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<?php |
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/** |
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* TBitHelper class file |
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* |
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* @author Brad Anderson <[email protected]> |
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* @link https://github.com/pradosoft/prado |
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* @license https://github.com/pradosoft/prado/blob/master/LICENSE |
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*/ |
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namespace Prado\Util\Helpers; |
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use Prado\Exceptions\TInvalidDataValueException; |
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/** |
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* TBitHelper class. |
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* |
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* This class contains static functions for bit-wise and byte operations, like color |
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* bit shifting, unsigned right bit shift, mirroring the order of bits, flipping |
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* endian, and formatting floats into and from smaller float representations like |
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* half floats (Fp16, Bf16) and mini floats (Fp8). It also can check for negative |
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* floats including negative zero. |
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* |
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* Shifting bits for color accuracy requires repeating the bits rather than |
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* just adding extra 0/1 bits. {@see colorBitShift} properly adds and removes bits |
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* to an integer color value by replicating the bits for new bits. |
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* |
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* There are specific floating point conversion methods for converting float to: |
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* - Fp16 with {@see floatToFp16} and back with {@see fp16ToFloat}. |
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* - Bf16 with {@see floatToBf16} and back with {@see bf16ToFloat}. |
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* - Fp8-e5m2 with {@see floatToFp8Range} and back with {@see fp8RangeToFloat}. |
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* - Fp8-e4m3 with {@see floatToFp8Precision} and back with {@see fp8PrecisionToFloat}. |
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* These functions use the general conversion functions {@see floatToFpXX} and |
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* {@see fpXXToFloat} where the number of bits for the exponent and mantissa are |
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* parameters. For example, 24 bit floats or 14 bit floats can be created. |
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* |
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* {@see mirrorBits} can mirror arbitrary runs of bits in an integer. There is |
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* quick mirroring for specific exponents of two: {@see mirrorByte} for 8 bits, |
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* {@see mirrorShort} for 16 bits, {@see mirrorLong} for 32 bits, and, on 64 bit |
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* instances of PHP, {@see mirrorLongLong} for 64 bits. |
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* |
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* There are endian byte reversal functions: {@see flipEndianShort}, {@see flipEndianLong}, |
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* and, on 64 bit instances of PHP, {@see flipEndianLongLong}. |
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* |
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* {@see bitCount} calculates the number of bits required to represent a specific |
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* number. 255 return 8 bits, 256 returns 9 bits. |
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* |
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* {@see isNegativeFloat} is used to determine if a float has the negative bit |
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* set. It will return true on any negative float number, including negative zero. |
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* {@see isNegativeZero} can check if a float is a negative zero. PHP cannot normally |
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* check for negative zero float and requires these special functions to so. |
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* |
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* The Levels and Masks are for O(1) time bit reversals of 8, 16, 32, and 64 bit integers. |
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* The TBitHelper class automatically adjusts itself for 32 or 64 bit PHP environments. |
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* |
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* When quickly mirroring bits or switching endian, the high bits are also converted |
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* like the low bits. E.g. When mirroring a Byte, all bytes in the integer are |
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* individually mirrored in place. When converting a Short, each short in the integer |
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* will be converted in place. In the instance of a Long, for 64 bit systems will |
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* convert both Longs -in place- in its LongLong (64 bit) unit integer type. |
