] is the most significant term in the generator,
// which is always 1.
// To avoid repeated work, we store various values as
// lv, not v, where lv = log[v].
f := rs.f
lgen := rs.lgen[1:]
for i := 0; i < len(data); i++ {
c := p[i]
if c == 0 {
continue
}
q := p[i+1:]
exp := f.exp[f.log[c]:]
for j, lg := range lgen {
if lg != 255 { // lgen uses 255 for log 0
q[j] ^= exp[lg]
}
}
}
copy(check, p[len(data):])
rs.p = p
}