<?php /* * MODIFICATIONS * - Removed `\` for php5.2 support (does not support namespaces). * - Renamed with prefix to avoid naming collisions. * - Updated references to the EOS Stack class to reflect name changes. */ /** * Equation Operating System Classes. * * This class was created for the safe parsing of mathematical equations * in PHP. There is a need for a way to successfully parse equations * in PHP that do NOT require the use of `eval`. `eval` at its core * opens the system using it to so many security vulnerabilities it is oft * suggested /never/ to use it, and for good reason. This class set will * successfully take an equation, parse it, and provide solutions to the * developer. It is a safe way to evaluate expressions without putting * the system at risk. * * 2015/07 * - Added all real number factorial support * - Added gamma function to class * * 2014/08 * - Added scientific notation support * - Added basic factorial support * * 2013/06 UPDATE: * - Added 'abs' (absolute value) support per tjbaron's update. * * 2013/04 UPDATE: * - Moved to native class functions for PHP5 * - Removed deprecated `eregi` calls to `preg_match` * - Updated to PHPDoc comment syntax * - Added Exception throwing instead of silent exits * - Added additional variable prefix of '$', '&' is still allowed as well * - Fixed small implied multiplication problem * * @author Jon Lawrence <jlawrence11@gmail.com> * @copyright Copyright 2005-2015, Jon Lawrence * @license http://opensource.org/licenses/LGPL-2.1 LGPL 2.1 License * @package EOS * @version 2.2.1 */ require_once 'Stack.php'; /** * Equation Operating System (EOS) Parser * * An EOS that can safely parse equations from unknown sources returning * the calculated value of it. Can also handle solving equations with * variables, if the variables are defined (useful for the Graph creation * that the second and extended class in this file provides. {@see eqGraph}) * This class was created for PHP4 in 2005, updated to fully PHP5 in 2013. * * @author Jon Lawrence <jlawrence11@gmail.com> * @copyright Copyright �2005-2013, Jon Lawrence * @license http://opensource.org/licenses/LGPL-2.1 LGPL 2.1 License * @package Math * @subpackage EOS * @version 2.2.1 */ class NF_EOS_Parser { /** * No matching Open/Close pair */ const E_NO_SET = 5500; /** * Division by 0 */ const E_DIV_ZERO = 5501; /** * No Equation */ const E_NO_EQ = 5502; /** * No variable replacement available */ const E_NO_VAR = 5503; /** * Not a number */ const E_NAN = 5504; /** * @var bool Activate Debug output. * @see __construct() * @see solveIF() */ public static $debug = FALSE; /**#@+ *Private variables */ private $postFix; private $inFix; /**#@-*/ /**#@+ * Protected variables */ //What are opening and closing selectors protected $SEP = array('open' => array('(', '['), 'close' => array(')', ']')); //Top presedence following operator - not in use protected $SGL = array('!'); //Order of operations arrays follow protected $ST = array('^', '!'); protected $ST1 = array('/', '*', '%'); protected $ST2 = array('+', '-'); //Allowed functions protected $FNC = array('sin', 'cos', 'tan', 'csc', 'sec', 'cot', 'abs', 'log', 'log10', 'sqrt'); /**#@-*/ /** * Construct method * * Will initiate the class. If variable given, will assign to * internal variable to solve with this::solveIF() without needing * additional input. Initializing with a variable is not suggested. * * @see Parser::solveIF() * @param String $inFix Standard format equation */ public function __construct($inFix = null) { if(defined('DEBUG') && DEBUG) { self::$debug = true; } $this->inFix = (isset($inFix)) ? $inFix : null; $this->postFix = array(); } /** * Check Infix for opening closing pair matches. * * This function is meant to solely check to make sure every opening * statement has a matching closing one, and throws an exception if * it doesn't. * * @param String $infix Equation to check * @throws Exception if malformed. * @return Bool true if passes - throws an exception if not. */ private function checkInfix($infix) { if(trim($infix) == "") { throw new Exception("No Equation given", NF_EOS_Parser::E_NO_EQ); } //Make sure we have the same number of '(' as we do ')' // and the same # of '[' as we do ']' if(substr_count($infix, '(') != substr_count($infix, ')')) { throw new Exception("Mismatched parenthesis in '{$infix}'", NF_EOS_Parser::E_NO_SET); } elseif(substr_count($infix, '[') != substr_count($infix, ']')) { throw new Exception("Mismatched brackets in '{$infix}'", NF_EOS_Parser::E_NO_SET); } $this->inFix = $infix; return true; } /** * Infix to Postfix * * Converts an infix (standard) equation to postfix (RPN) notation. * Sets the internal variable $this->postFix for the Parser::solvePF() * function to use. * * @link http://en.wikipedia.org/wiki/Infix_notation Infix Notation * @link http://en.wikipedia.org/wiki/Reverse_Polish_notation Reverse Polish Notation * @param String $infix A standard notation equation * @throws Exception When parenthesis are mismatched. * @return Array Fully formed RPN Stack */ public function in2post($infix = null) { // if an equation was not passed, use the one that was passed in the constructor $infix = (isset($infix)) ? $infix : $this->inFix; //check to make sure 'valid' equation $this->checkInfix($infix); $pf = array(); $ops = new NF_EOS_Stack(); //$vars = new Stack(); // remove all white-space $infix = preg_replace("/\s/", "", $infix); // Create postfix array index $pfIndex = 0; //what was the last character? (useful for decerning between a sign for negation and subtraction) $lChar = ''; //loop through all the characters and start doing stuff ^^ for($i=0;$i<strlen($infix);$i++) { // pull out 1 character from the string $chr = substr($infix, $i, 1); // if the character is numerical if(preg_match('/[0-9.]/i', $chr)) { // if the previous character was not a '-' or a number if((!preg_match('/[0-9.]/i', $lChar) && ($lChar != "")) && (isset($pf[$pfIndex]) && ($pf[$pfIndex]!="-"))) $pfIndex++; // increase the index so as not to overlap anything // Add the number character to the array if(isset($pf[$pfIndex])) { $pf[$pfIndex] .= $chr; } else { $pf[$pfIndex] = $chr; } } // If the character opens a set e.g. '(' or '[' elseif(in_array($chr, $this->SEP['open'])) { // if the last character was a number, place an assumed '*' on the stack if(preg_match('/[0-9.]/i', $lChar)) $ops->push('*'); $ops->push($chr); } // if the character closes a set e.g. ')' or ']' elseif(in_array($chr, $this->SEP['close'])) { // find what set it was i.e. matches ')' with '(' or ']' with '[' $key = array_search($chr, $this->SEP['close']); // while the operator on the stack isn't the matching pair...pop it off while($ops->peek() != $this->SEP['open'][$key]) { $nchr = $ops->pop(); if($nchr) $pf[++$pfIndex] = $nchr; else { throw new Exception("Error while searching for '". $this->SEP['open'][$key] ."' in '{$infix}'.", NF_EOS_Parser::E_NO_SET); } } $ops->pop(); } // If a special operator that has precedence over everything else