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* Converting LongLong is only supported in 64 bit PHP environments. |
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* |
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* @author Brad Anderson <[email protected]> |
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* @since 4.3.0 |
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*/ |
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class TBitHelper |
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{ |
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// Defined constants for 32 bit computation |
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public const PHP_INT32_MIN = -2147483648; // 0x80000000 |
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public const PHP_INT32_MAX = 2147483647; // 0x7FFFFFFF |
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// on 32 bit systems the PHP_INT64_UMAX is a float and not a integer. |
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public const PHP_INT32_UMAX = 4294967295; // 0xFFFFFFFF (unsigned) |
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public const PHP_INT32_MASK = (PHP_INT_SIZE > 4) ? self::PHP_INT32_UMAX : -1; |
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// Defined constants for 64 bit computation |
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// on 32 bit systems these values are only approximate floats and not integers. |
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public const PHP_INT64_MIN = -9223372036854775808; // 0x80000000_00000000 |
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public const PHP_INT64_MAX = 9223372036854775807; // 0x7FFFFFFF_FFFFFFFF |
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//PHP_INT64_UMAX is a float that only approximates the maximum, unless using 16 byte int |
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public const PHP_INT64_UMAX = 18446744073709551615; // 0xFFFFFFFF_FFFFFFFF (unsigned) |
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public const PHP_INT64_MASK = -1; // Assuming 64 bit is validated. |
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public const Level1 = (PHP_INT_SIZE >= 8) ? 0x5555555555555555 : 0x55555555; |
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public const NLevel1 = ~self::Level1; |
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public const Mask1 = (PHP_INT_SIZE >= 8) ? 0x7FFFFFFFFFFFFFFF : 0x7FFFFFFF; |
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public const Level2 = (PHP_INT_SIZE >= 8) ? 0x3333333333333333 : 0x33333333; |
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public const NLevel2 = ~self::Level2; |
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public const Mask2 = self::Mask1 >> 1; |
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public const Level3 = (PHP_INT_SIZE >= 8) ? 0x0F0F0F0F0F0F0F0F : 0x0F0F0F0F; |
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public const NLevel3 = ~self::Level3; |
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public const Mask3 = self::Mask1 >> 3; |
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public const Level4 = (PHP_INT_SIZE >= 8) ? 0x00FF00FF00FF00FF : 0x00FF00FF; |
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public const NLevel4 = ~self::Level4; |
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public const Mask4 = self::Mask1 >> 7; |
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public const Level5 = (PHP_INT_SIZE >= 8) ? 0x0000FFFF0000FFFF : 0x0000FFFF; |
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public const NLevel5 = ~self::Level5; |
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public const Mask5 = self::Mask1 >> 15; |
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public const Level6 = (PHP_INT_SIZE >= 8) ? 0x00000000FFFFFFFF : -1; |
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public const NLevel6 = ~self::Level6; |
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public const Mask6 = self::Mask1 >> 31; |
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/** |
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* Motorola is Big Endian with the Most Significant Byte first whereas Intel uses |
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* Little Endian with the Least Significant Byte first. This mainly only affects |
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* the binary reading and writing of data types that are 2 bytes or larger. |
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* @return bool Is the PHP environment in Big Endian Motorola Byte format. |
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*/ |
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public static function isSystemBigEndian(): bool |
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{ |
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static $bigEndian = null; |
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if ($bigEndian === null) { |
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$bigEndian = unpack('S', "\x00\x01")[1] === 1; |
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} |
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return $bigEndian; |
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} |
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/** |
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* @return bool Is the PHP environment 64 bit and supports the 64 bit LongLong type. |
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*/ |
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public static function hasLongLong(): bool |
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{ |
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return PHP_INT_SIZE >= 8; |
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} |
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/** |
