469 Zeilen
15 KiB
PHP
469 Zeilen
15 KiB
PHP
<?php
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declare(strict_types = 1);
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namespace BaconQrCode\Common;
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use BaconQrCode\Exception\InvalidArgumentException;
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use BaconQrCode\Exception\RuntimeException;
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use SplFixedArray;
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/**
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* Reed-Solomon codec for 8-bit characters.
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*
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* Based on libfec by Phil Karn, KA9Q.
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*/
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final class ReedSolomonCodec
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{
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/**
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* Symbol size in bits.
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*
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* @var int
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*/
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private $symbolSize;
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/**
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* Block size in symbols.
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*
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* @var int
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*/
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private $blockSize;
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/**
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* First root of RS code generator polynomial, index form.
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*
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* @var int
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*/
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private $firstRoot;
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/**
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* Primitive element to generate polynomial roots, index form.
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*
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* @var int
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*/
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private $primitive;
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/**
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* Prim-th root of 1, index form.
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*
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* @var int
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*/
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private $iPrimitive;
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/**
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* RS code generator polynomial degree (number of roots).
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*
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* @var int
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*/
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private $numRoots;
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/**
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* Padding bytes at front of shortened block.
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*
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* @var int
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*/
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private $padding;
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/**
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* Log lookup table.
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*
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* @var SplFixedArray
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*/
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private $alphaTo;
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/**
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* Anti-Log lookup table.
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*
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* @var SplFixedArray
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*/
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private $indexOf;
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/**
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* Generator polynomial.
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*
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* @var SplFixedArray
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*/
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private $generatorPoly;
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/**
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* @throws InvalidArgumentException if symbol size ist not between 0 and 8
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* @throws InvalidArgumentException if first root is invalid
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* @throws InvalidArgumentException if num roots is invalid
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* @throws InvalidArgumentException if padding is invalid
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* @throws RuntimeException if field generator polynomial is not primitive
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*/
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public function __construct(
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int $symbolSize,
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int $gfPoly,
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int $firstRoot,
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int $primitive,
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int $numRoots,
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int $padding
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) {
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if ($symbolSize < 0 || $symbolSize > 8) {
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throw new InvalidArgumentException('Symbol size must be between 0 and 8');
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}
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if ($firstRoot < 0 || $firstRoot >= (1 << $symbolSize)) {
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throw new InvalidArgumentException('First root must be between 0 and ' . (1 << $symbolSize));
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}
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if ($numRoots < 0 || $numRoots >= (1 << $symbolSize)) {
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throw new InvalidArgumentException('Num roots must be between 0 and ' . (1 << $symbolSize));
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}
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if ($padding < 0 || $padding >= ((1 << $symbolSize) - 1 - $numRoots)) {
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throw new InvalidArgumentException(
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'Padding must be between 0 and ' . ((1 << $symbolSize) - 1 - $numRoots)
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);
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}
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$this->symbolSize = $symbolSize;
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$this->blockSize = (1 << $symbolSize) - 1;
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$this->padding = $padding;
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$this->alphaTo = SplFixedArray::fromArray(array_fill(0, $this->blockSize + 1, 0), false);
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$this->indexOf = SplFixedArray::fromArray(array_fill(0, $this->blockSize + 1, 0), false);
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// Generate galous field lookup table
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$this->indexOf[0] = $this->blockSize;
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$this->alphaTo[$this->blockSize] = 0;
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$sr = 1;
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for ($i = 0; $i < $this->blockSize; ++$i) {
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$this->indexOf[$sr] = $i;
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$this->alphaTo[$i] = $sr;
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$sr <<= 1;
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if ($sr & (1 << $symbolSize)) {
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$sr ^= $gfPoly;
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}
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$sr &= $this->blockSize;
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}
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if (1 !== $sr) {
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throw new RuntimeException('Field generator polynomial is not primitive');
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}
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// Form RS code generator polynomial from its roots
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$this->generatorPoly = SplFixedArray::fromArray(array_fill(0, $numRoots + 1, 0), false);
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$this->firstRoot = $firstRoot;
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$this->primitive = $primitive;
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$this->numRoots = $numRoots;
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// Find prim-th root of 1, used in decoding
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for ($iPrimitive = 1; ($iPrimitive % $primitive) !== 0; $iPrimitive += $this->blockSize) {
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}
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$this->iPrimitive = intdiv($iPrimitive, $primitive);
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$this->generatorPoly[0] = 1;
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for ($i = 0, $root = $firstRoot * $primitive; $i < $numRoots; ++$i, $root += $primitive) {
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$this->generatorPoly[$i + 1] = 1;
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for ($j = $i; $j > 0; $j--) {
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if ($this->generatorPoly[$j] !== 0) {
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$this->generatorPoly[$j] = $this->generatorPoly[$j - 1] ^ $this->alphaTo[
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$this->modNn($this->indexOf[$this->generatorPoly[$j]] + $root)
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];
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} else {
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$this->generatorPoly[$j] = $this->generatorPoly[$j - 1];
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}
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}
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$this->generatorPoly[$j] = $this->alphaTo[$this->modNn($this->indexOf[$this->generatorPoly[0]] + $root)];
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}
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// Convert generator poly to index form for quicker encoding
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for ($i = 0; $i <= $numRoots; ++$i) {
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$this->generatorPoly[$i] = $this->indexOf[$this->generatorPoly[$i]];
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}
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}
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/**
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* Encodes data and writes result back into parity array.