elseif(in_array($chr, $this->ST)) { while(in_array($ops->peek(), $this->ST)) $pf[++$pfIndex] = $ops->pop(); $ops->push($chr); $pfIndex++; } // Any other operator other than '+' and '-' elseif(in_array($chr, $this->ST1)) { while(in_array($ops->peek(), $this->ST1) || in_array($ops->peek(), $this->ST)) $pf[++$pfIndex] = $ops->pop(); $ops->push($chr); $pfIndex++; } // if a '+' or '-' elseif(in_array($chr, $this->ST2)) { // if it is a '-' and the character before it was an operator or nothingness (e.g. it negates a number) if((in_array($lChar, array_merge($this->ST1, $this->ST2, $this->ST, $this->SEP['open'])) || $lChar=="") && $chr=="-") { // increase the index because there is no reason that it shouldn't.. $pfIndex++; $pf[$pfIndex] = $chr; } // Otherwise it will function like a normal operator else { while(in_array($ops->peek(), array_merge($this->ST1, $this->ST2, $this->ST))) $pf[++$pfIndex] = $ops->pop(); $ops->push($chr); $pfIndex++; } } // make sure we record this character to be referred to by the next one $lChar = $chr; } // if there is anything on the stack after we are done...add it to the back of the RPN array while(($tmp = $ops->pop()) !== false) $pf[++$pfIndex] = $tmp; // re-index the array at 0 $pf = array_values($pf); // set the private variable for later use if needed $this->postFix = $pf; // return the RPN array in case developer wants to use it fro some insane reason (bug testing ;] return $pf; } //end function in2post /** * Solve Postfix (RPN) * * This function will solve a RPN array. Default action is to solve * the RPN array stored in the class from Parser::in2post(), can take * an array input to solve as well, though default action is preferred. * * @link http://en.wikipedia.org/wiki/Reverse_Polish_notation Postix Notation * @param Array $pfArray RPN formatted array. Optional. * @throws Exception On division by zero. * @return Float Result of the operation. */ public function solvePF($pfArray = null) { // if no RPN array is passed - use the one stored in the private var $pf = (!is_array($pfArray)) ? $this->postFix : $pfArray; // create our temporary function variables $temp = array(); //$tot = 0; $hold = 0; // Loop through each number/operator for($i=0;$i<count($pf); $i++) { // If the string isn't an operator, add it to the temp var as a holding place if(!in_array($pf[$i], array_merge($this->ST, $this->ST1, $this->ST2))) { $temp[$hold++] = $pf[$i]; } // ...Otherwise perform the operator on the last two numbers else { switch ($pf[$i]) { case '+': $temp[$hold-2] = $temp[$hold-2] + $temp[$hold-1]; break; case '-': $temp[$hold-2] = $temp[$hold-2] - $temp[$hold-1]; break; case '*': $temp[$hold-2] = $temp[$hold-2] * $temp[$hold-1]; break; case '/': if($temp[$hold-1] == 0) { throw new Exception("Division by 0 on: '{$temp[$hold-2]} / {$temp[$hold-1]}' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO); } $temp[$hold-2] = $temp[$hold-2] / $temp[$hold-1]; break; case '^': $temp[$hold-2] = pow($temp[$hold-2], $temp[$hold-1]); break; case '!': $temp[$hold-1] = $this->factorial($temp[$hold-1]); $hold++; break; case '%': if($temp[$hold-1] == 0) { throw new Exception("Division by 0 on: '{$temp[$hold-2]} % {$temp[$hold-1]}' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO); } $temp[$hold-2] = bcmod($temp[$hold-2], $temp[$hold-1]); break; } // Decrease the hold var to one above where the last number is $hold = $hold-1; } } // return the last number in the array return $temp[$hold-1]; } //end function solvePF public function solve($equation, $values = null) { if(is_array($equation)) { return $this->solvePF($equation); } else { return $this->solveIF($equation, $values); } } /** * Solve Infix (Standard) Notation Equation * * Will take a standard equation with optional variables and solve it. Variables * must begin with '&' or '$' * The variable array must be in the format of 'variable' => value. If * variable array is scalar (ie 5), all variables will be replaced with it. * * @param String $infix Standard Equation to solve * @param String|Array $vArray Variable replacement * @throws Exception On division by zero and on NaN and lack of variable replacement. * @return Float Solved equation */ function solveIF($infix, $vArray = null) { $infix = ($infix != "") ? $infix : $this->inFix; //Check to make sure a 'valid' expression $this->checkInfix($infix); //$ops = new Stack(); //$vars = new Stack(); $hand = null; //remove all white-space $infix = preg_replace("/\s/", "", $infix); if(NF_EOS_Parser::$debug) { $hand=fopen("eq.txt","a"); } //replace scientific notation with normal notation (2e-9 to 2*10^-9) $infix = preg_replace('/([\d])([eE])(-?\d)/', '$1*10^$3', $infix); if(NF_EOS_Parser::$debug) { fwrite($hand, "$infix\n"); } // Finds all the 'functions' within the equation and calculates them // NOTE - when using function, only 1 set of parenthesis will be found, instead use brackets for sets within functions!! //while((preg_match("/(". implode("|", $this->FNC) . ")$([^$$]*(\([^$]*\)[^]*)*[^\)$]*)$/", $infix, $match)) != 0) { //Nested parenthesis are now a go! while((preg_match("/(". implode("|", $this->FNC) . ")$((?:[^()]|\((?2)$)*+)\)/", $infix, $match)) != 0) { $func = $this->solveIF($match[2], $vArray); switch($match[1]) { case "cos": $ans = cos($func); break; case "sin": $ans = sin($func); break; case "tan": $ans = tan($func); break; case "sec": $tmp = cos($func); if($tmp == 0) { throw new Exception("Division by 0 on: 'sec({$func}) = 1/cos({$func})' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO); } $ans = 1/$tmp; break; case "csc": $tmp = sin($func); if($tmp == 0) { throw new Exception("Division by 0 on: 'csc({$func}) = 1/sin({$func})' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO); } $ans = 1/$tmp; break; case "cot": $tmp = tan($func); if($tmp == 0) { throw new Exception("Division by 0 on: 'cot({$func}) = 1/tan({$func})' in {$this->inFix}", NF_EOS_Parser::E_DIV_ZERO); } $ans = 1/$tmp; break; case "abs": $ans = abs($func); break; case "log": $ans = log($func); if(is_nan($ans) || is_infinite($ans)) { throw new Exception("Result of 'log({$func}) = {$ans}' is either infinite or a non-number in {$this->inFix}", NF_EOS_Parser::E_NAN); } break; case "log10": $ans = log10($func); if(is_nan($ans) || is_infinite($ans)) { throw new Exception("Result of 'log10({$func}) = {$ans}' is either infinite or a non-number in {$this->inFix}", NF_EOS_Parser::E_NAN); } break; case "sqrt": if($func < 0) { throw new Exception("Result of 'sqrt({$func}) = i. We can't handle imaginary numbers", NF_EOS_Parser::E_NAN); } $ans = sqrt($func); break; default: $ans = 0; break; } $infix = str_replace($match[0], "({$ans})", $infix); } $infix = preg_replace('/[$&]/', "", $infix); //Find all the variables that were passed and replaces them while((preg_match('/([^a-zA-Z]){0,1}([a-zA-Z]+)([^a-zA-Z]){0,1}/', $infix, $match)) != 0) { //remove notices by defining if undefined. if(!isset($match[3])) { $match[3] = ""; } if(NF_EOS_Parser::$debug) fwrite($hand, "{$match[1]} || {$match[3]}\n"); // Ensure that the variable has an operator or something of that sort in front and back - if it doesn't, add an implied '*' if((!in_array($match[1], array_merge($this->ST, $this->ST1, $this->ST2, $this->SEP['open'])) && $match[1] != "") || is_numeric($match[1])) //$this->SEP['close'] removed $front = "*"; else $front = ""; if((!in_array($match[3], array_merge($this->ST, $this->ST1, $this->ST2, $this->SEP['close'])) && $match[3] != "") || is_numeric($match[3])) //$this->SEP['open'] removed $back = "*"; else $back = ""; //Make sure that the variable does have a replacement //First check for pi and e variables that wll automagically be replaced if(in_array(strtolower($match[2]), array('pi', 'e'))) { $t = (strtolower($match[2])=='pi') ? pi() : exp(1); $infix = str_replace($match[0], $match[1] . $front. $t. $back . $match[3], $infix); } elseif(!isset($vArray[$match[2]]) && (!is_array($vArray != "") && !is_numeric($vArray) && 0 !== $vArray)) { throw new Exception("Variable replacement does not exist for '". substr($match[0], 1, 1). $match[2] ."' in {$this->inFix}", NF_EOS_Parser::E_NO_VAR); } elseif(!isset($vArray[$match[2]]) && (!is_array($vArray != "") && is_numeric($vArray))) { $infix = str_replace($match[0], $match[1] . $front. $vArray. $back . $match[3], $infix); } elseif(isset($vArray[$match[2]])) { $infix = str_replace($match[0], $match[1] . $front. $vArray[$match[2]]. $back . $match[3], $infix); } } if(NF_EOS_Parser::$debug) fclose($hand); return $this->solvePF($this->in2post($infix)); } //end function solveIF /** * Solve factorial (!) * * Will take any real positive number and solve for it's factorial. Eg. * `5!` will become `1*2*3*4*5` = `120` For integers * and * 5.2! will become gamma(6.2) for non-integers * DONE: * Solve for non-integer factorials 2015/07/02 * * @param Float $num Non-negative real number to get factorial of * @throws Exception if number is at or less than 0 * @return Float Solved factorial */ protected function factorial($num) { if($num < 0) { throw new Exception("Factorial Error: Factorials don't exist for numbers < 0", NF_EOS_Parser::E_NAN); } //A non-integer! Gamma that sucker up! if(intval($num) != $num) { return $this->gamma($num + 1); } $tot = 1; for($i=1;$i<=$num;$i++) { $tot *= $i; } return $tot; } //end function factorial /** * Gamma Function * * Because we can. This function exists as a catch-all for different * numerical approx. of gamma if I decide to add any past Lanczos'. * This method is public because a function doesn't currently exist * within this parser to use it. That will change in the future. * * @param $z Number to compute gamma from * @return Float The gamma (hopefully, I'll test it after writing the code) */ public function gamma($z) { return $this->laGamma($z); } /** * Lanczos Approximation * * The Lanczos Approximation method of finding gamma values * * @link http://www.rskey.org/CMS/index.php/the-library/11 * @link http://algolist.manual.ru/maths/count_fast/gamma_function.php * @link https://en.wikipedia.org/wiki/Lanczos_approximation * @param float $z Number to obtain the gamma of * @return float Gamma of inputted number * @throws Exception if Number is less than or equal to 0 */ protected function laGamma($z) { //check validity of $z, throw error if not a valid number to be used with gamma if($z <= 0) { throw new Exception("Gamma cannot be calculated on numbers less than or equal to 0", NF_EOS_Parser::E_NAN); } // Set up coefficients $p = array( 0 => 1.000000000190015, 1 => 76.18009172947146, 2 => -86.50532032941677, 3 => 24.01409824083091, 4 => -1.231739572450155, 5 => 1.208650973866179E-3, 6 => -5.395239384953E-6 ); //formula: // ((sqrt(2pi)/z)(p[0]+sum(p[n]/(z+n), 1, 6)))(z+5.5)^(z+0.5)*e^(-(z+5.5)) // Break it down now... $g1 = sqrt(2*pi())/$z; //Next comes our summation $g2 =0; for($n=1;$n<=6;$n++) { $g2 += $p[$n]/($z+$n); } // Don't forget to add p[0] to it... $g2 += $p[0]; $g3 = pow($z+5.5, $z + .5); $g4 = exp(-($z+5.5)); //now just multiply them all together $gamma = $g1 * $g2 * $g3 * $g4; return $gamma; } } //end class 'Parser'

خطوة

من يقود مستقبل الذكاء الاصطناعي ChatGPT أم Deep Seek

مايو 18, 2025

3٬705 2 دقائق

‏كتبت شروق عارف
مع التطور الهائل في تقنيات الذكاء الاصطناعي أصبح هذا المجال ساحة تنافس شرسة خاصة بين الولايات المتحدة والصين لم تعد الدول تنظر إلى الذكاء الاصطناعي كأداة مساعدة فقط بل كقوة ‏عظيمة تحدد ملامح المستقبل وتمنح الأفضلية لمن يتفوق فيه على الساحة العالمية فما هي أبرز التطورات الأخيرة في مجال الذكاء الاصطناعي بين الولايات المتحدة والصين؟
في البداية، تصدرت الولايات المتحدة المشهد عبر نظام ChatGPT الذي طورته شركة OpenAI والذي أحدث ثورة في عالم الذكاء الاصطناعي التفاعلي. لكن الصين لم تلبث أن ردت بقوة من خلال نظام DeepSeek V3، الذي سرعان ما تصدر قائمة التنزيلات في الولايات المتحدة، متفوق على ChatGPT في بعض الجوانب مما أعاد إشعال المنافسة مجددا

Deep Seek منافس قوي لكنه ما زال تحت التجربة
يرى الدكتور إبراهيم عبد الله أستاذ تكنولوجيا المعلومات في المعاهد العليا للدراسات النوعية إن منصة DeepSeek تقدم خدمات قوية ومجانية قد تدفع البعض لتفضيلها على ChatGPT لكنها لا تزال تحت التجربة، ولا يمكن الاعتماد عليها كليًا في الوقت الحالي وأضاف أن دعم البرمجيات مفتوحة المصدر يمثل فرصة مهمة للتطوير والابتكار لكن استخدامها يجب أن يتم بحذر وذلك لتجنب أي تهديدات أمنية محتمل
‏أبرز الاختلافات بين ChatGPT وDeep Seek
‏ بحسب ما ورد في موقع click up وما ذكره ماركو ممدوح يعتبر Deep Seek نموذج ذكي من تطوير شركة صينية الذي أسسها رجل الأعمال لينج وينفينج ويعتمد على أكثر من 37 مليار معلومة وذلك يمنحه دقة عالية في الإجابة يتميز بأنه مجاني بالكامل ويدعم أكثر من 95 لغة من بينها العربية حيث يظهر اداء قوي قد يتفوق علي ChatGPT في بعض الأحيان
أما ChatGPT فهو من تطوير شركة OpenAI الأمريكية وانطلق في نوفمبر 2022 بدعم من شركة مايكروسوفت يشتهر بقدرته على التفاعل بلغة طبيعي وتميزه في الكتابة الإبداعية وصناعة الصور وتحويل النصوص إلى صوت. ومع ذلك فإن نسخته الأقوى GPT-4 تتطلب اشتراك مدفوع
أيهما يتفوق
رغم أن ChatGPT يتميز بالتفاعل الواسع والإبداع في اللغة إلا أن Deep Seek يتفوق عليه في تحليل البيانات، التفكير المنطقي والرياضيات بالإضافة إلى دعمه القوي للبرمجيات مفتوحة المصدر كما يمنح المستخدمين تحكم كامل في بياناتهم في مقابل بيئة مغلقة نسبيا في ChatGPT
لكن Deep Seek لم يسلم من الانتقادات خاصة بعد كشف تقارير عن ثغرات أمنية خطيرة، منها تعطيل أنظمة تشفير على أجهزة iPhone واستخدام تقنيات قديمة قالت هيئة حماية البيانات الإيطالية أنها حظرت نموذج DeepSeek من استخدامه كما حذّرت دول مثل تايوان من استخدامه خوفًا من تسريب بيانات حساسة في المقابل يواجه ChatGPT تحديات تتعلق بالدقة والتحيز السياسي أحيانا وعدم تقديمه دائما معلومات مكتملة أو صحيحة بالإضافة إلى إمكانية تجاوزه لقيود الأمان وذلك من خلال إعادة صياغة الأسئلة

Deep Seek ينافس بقوة و لكن ChatGPTيتفوق في الأداء
من جانبه يرى عمر عاطف خبير التكنولوجيا أن الذكاء الاصطناعي أصبح منافس حقيقي في عدة مجالات سواء في كتابة المحتوى أو تحليل البيانات أو حتى التعليم، ومع ظهور أدوات مثل DeepSeek أصبح المستخدم أمام خيارات متعددة تتيح له تجربة تقنيات متقدمة بشكل مجاني وأشار إلى أن رغم قوة هذه الأدوات فإن ChatGPT لا يزال متفوق من حيث الأداء ودقة النتائج خاصة في النسخ المدفوعة التي توفر ميزات أوسع لكن المنافسة تدفع الجميع للتطوير باستمرار

ولكن يبقى الرهان الحقيقي بين عمالقة الذكاء الاصطناعي على من يستطيع تلبية احتياجات المستخدمين بذكاء وأمان وأفضل الإمكانيات في ان واحد

مايو 18, 2025

3٬705 2 دقائق