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* This is a CRC32 replacement multi-tool. This acts exactly as crc32 with the |
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* added functionality that it accepts file paths (when $crc = true) which computes |
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* the CRC32 of the file. This also accepts a $crc computed from existing data and |
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* continues to update the $crc with new data form $string as if $string were appended. |
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* |
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* If an array is passed in $string, [0] is the string data, filepath, or stream |
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* resource, element [1] is the size to read, and element [2] is the startOffset. |
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* If an array is passed, $crc = true still means that the $string is a FilePath. |
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* If the $string is a stream-resource, it reads until fgetc returns false or '', |
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* or size is hit. |
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* |
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* If using this on a file (with $crc = true) then $crc2 can be used for the existing |
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* crc32 for continued computation. |
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* |
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* A continued CRC32 can also be generated with HashContext using {@link hash_init}, |
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* {@link hash_update}, and {@link hash_update_stream}, and {@link hash_final}. |
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* @param mixed $string String of Data, File Path, Stream Resource, or array. |
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* An Array format is [0] => String Data, File Path, or Stream Resource, [1] is |
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* the total size to read, and [2] is the startOffset. |
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* @param bool|int $crc The running CRC32 to continue calculating. When true, |
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* this expects $string to be a File Path rather than data. Default 0 for normal |
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* crc32 function without any prior running data. |
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* @param ?int $crc2 The existing CRC to update when specifying $string as a file |
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* (with $crc = true). Default null for new initial $crc for a file. |
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*/ |
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public static function crc32(mixed $string, bool|int $crc = 0, ?int $crc2 = null): false|int |
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{ |
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static $crc_table = [ |
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0x00000000, 0x77073096, 0xEE0E612C, 0x990951BA, 0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3, |
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0x0EDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988, 0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91, |
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0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE, 0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7, |
157
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0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC, 0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5, |
158
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0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172, 0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B, |
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0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940, 0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59, |
160
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0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116, 0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F, |
161
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0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924, 0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D, |
162
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0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A, 0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433, |
163
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0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818, 0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01, |
164
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0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E, 0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457, |
165
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0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C, 0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65, |
166
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0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2, 0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB, |
167
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0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0, 0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9, |
168
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0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086, 0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F, |
169
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0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4, 0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD, |
170
