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<?php // Mirrored from https://github.com/Danack/HexFloat require_once __DIR__ . "/FloatInfo.php"; require_once __DIR__ . "/Float32Info.php"; use HexFloat\FloatInfo; use HexFloat\Float32Info; /** * Returns a string containing a hexadecimal representation of the given float, * using 64 bits of info * * @param float $number * @return string */ function floathex(float $number) { return strrev(unpack('h*', pack('d', $number))[1]); } /** * Returns a string containing a hexadecimal representation of the given float, * using 32 bits of info * * @param float $number * @return string */ function floathex32(float $num) { return strrev(unpack('h*', pack('f', $num))[1]); } /** * Convert a floating point number to a FloatInfo object, * which contains string representations of the float's sign, * exponent and mantissa * @param float $num * @return FloatInfo */ function float_info(float $num) { $float64 = floathex($num); //Sign bit: 1 bit //Exponent: 11 bits //Significand precision: 53 bits (52 explicitly stored) $chars = str_split($float64); // 3 bits from this $byte1 = hexdec($chars[0]); // 4 bits from this $byte2 = hexdec($chars[1]); // 1 bit from this $byte3 = hexdec($chars[2]); $sign = '0'; if ($byte1 >= 8) { $sign = '1'; } $exponentString = substr($float64, 0, 3); $exponentValue = hexdec($exponentString) & 0x7ff; $exponent = sprintf("%b", $exponentValue); $exponent = str_pad($exponent, 11, '0', STR_PAD_LEFT); $mantissa = substr($float64, 2); $mantissa = hexdec($mantissa) & 0xfffffffffffff; $mantissa = sprintf("%b", $mantissa); $mantissa = str_pad($mantissa, 52, '0', STR_PAD_LEFT); return new FloatInfo( $sign, $exponent, $mantissa ); } /** * Convert a floating point number to a Float32Info object, * which contains string representations of the float's sign, * exponent and mantissa * * @param float $num * @return Float32Info */ function float_info_32(float $num) { $float32 = floathex32($num); $chars = str_split($float32); // 3 bits from this $byte1 = hexdec($chars[0]); // 4 bits from this $byte2 = hexdec($chars[1]); // 1 bit from this $byte3 = hexdec($chars[2]); $sign = '0'; if ($byte1 >= 8) { $sign = '1'; } $exponent3Bits = ($byte1 & 0x7); $exponent4Bits = $byte2; $exponent1Bit = ($byte3 & 0x8) >> 3; $exponent = ($exponent3Bits << 5) | ($exponent4Bits << 1) | $exponent1Bit; $exponent = sprintf("%b", $exponent); $exponent = str_pad($exponent, 8, '0', STR_PAD_LEFT); $mantissa = substr($float32, 2, 6); $mantissa = hexdec($mantissa) & 0x7fffff; $mantissa = sprintf("%b", $mantissa); $mantissa = str_pad($mantissa, 23, '0', STR_PAD_LEFT); return new Float32Info( $sign, $exponent, $mantissa ); } /** * Produce a debug string that shows the Sign, Exponent and Mantissa for * two floating point numbers, using 64bit precision * * * @param float $value1 * @param float $value2 * @return string * * Example result * ┌──────┬─────────────┬──────────────────────────────────────────────────────┐ * │ Sign │ Exponent │ Mantissa │ * │ 0 │ 01111111011 │ 1001100110011001100110011001100110011001100110011010 │ * │ 0 │ 10000011001 │ 0111110101111000010000000100000000000000000000000000 │ * └──────┴─────────────┴──────────────────────────────────────────────────────┘ * */ function float_compare(float $value1, float $value2) { $float_info_1 = float_info($value1); $float_info_2 = float_info($value2); //Sign bit: 1 bit //Exponent: 11 bits //Significand precision: 53 bits (52 explicitly stored) $output = "┌──────┬─────────────┬──────────────────────────────────────────────────────┐\n"; $output .= "│ Sign │ Exponent │ Mantissa │\n"; $format_string = "│ %s │ %s │ %s │\n"; $output .= sprintf($format_string, $float_info_1->getSign(), $float_info_1->getExponent(), $float_info_1->getMantissa()); $output .= sprintf($format_string, $float_info_2->getSign(), $float_info_2->getExponent(), $float_info_2->getMantissa()); $output .= "└──────┴─────────────┴──────────────────────────────────────────────────────┘\n"; return $output; } /** * Produce a debug string that shows the Sign, Exponent and Mantissa for * two floating point numbers, using 32bit precision * * @param float $value1 * @param float $value2 * @return string * * Example result * ┌──────┬──────────┬─────────────────────────┐ * │ Sign │ Exponent │ Mantissa │ * │ 0 │ 01111011 │ 10011001100110011001101 │ * │ 0 │ 10011001 │ 01111101011110000100000 │ * └──────┴──────────┴─────────────────────────┘ * */ function float_compare_32(float $value1, float $value2) { $float_info_1 = float_info_32($value1); $float_info_2 = float_info_32($value2); $output = "┌──────┬──────────┬─────────────────────────┐\n"; $output .= "│ Sign │ Exponent │ Mantissa │\n"; $format_string = "│ %s │ %s │ %s │\n"; $output .= sprintf($format_string, $float_info_1->getSign(), $float_info_1->getExponent(), $float_info_1->getMantissa()); $output .= sprintf($format_string, $float_info_2->getSign(), $float_info_2->getExponent(), $float_info_2->getMantissa()); $output .= "└──────┴──────────┴─────────────────────────┘\n"; return $output; } /** * So. One of the disadvantages of non-HDRI compiled Image Magick * is that it can't accurately represent a '50%' color accurately. * * For example, if ImageMagick is compiled with 16bit color depth * then the two closest colors to midpoint are: * 32767 / 65535 = 0.5 - (1 / (2 ^ 17)) = 0.499992370... * or * 32768 / 65535 = 0.5 + (1 / (2 ^ 17)) = 0.50000762951 * * Either way there is going to be 'error' of * 0.00000762939453125 * * The problem is even worse when ImageMagick is compiled with 8-bit * numbers (though this really shouldn't be used any more) and the * error would be 0.001953125 * */ function get_epsilon_for_off_by_half_errors() { // These could be defined better... $epsilon_values_for_non_hdri = [ '255' => (1 / (pow(2, 8) - 1)) + 0.0000000000001, '65535' => (1 / (pow(2, 16) - 1)) + 0.0000000000001, '16777215' => (1 / (pow(2, 24) - 1) ) + 0.0000000000001, '4294967295' => (1 / (pow(2, 32) - 1)) + 0.0000000000001, ]; // These could definitely be defined better... $epsilon_values_for_hdri = [ '255' => 0.0000000000001, '65535' => 0.0000000000001, '16777215' => 0.0000000000001, '4294967295' => 0.0000000000001 ]; if (Imagick::getHdriEnabled() === false) { $quantum = (string)Imagick::getQuantum(); if (array_key_exists($quantum, $epsilon_values_for_non_hdri) !== true) { throw new Exception( "Quantum values is $quantum which is not any of (2^(8|16|24|32)) - 1. Please report this as a bug." ); } return $epsilon_values_for_non_hdri[$quantum]; } $quantum = Imagick::getQuantum(); if (array_key_exists($quantum, $epsilon_values_for_hdri) !== true) { throw new Exception( "Quantum values is $quantum which is not any of (2^(8|16|24|32)) - 1. Please report this as a bug." ); } return $epsilon_values_for_hdri[$quantum]; }
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