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✨
This commit is contained in:
codemasher
@@ -0,0 +1,152 @@
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<?php
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/**
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* Class GF256
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*
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* @filesource GF256.php
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* @created 16.01.2021
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* @package chillerlan\QRCode\Common
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* @author ZXing Authors
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* @author Smiley <smiley@chillerlan.net>
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* @copyright 2021 Smiley
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* @license Apache-2.0
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*/
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namespace chillerlan\QRCode\Common;
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use InvalidArgumentException;
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use function array_fill;
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/**
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* <p>This class contains utility methods for performing mathematical operations over
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* the Galois Fields. Operations use a given primitive polynomial in calculations.</p>
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*
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* <p>Throughout this package, elements of the GF are represented as an {@code int}
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* for convenience and speed (but at the cost of memory).
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* </p>
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*
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* @author Sean Owen
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* @author David Olivier
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*/
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final class GF256{
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/**
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* irreducible polynomial whose coefficients are represented by the bits of an int,
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* where the least-significant bit represents the constant coefficient
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*/
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# private int $primitive = 0x011D;
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private const logTable = [
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null, 0, 1, 25, 2, 50, 26, 198, 3, 223, 51, 238, 27, 104, 199, 75,
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4, 100, 224, 14, 52, 141, 239, 129, 28, 193, 105, 248, 200, 8, 76, 113,
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5, 138, 101, 47, 225, 36, 15, 33, 53, 147, 142, 218, 240, 18, 130, 69,
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29, 181, 194, 125, 106, 39, 249, 185, 201, 154, 9, 120, 77, 228, 114, 166,
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6, 191, 139, 98, 102, 221, 48, 253, 226, 152, 37, 179, 16, 145, 34, 136,
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54, 208, 148, 206, 143, 150, 219, 189, 241, 210, 19, 92, 131, 56, 70, 64,
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30, 66, 182, 163, 195, 72, 126, 110, 107, 58, 40, 84, 250, 133, 186, 61,
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202, 94, 155, 159, 10, 21, 121, 43, 78, 212, 229, 172, 115, 243, 167, 87,
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7, 112, 192, 247, 140, 128, 99, 13, 103, 74, 222, 237, 49, 197, 254, 24,
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227, 165, 153, 119, 38, 184, 180, 124, 17, 68, 146, 217, 35, 32, 137, 46,
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55, 63, 209, 91, 149, 188, 207, 205, 144, 135, 151, 178, 220, 252, 190, 97,
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242, 86, 211, 171, 20, 42, 93, 158, 132, 60, 57, 83, 71, 109, 65, 162,
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31, 45, 67, 216, 183, 123, 164, 118, 196, 23, 73, 236, 127, 12, 111, 246,
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108, 161, 59, 82, 41, 157, 85, 170, 251, 96, 134, 177, 187, 204, 62, 90,
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203, 89, 95, 176, 156, 169, 160, 81, 11, 245, 22, 235, 122, 117, 44, 215,
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79, 174, 213, 233, 230, 231, 173, 232, 116, 214, 244, 234, 168, 80, 88, 175,
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];
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private const expTable = [
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1, 2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, 205, 135, 19, 38,
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76, 152, 45, 90, 180, 117, 234, 201, 143, 3, 6, 12, 24, 48, 96, 192,
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157, 39, 78, 156, 37, 74, 148, 53, 106, 212, 181, 119, 238, 193, 159, 35,
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70, 140, 5, 10, 20, 40, 80, 160, 93, 186, 105, 210, 185, 111, 222, 161,
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95, 190, 97, 194, 153, 47, 94, 188, 101, 202, 137, 15, 30, 60, 120, 240,
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253, 231, 211, 187, 107, 214, 177, 127, 254, 225, 223, 163, 91, 182, 113, 226,
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217, 175, 67, 134, 17, 34, 68, 136, 13, 26, 52, 104, 208, 189, 103, 206,
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129, 31, 62, 124, 248, 237, 199, 147, 59, 118, 236, 197, 151, 51, 102, 204,
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133, 23, 46, 92, 184, 109, 218, 169, 79, 158, 33, 66, 132, 21, 42, 84,
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168, 77, 154, 41, 82, 164, 85, 170, 73, 146, 57, 114, 228, 213, 183, 115,
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230, 209, 191, 99, 198, 145, 63, 126, 252, 229, 215, 179, 123, 246, 241, 255,
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227, 219, 171, 75, 150, 49, 98, 196, 149, 55, 110, 220, 165, 87, 174, 65,
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130, 25, 50, 100, 200, 141, 7, 14, 28, 56, 112, 224, 221, 167, 83, 166,
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81, 162, 89, 178, 121, 242, 249, 239, 195, 155, 43, 86, 172, 69, 138, 9,
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18, 36, 72, 144, 61, 122, 244, 245, 247, 243, 251, 235, 203, 139, 11, 22,
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44, 88, 176, 125, 250, 233, 207, 131, 27, 54, 108, 216, 173, 71, 142, 1,
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];
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/**
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* Implements both addition and subtraction -- they are the same in GF(size).