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0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A, 0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683, |
171
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0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8, 0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1, |
172
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0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE, 0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7, |
173
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0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC, 0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5, |
174
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0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252, 0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B, |
175
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0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60, 0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79, |
176
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0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236, 0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F, |
177
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0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04, 0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D, |
178
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0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A, 0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713, |
179
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0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38, 0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21, |
180
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0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E, 0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777, |
181
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0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C, 0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45, |
182
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0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2, 0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB, |
183
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0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0, 0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9, |
184
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0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6, 0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF, |
185
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0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94, 0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D, |
186
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]; |
187
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$length = null; |
188
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$startOffset = 0; |
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$close = false; |
190
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if (is_array($string)) { |
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$startOffset = $string[2] ?? $string['offset'] ?? 0; |
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$length = $string[1] ?? $string['length'] ?? null; |
193
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$string = $string[0] ?? $string['source'] ?? null; |
194
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} |
195
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if ($crc === false) { |
196
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$crc = $crc2 === null ? 0 : $crc2; |
197
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} |
198
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if (is_string($string)) { |
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if (is_int($crc)) { |
200
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if ($length !== null || $startOffset) { |
201
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$string = substr($string, $startOffset, $length); |
202
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} |
203
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if ($crc === 0) { |
204
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return crc32($string); |
205
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} |
206
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$crc ^= 0xFFFFFFFF; |
207
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$length = strlen($string); |
208
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for ($i = 0; $i < $length; $i++) { |
209
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$crc = (($crc >> 8) & 0x00FFFFFF) ^ $crc_table[($crc & 0xFF) ^ ord($string[$i])]; |
210
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} |
211
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$crc ^= 0xFFFFFFFF; |
212
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return $crc; |
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} elseif (realpath($string) || preg_match('/^[-+\.\w\d]{1,20}\:\/\//i', $string)) { |
214
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if ($length === null && !$startOffset && !$crc2) { |
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215
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$hash = hash_file('crc32b', $string, true); |
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$value = unpack('N', $hash)[1]; |
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if (PHP_INT_SIZE === 4 && $value > self::PHP_INT32_MAX) { |
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$value = (int) ($value - self::PHP_INT32_UMAX - 1); |
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} |
220
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return $value; |
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} |
222
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$string = fopen($string, 'rb'); |
223
