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authorWim <wim@42.be>2022-01-31 00:27:37 +0100
committerWim <wim@42.be>2022-03-20 14:57:48 +0100
commite3cafeaf9292f67459ff1d186f68283bfaedf2ae (patch)
treeb69c39620aa91dba695b3b935c6651c0fb37ce75 /vendor/rsc.io/qr/gf256/gf256.go
parente7b193788a56ee7cdb02a87a9db0ad6724ef66d5 (diff)
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Diffstat (limited to 'vendor/rsc.io/qr/gf256/gf256.go')
-rw-r--r--vendor/rsc.io/qr/gf256/gf256.go241
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diff --git a/vendor/rsc.io/qr/gf256/gf256.go b/vendor/rsc.io/qr/gf256/gf256.go
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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 "rsc.io/qr/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 < 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 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
+}