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*/
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public function encode(SplFixedArray $data, SplFixedArray $parity) : void
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{
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for ($i = 0; $i < $this->numRoots; ++$i) {
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$parity[$i] = 0;
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}
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$iterations = $this->blockSize - $this->numRoots - $this->padding;
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for ($i = 0; $i < $iterations; ++$i) {
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$feedback = $this->indexOf[$data[$i] ^ $parity[0]];
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if ($feedback !== $this->blockSize) {
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// Feedback term is non-zero
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$feedback = $this->modNn($this->blockSize - $this->generatorPoly[$this->numRoots] + $feedback);
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for ($j = 1; $j < $this->numRoots; ++$j) {
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$parity[$j] = $parity[$j] ^ $this->alphaTo[
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$this->modNn($feedback + $this->generatorPoly[$this->numRoots - $j])
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];
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}
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}
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for ($j = 0; $j < $this->numRoots - 1; ++$j) {
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$parity[$j] = $parity[$j + 1];
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}
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if ($feedback !== $this->blockSize) {
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$parity[$this->numRoots - 1] = $this->alphaTo[$this->modNn($feedback + $this->generatorPoly[0])];
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} else {
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$parity[$this->numRoots - 1] = 0;
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}
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}
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}
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/**
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* Decodes received data.
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*/
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public function decode(SplFixedArray $data, SplFixedArray $erasures = null) : ?int
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{
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// This speeds up the initialization a bit.
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$numRootsPlusOne = SplFixedArray::fromArray(array_fill(0, $this->numRoots + 1, 0), false);
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$numRoots = SplFixedArray::fromArray(array_fill(0, $this->numRoots, 0), false);
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$lambda = clone $numRootsPlusOne;
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$b = clone $numRootsPlusOne;
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$t = clone $numRootsPlusOne;
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$omega = clone $numRootsPlusOne;
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$root = clone $numRoots;
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$loc = clone $numRoots;
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$numErasures = (null !== $erasures ? count($erasures) : 0);
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// Form the Syndromes; i.e., evaluate data(x) at roots of g(x)
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$syndromes = SplFixedArray::fromArray(array_fill(0, $this->numRoots, $data[0]), false);
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for ($i = 1; $i < $this->blockSize - $this->padding; ++$i) {
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for ($j = 0; $j < $this->numRoots; ++$j) {
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if ($syndromes[$j] === 0) {
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$syndromes[$j] = $data[$i];
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} else {
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$syndromes[$j] = $data[$i] ^ $this->alphaTo[
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$this->modNn($this->indexOf[$syndromes[$j]] + ($this->firstRoot + $j) * $this->primitive)
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];
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}
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}
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}
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// Convert syndromes to index form, checking for nonzero conditions
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$syndromeError = 0;
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for ($i = 0; $i < $this->numRoots; ++$i) {
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$syndromeError |= $syndromes[$i];
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$syndromes[$i] = $this->indexOf[$syndromes[$i]];
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}
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if (! $syndromeError) {
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// If syndrome is zero, data[] is a codeword and there are no errors to correct, so return data[]
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// unmodified.
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return 0;
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}
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$lambda[0] = 1;
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if ($numErasures > 0) {
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// Init lambda to be the erasure locator polynomial
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$lambda[1] = $this->alphaTo[$this->modNn($this->primitive * ($this->blockSize - 1 - $erasures[0]))];
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for ($i = 1; $i < $numErasures; ++$i) {
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$u = $this->modNn($this->primitive * ($this->blockSize - 1 - $erasures[$i]));
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for ($j = $i + 1; $j > 0; --$j) {
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$tmp = $this->indexOf[$lambda[$j - 1]];
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if ($tmp !== $this->blockSize) {
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$lambda[$j] = $lambda[$j] ^ $this->alphaTo[$this->modNn($u + $tmp)];
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}
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}
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}
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}
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for ($i = 0; $i <= $this->numRoots; ++$i) {
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$b[$i] = $this->indexOf[$lambda[$i]];
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}
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// Begin Berlekamp-Massey algorithm to determine error+erasure locator polynomial
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$r = $numErasures;
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$el = $numErasures;
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while (++$r <= $this->numRoots) {
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// Compute discrepancy at the r-th step in poly form
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$discrepancyR = 0;
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for ($i = 0; $i < $r; ++$i) {
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if ($lambda[$i] !== 0 && $syndromes[$r - $i - 1] !== $this->blockSize) {
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$discrepancyR ^= $this->alphaTo[
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$this->modNn($this->indexOf[$lambda[$i]] + $syndromes[$r - $i - 1])
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];
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}
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}
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$discrepancyR = $this->indexOf[$discrepancyR];
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if ($discrepancyR === $this->blockSize) {
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$tmp = $b->toArray();
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array_unshift($tmp, $this->blockSize);
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array_pop($tmp);
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$b = SplFixedArray::fromArray($tmp, false);
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continue;
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}
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$t[0] = $lambda[0];
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for ($i = 0; $i < $this->numRoots; ++$i) {
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if ($b[$i] !== $this->blockSize) {
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$t[$i + 1] = $lambda[$i + 1] ^ $this->alphaTo[$this->modNn($discrepancyR + $b[$i])];
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} else {
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$t[$i + 1] = $lambda[$i + 1];
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}
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}
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if (2 * $el <= $r + $numErasures - 1) {
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$el = $r + $numErasures - $el;
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for ($i = 0; $i <= $this->numRoots; ++$i) {
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$b[$i] = (
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$lambda[$i] === 0
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? $this->blockSize
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: $this->modNn($this->indexOf[$lambda[$i]] - $discrepancyR + $this->blockSize)
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);
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}
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} else {
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$tmp = $b->toArray();
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array_unshift($tmp, $this->blockSize);
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array_pop($tmp);
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$b = SplFixedArray::fromArray($tmp, false);
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}
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$lambda = clone $t;
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}
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// Convert lambda to index form and compute deg(lambda(x))
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$degLambda = 0;
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for ($i = 0; $i <= $this->numRoots; ++$i) {
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$lambda[$i] = $this->indexOf[$lambda[$i]];
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if ($lambda[$i] !== $this->blockSize) {
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$degLambda = $i;
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}
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}
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// Find roots of the error+erasure locator polynomial by Chien search.