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if (!$string) { |
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return false; |
225
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} |
226
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$close = true; |
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} |
228
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} |
229
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if (is_resource($string) && get_resource_type($string) === 'stream') { |
230
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if ($crc === true) { |
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$crc = $crc2 === null ? 0 : $crc2; |
232
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} |
233
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if ($startOffset) { |
234
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$meta = stream_get_meta_data($string); |
235
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if ($meta['seekable']) { |
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fseek($string, $startOffset); |
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} else { |
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fread($string, $startOffset); |
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} |
240
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} |
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|
|
$crc ^= 0xFFFFFFFF; |
242
|
|
|
while ($length === null || $length > 0) { |
243
|
|
|
$d = fgetc($string); |
244
|
|
|
if ($d === false || strlen($d) === 0) { |
245
|
|
|
break; |
246
|
|
|
} |
247
|
|
|
$crc = (($crc >> 8) & 0x00FFFFFF) ^ $crc_table[($crc & 0xFF) ^ ord($d)]; |
248
|
|
|
if ($length !== null) { |
249
|
|
|
$length--; |
250
|
|
|
} |
251
|
|
|
} |
252
|
|
|
$crc ^= 0xFFFFFFFF; |
253
|
|
|
if ($close) { |
|
|
|
|
254
|
|
|
fclose($string); |
255
|
|
|
} |
256
|
|
|
return $length === null || $length === 0 ? $crc : false; |
257
|
|
|
} |
258
|
|
|
return false; |
259
|
|
|
} |
260
|
|
|
|
261
|
|
|
/** |
262
|
|
|
* This returns true with all negative floats, including -0.0. Normally "$float < 0" |
263
|
|
|
* will not include -0.0, where this function does include -0.0. |
264
|
|
|
* @param float $value The float to check for being negative. |
265
|
|
|
* @return bool Is a negative float. |
266
|
|
|
*/ |
267
|
|
|
public static function isNegativeFloat(float $value): bool |
268
|
|
|
{ |
269
|
|
|
return $value < 0 || $value === -0.0 && (ord(pack('G', $value)) & 0x80) !== 0; |
270
|
|
|
} |
271
|
|
|
|
272
|
|
|
/** |
273
|
|
|
* This returns true with negative zero (-0.0). Checking for negative zero floats |
274
|
|
|
* requires this special function because PHP cannot be directly check for negative |
275
|
|
|
* zero due to '-0.0 === 0.0'. |
276
|
|
|
* @param float $value The float to check for being negative. |
277
|
|
|
* @return bool Is a negative zero float. |
278
|
|
|
*/ |
279
|
|
|
public static function isNegativeZero(float $value): bool |
280
|
|
|
{ |
281
|
|
|
return $value === -0.0 && (ord(pack('G', $value)) & 0x80) !== 0; |
282
|
|
|
} |
283
|
|
|
|
284
|
|
|
/** |
285
|
|
|
* Encodes a PHP float into an N-bit floating point number (in an integer) representation. |
286
|
|
|
* This function can be configured with arbitrary number of Exponent Bits, Mantissa Bits, |
287
|
|
|
* Exponent Bias, and IEEE Conformance (for subnormal numbers, INF, -INF, and NAN). |
288
|
|
|
* The total number of floating point bits to be parsed is "$exponentBits + $mantissaBits + 1". |
289
|
|
|
* |
290
|
|
|
* With default parameter values, this functions as floatToFp16. |
291
|
|
|
* @param float $value The PHP float to encode. |
292
|
|
|
* @param int $exponentBits The number of bits used for the exponent, default: null for 5. |
293
|
|
|
* @param int $mantissaBits The number of bits used for the mantissa, default: null for 10. |
294
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
295
|
|
|
* half the maximum exponent value. Default: null. |
296
|
|
|
* @param bool $IEEEConformance Whether to follow the IEEE 754 standard for special values |
297
|
|
|
* (NaN, INF, -INF, and subnormal). Default true |
298
|
|
|
* @throws TInvalidDataValueException on bad floating point configuration values. |
299
|
|
|
* @return int The a short form float representation of the float $value. |
300
|
|
|
*/ |
301
|
|
|
public static function floatToFpXX(float $value, ?int $exponentBits = null, ?int $mantissaBits = null, ?int $exponentBias = null, bool $IEEEConformance = true): int |
302
|
|
|
{ |
303
|
|
|
$exponentBits = ($exponentBits === null) ? 5 : $exponentBits; |
304
|
|
|
$mantissaBits = ($mantissaBits === null) ? 10 : $mantissaBits; |
305
|
|
|
$exponentMaxValue = ~(-1 << $exponentBits); |
306
|
|
|
$exponentBias = ($exponentBias === null) ? $exponentMaxValue >> 1 : $exponentBias; |
307
|
|
|
if ($exponentBits <= 0 || $mantissaBits <= 0 || ($exponentBits + $mantissaBits + 1) > PHP_INT_SIZE * 8 || $exponentBias < 0 || $exponentBias > $exponentMaxValue) { |
308
|
|
|
throw new TInvalidDataValueException('bithelper_bad_fp_format', $exponentBits, $mantissaBits, $exponentBias, PHP_INT_SIZE * 8); |
309
|
|
|
} |
310
|
|
|
$sign = self::isNegativeFloat($value) ? 1 : 0; |
311
|
|
|
$value = abs($value); |
312
|
|
|
$exponent = 0; |
313
|
|
|
$mantissa = 0; |
314
|
|
|
|
315
|
|
|
if ($IEEEConformance && is_nan($value)) { |
316
|
|
|
$exponent = $exponentMaxValue; |
317
|
|
|
$mantissa = 1 << ($mantissaBits - 1); |
318
|
|
|
} elseif ($IEEEConformance && (is_infinite($value) || $value >= pow(2, ($exponentMaxValue - 1) - $exponentBias) * (1 << $mantissaBits))) { |
319
|
|
|
$exponent = $exponentMaxValue; |
320
|
|
|
} elseif ($value == 0) { |
321
|
|
|
$mantissa = 0; |
322
|
|
|
} else { |
323
|
|
|
$exponent = floor(log($value, 2)) + $exponentBias; |
324
|
|
|
if ($exponent <= 0) { |
325
|
|
|
$mantissa = round($value / pow(2, 1 - $exponentBias - $mantissaBits)); |
326
|
|
|
$exponent = 0; |
327
|
|
|