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*
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* @return int sum/difference of a and b
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*/
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public static function addOrSubtract(int $a, int $b):int{
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return $a ^ $b;
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}
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/**
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* @return GenericGFPoly the monomial representing coefficient * x^degree
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*/
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public static function buildMonomial(int $degree, int $coefficient):GenericGFPoly{
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if($degree < 0){
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throw new InvalidArgumentException();
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}
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$coefficients = array_fill(0, $degree + 1, 0);
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$coefficients[0] = $coefficient;
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return new GenericGFPoly($coefficients);
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}
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/**
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* @return int 2 to the power of a in GF(size)
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*/
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public static function exp(int $a):int{
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if($a < 0){
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$a += 255;
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}
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elseif($a >= 256){
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$a -= 255;
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}
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return self::expTable[$a];
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}
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/**
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* @return int base 2 log of a in GF(size)
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*/
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public static function log(int $a):int{
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if($a < 1){
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throw new InvalidArgumentException();
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}
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return self::logTable[$a];
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}
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/**
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* @return int multiplicative inverse of a
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*/
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public static function inverse(int $a):int{
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if($a === 0){
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throw new InvalidArgumentException();
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}
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return self::expTable[256 - self::logTable[$a] - 1];
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}
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/**
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* @return int product of a and b in GF(size)
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*/
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public static function multiply(int $a, int $b):int{
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if($a === 0 || $b === 0){
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return 0;
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}
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return self::expTable[(self::logTable[$a] + self::logTable[$b]) % 255];
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}
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}
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@@ -0,0 +1,278 @@
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<?php
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/**
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* Class GenericGFPoly
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*
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* @filesource GenericGFPoly.php
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* @created 16.01.2021
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* @package chillerlan\QRCode\Common
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* @author ZXing Authors
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* @author Smiley <smiley@chillerlan.net>
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* @copyright 2021 Smiley
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* @license Apache-2.0
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*/
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namespace chillerlan\QRCode\Common;
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use InvalidArgumentException;
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use function array_fill, array_slice, array_splice, count;
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/**
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* <p>Represents a polynomial whose coefficients are elements of a GF.
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* Instances of this class are immutable.</p>
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*
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* <p>Much credit is due to William Rucklidge since portions of this code are an indirect
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* port of his C++ Reed-Solomon implementation.</p>
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*
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* @author Sean Owen
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*/
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final class GenericGFPoly{
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private array $coefficients;
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/**
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* @param array|null $coefficients array coefficients as ints representing elements of GF(size), arranged
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* from most significant (highest-power term) coefficient to least significant
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* @param int|null $degree
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*
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* @throws \InvalidArgumentException if argument is null or empty, or if leading coefficient is 0 and this is not a
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* constant polynomial (that is, it is not the monomial "0")
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*/
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public function __construct(array $coefficients, int $degree = null){
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$degree ??= 0;
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if(empty($coefficients)){
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throw new InvalidArgumentException('arg $coefficients is empty');
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}
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if($degree < 0){
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throw new InvalidArgumentException('negative degree');
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}
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$coefficientsLength = count($coefficients);
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// Leading term must be non-zero for anything except the constant polynomial "0"
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$firstNonZero = 0;
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while($firstNonZero < $coefficientsLength && $coefficients[$firstNonZero] === 0){
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$firstNonZero++;
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}
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if($firstNonZero === $coefficientsLength){
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$this->coefficients = [0];
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}
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else{
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$this->coefficients = array_fill(0, $coefficientsLength - $firstNonZero + $degree, 0);
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for($i = 0; $i < $coefficientsLength - $firstNonZero; $i++){
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$this->coefficients[$i] = $coefficients[$i + $firstNonZero];
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}
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}
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}
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/**
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* @return int $coefficient of x^degree term in this polynomial
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*/
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public function getCoefficient(int $degree):int{
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return $this->coefficients[count($this->coefficients) - 1 - $degree];
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}
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/**
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* @return int[]
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*/
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public function getCoefficients():array{
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return $this->coefficients;
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}
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/**
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* @return int $degree of this polynomial
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*/
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public function getDegree():int{
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return count($this->coefficients) - 1;
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}
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/**
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* @return bool true if this polynomial is the monomial "0"
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*/
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public function isZero():bool{
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return $this->coefficients[0] === 0;
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}
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/**
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* @return int evaluation of this polynomial at a given point