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$reg = clone $lambda;
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$reg[0] = 0;
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$count = 0;
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$i = 1;
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for ($k = $this->iPrimitive - 1; $i <= $this->blockSize; ++$i, $k = $this->modNn($k + $this->iPrimitive)) {
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$q = 1;
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for ($j = $degLambda; $j > 0; $j--) {
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if ($reg[$j] !== $this->blockSize) {
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$reg[$j] = $this->modNn($reg[$j] + $j);
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$q ^= $this->alphaTo[$reg[$j]];
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}
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}
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if ($q !== 0) {
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// Not a root
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continue;
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}
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// Store root (index-form) and error location number
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$root[$count] = $i;
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$loc[$count] = $k;
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if (++$count === $degLambda) {
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break;
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}
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}
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if ($degLambda !== $count) {
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// deg(lambda) unequal to number of roots: uncorrectable error detected
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return null;
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}
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// Compute err+eras evaluate poly omega(x) = s(x)*lambda(x) (modulo x**numRoots). In index form. Also find
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// deg(omega).
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$degOmega = $degLambda - 1;
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for ($i = 0; $i <= $degOmega; ++$i) {
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$tmp = 0;
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for ($j = $i; $j >= 0; --$j) {
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if ($syndromes[$i - $j] !== $this->blockSize && $lambda[$j] !== $this->blockSize) {
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$tmp ^= $this->alphaTo[$this->modNn($syndromes[$i - $j] + $lambda[$j])];
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}
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}
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$omega[$i] = $this->indexOf[$tmp];
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}
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// Compute error values in poly-form. num1 = omega(inv(X(l))), num2 = inv(X(l))**(firstRoot-1) and
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// den = lambda_pr(inv(X(l))) all in poly form.
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for ($j = $count - 1; $j >= 0; --$j) {
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$num1 = 0;
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for ($i = $degOmega; $i >= 0; $i--) {
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if ($omega[$i] !== $this->blockSize) {
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$num1 ^= $this->alphaTo[$this->modNn($omega[$i] + $i * $root[$j])];
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}
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}
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$num2 = $this->alphaTo[$this->modNn($root[$j] * ($this->firstRoot - 1) + $this->blockSize)];
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$den = 0;
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// lambda[i+1] for i even is the formal derivativelambda_pr of lambda[i]
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for ($i = min($degLambda, $this->numRoots - 1) & ~1; $i >= 0; $i -= 2) {
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if ($lambda[$i + 1] !== $this->blockSize) {
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$den ^= $this->alphaTo[$this->modNn($lambda[$i + 1] + $i * $root[$j])];
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}
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}
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// Apply error to data
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if ($num1 !== 0 && $loc[$j] >= $this->padding) {
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$data[$loc[$j] - $this->padding] = $data[$loc[$j] - $this->padding] ^ (
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$this->alphaTo[
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$this->modNn(
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$this->indexOf[$num1] + $this->indexOf[$num2] + $this->blockSize - $this->indexOf[$den]
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)
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]
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);
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}
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}
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if (null !== $erasures) {
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if (count($erasures) < $count) {
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$erasures->setSize($count);
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}
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for ($i = 0; $i < $count; $i++) {
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$erasures[$i] = $loc[$i];
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}
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}
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return $count;
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}
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/**
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* Computes $x % GF_SIZE, where GF_SIZE is 2**GF_BITS - 1, without a slow divide.
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*/
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private function modNn(int $x) : int
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{
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while ($x >= $this->blockSize) {
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$x -= $this->blockSize;
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$x = ($x >> $this->symbolSize) + ($x & $this->blockSize);
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}
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return $x;
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}
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}
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