} elseif ($exponent >= $exponentMaxValue) { |
328
|
|
|
$exponent = $exponentMaxValue; |
329
|
|
|
$mantissa = 0; |
330
|
|
|
} else { |
331
|
|
|
$totalMantissaValues = (1 << $mantissaBits); |
332
|
|
|
$mantissa = round(($value / pow(2, $exponent - $exponentBias) - 1.0) * $totalMantissaValues); |
333
|
|
|
if ($mantissa === $totalMantissaValues) { |
334
|
|
|
$exponent++; |
335
|
|
|
$mantissa = 0; |
336
|
|
|
} |
337
|
|
|
} |
338
|
|
|
} |
339
|
|
|
$fpXX = ((($sign << $exponentBits) | $exponent) << $mantissaBits) | $mantissa; |
340
|
|
|
return $fpXX; |
341
|
|
|
} |
342
|
|
|
|
343
|
|
|
/** |
344
|
|
|
* This encodes a PHP float into a Fp16 (1 bit sign, 5 bits exponent, 10 bits mantissa) float. |
345
|
|
|
* @param float $value The float to encode. |
346
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
347
|
|
|
* half the maximum exponent value. Default: null. |
348
|
|
|
* @return int The encoded 2 byte Fp16 float. |
349
|
|
|
*/ |
350
|
|
|
public static function floatToFp16(float $value, ?int $exponentBias = null): int |
351
|
|
|
{ |
352
|
|
|
return self::floatToFpXX($value, 5, 10, $exponentBias); |
353
|
|
|
} |
354
|
|
|
|
355
|
|
|
/** |
356
|
|
|
* This encodes a PHP float into a Bf16 (1 bit sign, 8 bits exponent, 7 bits mantissa) |
357
|
|
|
* float. This preserves the range of typical 4 byte floats but drops 2 bytes of |
358
|
|
|
* precision from 23 bits to 7 bits. |
359
|
|
|
* @param float $value The float to encode. |
360
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
361
|
|
|
* half the maximum exponent value. Default: null. |
362
|
|
|
* @return int The encoded 2 byte Bf16 float. |
363
|
|
|
*/ |
364
|
|
|
public static function floatToBf16(float $value, ?int $exponentBias = null): int |
365
|
|
|
{ |
366
|
|
|
return self::floatToFpXX($value, 8, 7, $exponentBias); |
367
|
|
|
} |
368
|
|
|
|
369
|
|
|
/** |
370
|
|
|
* This encodes a PHP float into an FP8 (1 bit sign, 5 bits exponent, 2 bits mantissa) float. |
371
|
|
|
* The FP8 E5M2 format is for lower precision and higher range. |
372
|
|
|
* @param float $value The float to encode. |
373
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
374
|
|
|
* half the maximum exponent value. Default: null. |
375
|
|
|
* @return int The encoded 1 byte FP8-E5M2 float. |
376
|
|
|
*/ |
377
|
|
|
public static function floatToFp8Range(float $value, ?int $exponentBias = null): int |
378
|
|
|
{ |
379
|
|
|
return self::floatToFpXX($value, 5, 2, $exponentBias); |
380
|
|
|
} |
381
|
|
|
|
382
|
|
|
/** |
383
|
|
|
* This encodes a PHP float into an FP8 (1 bit sign, 4 bits exponent, 3 bits mantissa) float. |
384
|
|
|
* The FP8 E4M3 format is for higher precision and lower range. |
385
|
|
|
* @param float $value The float to encode. |
386
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
387
|
|
|
* half the maximum exponent value. Default: null. |
388
|
|
|
* @return int The encoded 1 byte FP8-E4M3 float. |
389
|
|
|
*/ |
390
|
|
|
public static function floatToFp8Precision(float $value, ?int $exponentBias = null): int |
391
|
|
|
{ |
392
|
|
|
return self::floatToFpXX($value, 4, 3, $exponentBias); |
393
|
|
|
} |
394
|
|
|
|
395
|
|
|
/** |
396
|
|
|
* Decodes an N-bit floating point encoded as an integer to a PHP floating-point number. |
397
|
|
|
* This function can be configured with arbitrary number of Exponent Bits, Mantissa Bits, |
398
|
|
|
* Exponent Bias, and IEEE Conformance (for subnormal numbers, INF, -INF, and NAN). |
399
|
|
|
* The total number of floating point bits to be parsed is "$exponentBits + $mantissaBits + 1". |
400
|
|
|
* |
401
|
|
|
* With default parameter values, this functions as fp16ToFloat. |
402
|
|
|
* @param int $fpXX The encoded N-bit floating point number. |
403
|
|
|
* @param int $exponentBits The number of bits used for the exponent, default: null for 5. |
404
|
|
|
* @param int $mantissaBits The number of bits used for the mantissa, default: null for 10. |
405
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
406
|
|
|
* half the maximum exponent value. Default: null. |
407
|
|
|
* @param bool $IEEEConformance Whether to follow the IEEE 754 standard for special values |
408
|
|
|
* (NaN, INF, -INF, and subnormal). Default true |
409
|
|
|
* @throws TInvalidDataValueException on bad floating point configuration values. |
410
|
|
|
* @return float The PHP float of the encoded $fpXX float. |
411
|
|
|
*/ |
412
|
|
|
public static function fpXXToFloat(int $fpXX, ?int $exponentBits = null, ?int $mantissaBits = null, ?int $exponentBias = null, bool $IEEEConformance = true): float |
413
|
|
|
{ |
414
|
|
|
$exponentBits = ($exponentBits === null) ? 5 : $exponentBits; |
415
|
|
|
$mantissaBits = ($mantissaBits === null) ? 10 : $mantissaBits; |
416
|
|
|
$exponentMaxValue = ~(-1 << $exponentBits); |
417
|
|
|
if ($exponentBits <= 0 || $mantissaBits <= 0 || ($exponentBits + $mantissaBits + 1) > PHP_INT_SIZE * 8 || |
418
|
|
|
($exponentBias !== null && ($exponentBias < 0 || $exponentBias > $exponentMaxValue))) { |
419
|
|
|
throw new TInvalidDataValueException('bithelper_bad_fp_format', $exponentBits, $mantissaBits, $exponentBias, PHP_INT_SIZE * 8); |
420
|
|
|
} |
421
|
|
|
$exponentBias = ($exponentBias === null) ? $exponentMaxValue >> 1 : $exponentBias; |
422
|
|
|
$sign = ($fpXX >> ($exponentBits + $mantissaBits)) & 0x1; |
423
|
|
|
$exponent = ($fpXX >> $mantissaBits) & $exponentMaxValue; |
424
|
|
|
$mantissa = $fpXX & ~(-1 << $mantissaBits); |
425
|
|
|
if ($IEEEConformance && $exponent == 0) { // subnormal numbers. |
426
|
|
|
$value = $mantissa * pow(2, 1 - $exponentBias - $mantissaBits); |
427
|
|
|
} elseif ($IEEEConformance && $exponent == $exponentMaxValue) { |
428
|
|
|
$value = ($mantissa == 0) ? INF : NAN; |
429
|
|
|
} else { |
430
|
|
|
$value = pow(2, $exponent - $exponentBias) * (1.0 + ($mantissa / (1 << $mantissaBits))); |
431
|
|
|
} |
432
|
|
|
if ($sign) { |
433
|
|
|
$value = -$value; |
434
|
|
|
} |
435
|
|
|
return $value; |
436
|
|
|
} |
437
|
|
|
|
