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