<?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'

معرفة

طبيبك في جيبك لكن هل يشعر بنبضك

مايو 18, 2025

4٬581 2 دقائق

كتبت شروق عارف مع التطور السريع للتكنولوجيا وتزايد اعتمدنا على الإنترنت في مختلف المجالات برز الطب عن بعد كأحد أهم التحولات في مجال الرعاية الصحية خصوصا بعد جائحة كورونا التي فرضت واقع جديد يحتم علينا العزلة مما دفعنا للبحث عن بدائل أمنة وفعالة للتشخيص والعلاج دون الحاجة لزيارة الطبيب ورغم ما يقدمه الطب عن بعد من من عدة حلول أهمها تقليل النفقات والحد من الازدحام ولكن مع هذا التطور بدأت تظهر تساؤلات مهمة أبرزهم هل يمكن الاعتماد عليه كبديل كامل للفحص التقليدي؟ وهل يضمن دقة التشخيص وكفاءة العلاج؟ أم أنه يظل أداة مساعدة مهمة لكنها لا تغني عن التواصل المباشر مع الطبيب في عيادته؟

الطب عن بعد دعم مكمل لا بديل
‏ صرح أحد الأطباء بأن الطب عن بعد يمكن أن يكون فعالا جدا في بعض الحالات مثل متابعة الأمراض المزمنة أو إعطاء نصائح أولية لكنه لا يمكن أن يحل محل الفحص وتابع حديثه قائلا هناك تفاصيل لا يمكن معرفتها من خلال شاشة الهاتف مثل نبض القلب أو ملامح التعب أو بعض التغيرات وهذه أمور لا تظهر عبر الكاميرا كما وأوضح أن الطب عن بعد ساهم في تقليل الضغط على المستشفيات وساعد في تقليل العدوى لكنه لا يمكن أن يعتمد عليه بشكل أساسي
الأسنان لا تفحص عن بعد
من جانبه صرح أحد الأطباء في جراحة الفم والأسنان أن الطب عن بعد لا يصلح في تخصص مثل الأسنان وذلك لاعتمادها الكبير على الفحص اليدوي والرؤية الدقيقة للحالة وأضاف كيف يمكنني أن اشخص التهاب في اللثة أو كسر في السن عبر شاشة هناك تفاصيل لا ترى إلا بالفحص المباشر سواء من خلال الأشعة أو أدوات الكشف الدقيقة وتابع قائلا الطب عن بعد قد يكون مفيد فقط في الاستشارة الأولية أو متابعة بعض الحالات البسيطة بعد العلاج لكن لا يمكن الاعتماد عليه في تشخيص أو وضع خطة علاجية دون معاينة فعلية

وأشار محذرا أن الطب عن بعد في مجال طب الأسنان قد يكون خطر وذلك لأن أي خطأ في التشخيص قد يؤدي إلى مضاعفات صحية للمريض موكدا أن التقنية تظل أداة مساعدة وليست بديلا عن الطبيب
ومن جانبه يؤكد أن التواصل المباشر بين الطبيب والمريض هو عنصر أساسي في طب الأسنان موضح أن بعض الأعراض قد لا تفهم بشكل دقيق إلا من خلال تفاعل مباشر وتابع حديثه قائلا حتى مع توفر صور أو مقاطع فيديو يظل هناك فارق كبير بين ما يرى عبر الشاشة وما يمكن للطبيب ملاحظته أثناء الكشف

ويبقى الطب عن بعد أداة فعالة في تحسين الوصول إلى ‏خدمات الرعاية الصحية لكنه في النهاية يظل وسيلة مساعدة لا تغني عن دور الطبيب والفحص المباشرة

مايو 18, 2025

4٬581 2 دقائق