438
|
|
|
/** |
439
|
|
|
* This decodes a Fp16 (5 bits exponent, 10 bits mantissa) encoded float into a PHP Float. |
440
|
|
|
* @param int $fp16 the Fp16 encoded float. |
441
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
442
|
|
|
* half the maximum exponent value. Default: null. |
443
|
|
|
* @return float The Fp16 float decoded as a PHP float. |
444
|
|
|
*/ |
445
|
|
|
public static function fp16ToFloat(int $fp16, ?int $exponentBias = null): float |
446
|
|
|
{ |
447
|
|
|
return self::fpXXToFloat($fp16, 5, 10, $exponentBias); |
448
|
|
|
} |
449
|
|
|
|
450
|
|
|
/** |
451
|
|
|
* This decodes a Bf16 (8 bits exponent, 7 bits mantissa) encoded float into a PHP |
452
|
|
|
* Float. |
453
|
|
|
* @param int $bf16 the BF16 encoded float. |
454
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
455
|
|
|
* half the maximum exponent value. Default: null. |
456
|
|
|
* @return float The Bf16 float decoded as a PHP float. |
457
|
|
|
*/ |
458
|
|
|
public static function bf16ToFloat(int $bf16, ?int $exponentBias = null): float |
459
|
|
|
{ |
460
|
|
|
return self::fpXXToFloat($bf16, 8, 7, $exponentBias); |
461
|
|
|
} |
462
|
|
|
|
463
|
|
|
/** |
464
|
|
|
* This decodes a FP8 (5 bits exponent, 2 bits mantissa) encoded float into a PHP Float. |
465
|
|
|
* @param int $fp8 the FP8-E5M2 encoded float. |
466
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
467
|
|
|
* half the maximum exponent value. Default: null. |
468
|
|
|
* @return float The FP8-E5M2 float decoded as a PHP float. |
469
|
|
|
*/ |
470
|
|
|
public static function fp8RangeToFloat(int $fp8, ?int $exponentBias = null): float |
471
|
|
|
{ |
472
|
|
|
return self::fpXXToFloat($fp8, 5, 2, $exponentBias); |
473
|
|
|
} |
474
|
|
|
|
475
|
|
|
/** |
476
|
|
|
* This decodes a FP8 (4 bits exponent, 3 bits mantissa) encoded float into a PHP Float. |
477
|
|
|
* @param int $fp8 the FP8-E4M3 encoded float. |
478
|
|
|
* @param null|int $exponentBias The bias to apply to the exponent. If null, it defaults to |
479
|
|
|
* half the maximum exponent value. Default: null. |
480
|
|
|
* @return float The FP8-E4M3 float decoded as a PHP float. |
481
|
|
|
*/ |
482
|
|
|
public static function fp8PrecisionToFloat(int $fp8, ?int $exponentBias = null): float |
483
|
|
|
{ |
484
|
|
|
return self::fpXXToFloat($fp8, 4, 3, $exponentBias); |
485
|
|
|
} |
486
|
|
|
|
487
|
|
|
/** |
488
|
|
|
* This calculates the number of bits required to represent a given number. |
489
|
|
|
* eg. If there are 256 colors, then the maximum representable number in 8 bits |
490
|
|
|
* is 255. A $value of 255 returns 8 bits, and 256 returns 9 bits, to represent |
491
|
|
|
* the number. |
492
|
|
|
* @param int $value The number to calculate the bits required to represent it. |
493
|
|
|
* @return int The number of bits required to represent $n |
494
|
|
|
*/ |
495
|
|
|
public static function bitCount(int $value): int |
496
|
|
|
{ |
497
|
|
|
if ($value === 0) { |
498
|
|
|
return 0; |
499
|
|
|
} elseif ($value < 0) { // Negative numbers need one more bit. |
500
|
|
|
$value = (-$value) << 1; |
501
|
|
|
} |
502
|
|
|
if ($value < 0) { |
503
|
|
|
return PHP_INT_SIZE * 8; |
504
|
|
|
} |
505
|
|
|
return (int) ceil(log($value + 1, 2)); |
506
|
|
|
} |
507
|
|
|
|
508
|
|
|
/** |
509
|
|
|
* This method shifts color bits. When removing bits, they are simply dropped. |
510
|
|
|
* When adding bits, it replicates the existing bits for new bits to create the |
511
|
|
|
* most accurate higher bit representation of the color. |
512
|
|
|
* @param int $value The color value to expand or contract bits. |
513
|
|
|
* @param int $inBits The number of bits of the input value. |
514
|
|
|
* @param int $outBits The number of bits of the output value. |
515
|
|
|
* @return int The $value shifted to $outBits in size. |
516
|
|
|
* @throw TInvalidDataValueException when the $inBits or $outBits are less than |
517
|
|
|
* 1 or greater than the Max Int Size for this PHP implementation. |
518
|
|
|
*/ |
519
|
|
|
public static function colorBitShift(int $value, int $inBits, int $outBits): int |
520
|
|
|
{ |
521
|
|
|
if ($inBits < 1 || $inBits > PHP_INT_SIZE * 8) { |
522
|
|
|
throw new TInvalidDataValueException("bithelper_invalid_color_in", $inBits); |
523
|
|
|
} |
524
|
|
|
if ($outBits < 1 || $outBits > PHP_INT_SIZE * 8) { |
525
|
|
|
throw new TInvalidDataValueException("bithelper_invalid_color_out", $outBits); |
526
|
|
|
} |
527
|
|
|
$dif = $outBits - $inBits; |
528
|
|
|
if ($dif > 0) { |
529
|
|
|
$return = $value; |
530
|
|
|
do { |
531
|
|
|
$dd = min($inBits, $dif); |
532
|
|
|
$return = ($return << $dd) | ($value >> ($inBits - $dd)); |
533
|
|
|
$dif -= $dd; |
534
|
|
|
} while ($dif > 0); |
535
|
|
|
return $return; |
536
|
|
|
} elseif ($dif < 0) { |
537
|
|
|
$dif = -$dif; |
538
|
|
|
return ($value >> $dif) & (PHP_INT_MAX >> ($dif - 1)); |
539
|
|
|
} |
540
|
|
|
return $value; |
541
|
|
|
} |
542
|
|
|
|
543
|
|
|
/** |
544
|
|
|
* This does a right bit shift but the signed bit is not replicated in the high |
545
|
|
|
* bit (with a bit-and). |
546
|
|
|
* In normal PHP right bit shift, the signed bit is what make up any new bit in |
547
|
|
|
* the shift. |
548
|
|
|
* @param int $value The integer to bit shift. |
549
|
|
|
* @param int $bits How much to shift the bits right. Positive is right shift, |
550
|
|
|
* Negative is left shift. |
551
|
|
|
* @return int The shifted integer without the high bit repeating. |
552
|
|
|
*/ |
553
|
|
|
public static function unsignedShift(int $value, int $bits): int |
554
|
|
|
{ |
555
|
|
|
if ($bits > 0) { |
556
|
|
|
return ($value >> $bits) & (PHP_INT_MAX >> ($bits - 1)); |
557
|
|
|
} elseif ($bits < 0) { |
558
|
|
|
return $value << -$bits; |
559
|
|
|
} else { |
560
|
|
|
return $value; |
561
|
|
|
} |
562
|
|
|
} |
563
|
|
|
|
564
|
|
|
/** |
565
|
|
|
* This mirrors $nbit bits from $value. For example, 0b100 becomes 0b001 @ $nbit = 3 |
566
|
|
|
* and 0x0100 become 0x0010 @ $nbit = 4. |
567
|