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*/
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public function evaluateAt(int $a):int{
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if($a === 0){
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// Just return the x^0 coefficient
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return $this->getCoefficient(0);
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}
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$result = 0;
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foreach($this->coefficients as $c){
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// if $a === 1 just the sum of the coefficients
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$result = GF256::addOrSubtract(($a === 1 ? $result : GF256::multiply($a, $result)), $c);
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}
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return $result;
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}
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/**
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* @param \chillerlan\QRCode\Common\GenericGFPoly $other
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*
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* @return \chillerlan\QRCode\Common\GenericGFPoly
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*/
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public function multiply(GenericGFPoly $other):GenericGFPoly{
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if($this->isZero() || $other->isZero()){
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return new self([0]);
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}
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$product = array_fill(0, count($this->coefficients) + count($other->coefficients) - 1, 0);
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foreach($this->coefficients as $i => $aCoeff){
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foreach($other->coefficients as $j => $bCoeff){
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$product[$i + $j] ^= GF256::multiply($aCoeff, $bCoeff);
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}
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}
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return new self($product);
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}
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/**
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* @param \chillerlan\QRCode\Common\GenericGFPoly $other
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*
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* @return \chillerlan\QRCode\Common\GenericGFPoly[] [quotient, remainder]
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*/
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public function divide(GenericGFPoly $other):array{
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if($other->isZero()){
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throw new InvalidArgumentException('Division by 0');
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}
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$quotient = new self([0]);
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$remainder = clone $this;
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$denominatorLeadingTerm = $other->getCoefficient($other->getDegree());
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$inverseDenominatorLeadingTerm = GF256::inverse($denominatorLeadingTerm);
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while($remainder->getDegree() >= $other->getDegree() && !$remainder->isZero()){
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$scale = GF256::multiply($remainder->getCoefficient($remainder->getDegree()), $inverseDenominatorLeadingTerm);
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$diff = $remainder->getDegree() - $other->getDegree();
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$quotient = $quotient->addOrSubtract(GF256::buildMonomial($diff, $scale));
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$remainder = $remainder->addOrSubtract($other->multiplyByMonomial($diff, $scale));
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}
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return [$quotient, $remainder];
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}
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/**
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* @param int $scalar
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*
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* @return \chillerlan\QRCode\Common\GenericGFPoly
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*/
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public function multiplyInt(int $scalar):GenericGFPoly{
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if($scalar === 0){
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return new self([0]);
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}
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if($scalar === 1){
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return $this;
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}
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$product = array_fill(0, count($this->coefficients), 0);
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foreach($this->coefficients as $i => $c){
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$product[$i] = GF256::multiply($c, $scalar);
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}
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return new self($product);
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}
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/**
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* @param int $degree
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* @param int $coefficient
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*
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* @return \chillerlan\QRCode\Common\GenericGFPoly
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*/
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public function multiplyByMonomial(int $degree, int $coefficient):GenericGFPoly{
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if($degree < 0){
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throw new InvalidArgumentException();
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}
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if($coefficient === 0){
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return new self([0]);
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}
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$product = array_fill(0, count($this->coefficients) + $degree, 0);
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foreach($this->coefficients as $i => $c){
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$product[$i] = GF256::multiply($c, $coefficient);
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}
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return new self($product);
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}
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/**
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* @param \chillerlan\QRCode\Common\GenericGFPoly $other
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*
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* @return \chillerlan\QRCode\Common\GenericGFPoly
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*/
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public function mod(GenericGFPoly $other):GenericGFPoly{
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if(count($this->coefficients) - count($other->coefficients) < 0){
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return $this;
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}
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$ratio = GF256::log($this->coefficients[0]) - GF256::log($other->coefficients[0]);
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foreach($other->coefficients as $i => $c){
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$this->coefficients[$i] ^= GF256::exp(GF256::log($c) + $ratio);
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}
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return (new self($this->coefficients))->mod($other);
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}
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/**
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* @param \chillerlan\QRCode\Common\GenericGFPoly $other
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*
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* @return \chillerlan\QRCode\Common\GenericGFPoly
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*/
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public function addOrSubtract(GenericGFPoly $other):GenericGFPoly{
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if($this->isZero()){
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return $other;
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}
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if($other->isZero()){
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return $this;
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}
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$smallerCoefficients = $this->coefficients;
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$largerCoefficients = $other->coefficients;
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if(count($smallerCoefficients) > count($largerCoefficients)){
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$temp = $smallerCoefficients;
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$smallerCoefficients = $largerCoefficients;
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$largerCoefficients = $temp;
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}
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$sumDiff = array_fill(0, count($largerCoefficients), 0);
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$lengthDiff = count($largerCoefficients) - count($smallerCoefficients);
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// Copy high-order terms only found in higher-degree polynomial's coefficients
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array_splice($sumDiff, 0, $lengthDiff, array_slice($largerCoefficients, 0, $lengthDiff));
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$countLargerCoefficients = count($largerCoefficients);
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for($i = $lengthDiff; $i < $countLargerCoefficients; $i++){
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$sumDiff[$i] = GF256::addOrSubtract($smallerCoefficients[$i - $lengthDiff], $largerCoefficients[$i]);
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}
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return new self($sumDiff);
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}
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}
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