|
|
* @param int $value The bits to reverse. |
568
|
|
|
* @param int $nbit The number of bits to reverse. |
569
|
|
|
* @throws TInvalidDataValueException when $nbits is over the maximum size of a PHP int. |
570
|
|
|
* @return int reversed bits of $value. |
571
|
|
|
*/ |
572
|
|
|
public static function mirrorBits(int $value, int $nbit): int |
573
|
|
|
{ |
574
|
|
|
if ($nbit > PHP_INT_SIZE * 8) { |
575
|
|
|
throw new TInvalidDataValueException('bithelper_bad_mirror_bits', $nbit, PHP_INT_SIZE * 8); |
576
|
|
|
} |
577
|
|
|
for ($i = 0, $result = 0; $i < $nbit; $i++) { |
578
|
|
|
$result <<= 1; |
579
|
|
|
$result |= $value & 1; |
580
|
|
|
$value >>= 1; |
581
|
|
|
} |
582
|
|
|
return $result; |
583
|
|
|
} |
584
|
|
|
|
585
|
|
|
/** |
586
|
|
|
* This quickly mirrors the 8 bits in each byte of $n. |
587
|
|
|
* @param int $n The integer to mirror the bits of each byte. |
588
|
|
|
* @return int reversed 8 bits of $n. |
589
|
|
|
*/ |
590
|
|
|
public static function mirrorByte(int $n): int |
591
|
|
|
{ |
592
|
|
|
$n = ((($n & self::NLevel1) >> 1) & self::Mask1) | (($n & self::Level1) << 1); |
593
|
|
|
$n = ((($n & self::NLevel2) >> 2) & self::Mask2) | (($n & self::Level2) << 2); |
594
|
|
|
return ((($n & self::NLevel3) >> 4) & self::Mask3) | (($n & self::Level3) << 4); |
595
|
|
|
} |
596
|
|
|
|
597
|
|
|
/** |
598
|
|
|
* This quickly mirrors the 16 bits in each [2 byte] short of $n. |
599
|
|
|
* @param int $n The integer to mirror the bits of each short. |
600
|
|
|
* @return int reversed 16 bits of $n. |
601
|
|
|
*/ |
602
|
|
|
public static function mirrorShort(int $n): int |
603
|
|
|
{ |
604
|
|
|
$n = ((($n & self::NLevel1) >> 1) & self::Mask1) | (($n & self::Level1) << 1); |
605
|
|
|
$n = ((($n & self::NLevel2) >> 2) & self::Mask2) | (($n & self::Level2) << 2); |
606
|
|
|
$n = ((($n & self::NLevel3) >> 4) & self::Mask3) | (($n & self::Level3) << 4); |
607
|
|
|
return ((($n & self::NLevel4) >> 8) & self::Mask4) | (($n & self::Level4) << 8); |
608
|
|
|
|
609
|
|
|
} |
610
|
|
|
|
611
|
|
|
/** |
612
|
|
|
* This quickly mirrors the 32 bits in each [4 byte] long of $n. |
613
|
|
|
* @param int $n The integer to mirror the bits of each long. |
614
|
|
|
* @return int reversed 32 bits of $n. |
615
|
|
|
*/ |
616
|
|
|
public static function mirrorLong(int $n): int |
617
|
|
|
{ |
618
|
|
|
$n = ((($n & self::NLevel1) >> 1) & self::Mask1) | (($n & self::Level1) << 1); |
619
|
|
|
$n = ((($n & self::NLevel2) >> 2) & self::Mask2) | (($n & self::Level2) << 2); |
620
|
|
|
$n = ((($n & self::NLevel3) >> 4) & self::Mask3) | (($n & self::Level3) << 4); |
621
|
|
|
$n = ((($n & self::NLevel4) >> 8) & self::Mask4) | (($n & self::Level4) << 8); |
622
|
|
|
return ((($n & self::NLevel5) >> 16) & self::Mask5) | (($n & self::Level5) << 16); |
623
|
|
|
} |
624
|
|
|
|
625
|
|
|
/** |
626
|
|
|
* This quickly mirrors the 64 bits of $n. This only works with 64 bit PHP systems. |
627
|
|
|
* For speed, there is no check to validate that the system is 64 bit PHP. You |
628
|
|
|
* must do the validation if/when needed with method {@see hasLongLong}. |
629
|
|
|
* @param int $n The 8 byte integer to mirror the bits of. |
630
|
|
|
* @return int reversed 64 bits of $n. |
631
|
|
|
*/ |
632
|
|
|
public static function mirrorLongLong(int $n): int |
633
|
|
|
{ |
634
|
|
|
$n = ((($n & self::NLevel1) >> 1) & self::Mask1) | (($n & self::Level1) << 1); |
635
|
|
|
$n = ((($n & self::NLevel2) >> 2) & self::Mask2) | (($n & self::Level2) << 2); |
636
|
|
|
$n = ((($n & self::NLevel3) >> 4) & self::Mask3) | (($n & self::Level3) << 4); |
637
|
|
|
$n = ((($n & self::NLevel4) >> 8) & self::Mask4) | (($n & self::Level4) << 8); |
638
|
|
|
$n = ((($n & self::NLevel5) >> 16) & self::Mask5) | (($n & self::Level5) << 16); |
639
|
|
|
return ((($n & self::NLevel6) >> 32) & self::Mask6) | (($n & self::Level6) << 32); |
640
|
|
|
} |
641
|
|
|
|
642
|
|
|
/** |
643
|
|
|
* This quickly flips the endian in each [2 byte] short of $n. |
644
|
|
|
* @param int $n The 2 byte short to reverse the endian. |
645
|
|
|
* @return int reversed endian of $n. |
646
|
|
|
*/ |
647
|
|
|
public static function flipEndianShort(int $n): int |
648
|
|
|
{ |
649
|
|
|
return ((($n & self::NLevel4) >> 8) & self::Mask4) | (($n & self::Level4) << 8); |
650
|
|
|
} |
651
|
|
|
|
652
|
|
|
/** |
653
|
|
|
* This quickly flips the endian in each [4 byte] long of $n. |
654
|
|
|
* @param int $n The 4 byte long to reverse the endian. |
655
|
|
|
* @return int The reversed endian of $n. |
656
|
|
|
*/ |
657
|
|
|
public static function flipEndianLong(int $n): int |
658
|
|
|
{ |
659
|
|
|
$n = ((($n & self::NLevel4) >> 8) & self::Mask4) | (($n & self::Level4) << 8); |
660
|
|
|
return ((($n & self::NLevel5) >> 16) & self::Mask5) | (($n & self::Level5) << 16); |
661
|
|
|
} |
662
|
|
|
|
663
|
|
|
/** |
664
|
|
|
* This quickly fligs the endian of an 8 byte integer. This only works with 64 |
665
|
|
|
* bit PHP systems. 32 bit systems will treat the bit field as floats and invariably |
666
|
|
|
* fail. |
667
|
|
|
* |
668
|
|
|
* For speed, there is no check to validate that the system is 64 bit PHP. You |
669
|
|
|
* must do the validation if/when needed with method {@see hasLongLong}. |
670
|
|
|
* @param int $n The 8 byte long long to reverse the endian. |
671
|
|
|
* @return int reversed 8 bytes endian of $n. |
672
|
|
|
*/ |
673
|
|
|
public static function flipEndianLongLong(int $n): int |
674
|
|
|
{ |
675
|
|
|
$n = ((($n & self::NLevel4) >> 8) & self::Mask4) | (($n & self::Level4) << 8); |
676
|
|
|
$n = ((($n & self::NLevel5) >> 16) & self::Mask5) | (($n & self::Level5) << 16); |
677
|
|
|
return ((($n & self::NLevel6) >> 32) & self::Mask6) | (($n & self::Level6) << 32); |
678
|
|
|
} |
679
|
|
|
} |
680
|
|
|
|
In PHP, under loose comparison (like
==
, or!=
, orswitch
conditions), values of different types might be equal.For
integer
values, zero is a special case, in particular the following results might be unexpected: