Mathematische Funktionen

    Inhaltsverzeichnis

    • abs — Absolutwert bzw. Betrag
    • acos — Arkuskosinus
    • acosh — Areakosinus hyperbolikus
    • asin — Arkussinus
    • asinh — Areasinus hyperbolikus
    • atan — Arkustangens
    • atan2 — Arkustangens-Variante mit zwei Parametern
    • atanh — Areatangens hyperbolikus
    • base_convert — Wandelt einen numerischen Wert zwischen verschiedenen Zahlensystemen um
    • bindec — Wandelt von binär zu dezimal um
    • ceil — Rundet Brüche auf
    • cos — Kosinus
    • cosh — Kosinus hyperbolikus
    • decbin — Wandelt von dezimal zu binär um
    • dechex — Wandelt von dezimal zu hexadezimal um
    • decoct — Wandelt von dezimal zu oktal um
    • deg2rad — Rechnet einen Winkel von Grad in Bogenmaß um
    • exp — Berechnet den Exponenten von e
    • expm1 — Berechnet exp(Zahl) - 1 mit guter Genauigkeit, auch wenn Zahl nahe bei Null liegt
    • fdiv — Dividiert zwei Zahlen gemäß IEEE 754
    • floor — Rundet Brüche ab
    • fmod — Rest einer Gleitkommadivision (Modulus)
    • fpow — Raise one number to the power of another, according to IEEE 754
    • hexdec — Wandelt von hexadezimal zu dezimal um
    • hypot — Berechnet die Länge der Hypotenuse eines rechtwinkligen Dreiecks
    • intdiv — Integer-Division
    • is_finite — Prüft, ob eine Gleitkommazahl endlich ist
    • is_infinite — Prüft, ob eine Gleitkommazahl unendlich ist
    • is_nan — Prüft, ob eine Gleitkommazahl NAN ist
    • log — Natürlicher Logarithmus
    • log10 — Dekadischer Logarithmus (Logarithmus zur Basis 10)
    • log1p — Berechnet log(1 + Zahl) mit guter Genauigkeit, auch wenn Zahl nahe bei Null liegt
    • max — Bestimmt den Maximalwert
    • min — Bestimmt den Minimalwert
    • octdec — Wandelt von oktal zu dezimal um
    • pi — Liefert den Wert von Pi
    • pow — Potenzfunktion
    • rad2deg — Rechnet einen Winkel vom Bogenmaß in Grad um
    • round — Rundet einen Gleitkommawert
    • sin — Sinus
    • sinh — Sinus hyperbolikus
    • sqrt — Quadratwurzel
    • tan — Tangens
    • tanh — Tangens hyperbolikus

    Improve This Page

    Learn How To Improve This Page • Submit a Pull Request • Report a Bug
    ＋add a note

    User Contributed Notes 26 notes

    up
    11
    pat.mat AT sympatico DOT com
    20 years ago
    For people interest in Differential Equations, I've done a function that receive a string like: x^2+x^3 and put it in
    2x+3x^2 witch is the differantial of the previous equation.

    In the code there is one thing missing: the $string{$i} is often going outOfBound (Uninitialized string offset: 6 in...)
    if your error setting is set a little too high... I just dont know how to fix this.

    So there is the code for differential equation with (+ and -) only:

    <?
    function differentiel($equa)
    {
    $equa = strtolower($equa);
    echo "Equation de depart: ".$equa."<br>";
    $final = "";

    for($i = 0; $i < strlen($equa); $i++)
    {
    //Make a new string from the receive $equa
    if($equa{$i} == "x" && $equa{$i+1} == "^")
    {
    $final .= $equa{$i+2};
    $final .= "x^";
    $final .= $equa{$i+2}-1;
    }
    elseif($equa{$i} == "+" || $equa{$i} == "-")
    {
    $final .= $equa{$i};
    }
    elseif(is_numeric($equa{$i}) && $i == 0)
    {
    //gerer parenthese et autre terme generaux + gerer ^apres: 2^2
    $final .= $equa{$i}."*";
    }
    elseif(is_numeric($equa{$i}) && $i > 0 && $equa{$i-1} != "^")
    {
    //gerer ^apres: 2^2
    $final .= $equa{$i}."*";
    }
    elseif($equa{$i} == "^")
    {
    continue;
    }
    elseif(is_numeric($equa{$i}) && $equa{$i-1} == "^")
    {
    continue;
    }
    else
    {
    if($equa{$i} == "x")
    {
    $final .= 1;
    }
    else
    {
    $final .= $equa{$i};
    }
    }
    }
    //
    //Manage multiplication add in the previous string $final
    //
    $finalMul = "";
    for($i = 0; $i < strlen($final); $i++)
    {
    if(is_numeric($final{$i}) && $final{$i+1} == "*" && is_numeric($final{$i+2}))
    {
    $finalMul .= $final{$i}*$final{$i+2};
    }
    elseif($final{$i} == "*")
    {
    continue;
    }
    elseif(is_numeric($final{$i}) && $final{$i+1} != "*" && $final{$i-1} == "*")
    {
    continue;
    }
    else
    {
    $finalMul .= $final{$i};
    }
    }
    echo "equa final: ".$finalMul;
    }
    ?>

    I know this is not optimal but i've done this quick :)
    If you guys have any comment just email me.
    I also want to do this fonction In C to add to phpCore maybe soon...
    Patoff
    up
    5
    daniel at g-loc dot org
    18 years ago
    If you're an aviator and needs to calculate windcorrection angles and groundspeed (e.g. during flightplanning) this can be very useful.

    $windcorrection = rad2deg(asin((($windspeed * (sin(deg2rad($tt - ($winddirection-180))))/$tas))));
    $groundspeed = $tas*cos(deg2rad($windcorrection)) + $windspeed*cos(deg2rad($tt-($winddirection-180)));

    You can probably write these lines more beautiful, but they work!
    up
    3
    lummox
    16 years ago
    Wouldn't the following function do the same but a lot easier than the one in the comment before?

    function trimInteger($targetNumber,$newLength) {
    return $targetNumber%pow(10,$newLength);
    }
    up
    1
    info at gavinvincent dot co dot uk
    20 years ago
    If you need to deal with polar co-ordinates for somereason you will need to convert to and from x,y for input and output in most situations: here are some functions to convert cartesian to polar and polar to cartesian
    <?
    //returns array of r, theta in the range of 0-2*pi (in radians)
    function rect2polar($x,$y)
    {
    if(is_numeric($x)&&is_numeric($y))
    {
    $r=sqrt(pow($x,2)+pow($y,2));
    if($x==0)
    {
    if($y>0) $theta=pi()/2;
    else $theta=3*pi()/2;
    }
    else if($x<0) $theta=atan($y/$x)+pi();
    else if($y<0) $theta=atan($y/$x)+2*pi();
    else $theta=atan($y/$x);
    $polar=array("r"=>$r,"theta"=>$theta);
    return $polar;
    }
    else return false;
    }

    //r must be in radians, returns array of x,y
    function polar2rect($r,$theta)
    {
    if(is_numeric($r)&&is_numeric($theta))
    {
    $x=$r*cos($theta);
    $y=$r*sin($theta);
    $rect=array("x"=>$x,"y"=>$y);
    }
    else
    {
    return false;
    }
    }
    ?>
    up
    0
    Anonymous
    6 years ago
    And the reason I needed a Factorial function is because I there were no nPr or nCr functions native to PHP, either.

    function n_pick_r($n,$r){$n=(int)$n; $r=(int)$r;return (fact($n)/fact($n-$r));}
    function n_choose_r($n,$r){$n=(int)$n; $r=(int)$r;return (n_pick_r($n,$r)/fact($r));}

    Hope that helps someone!
    exmple:https://vb.3dlat.com/
    up
    -1
    php at keith tyler dot com
    14 years ago
    Another ordinal method, which does not involve utilizing date functions:

    <?php
    sprintf    ( "%d%s", $t, array_pop( array_slice( array_merge( array( "th","st","nd","rd"), array_fill( 4,6,"th")), $t%10, 1)));'
    ?>
    up
    -1
    Mike
    16 years ago
    //had a mistake in last post, heres the corrected version

    /*
    Just a simple function to trim digits from the left side of an integer. TRIM DOWN TO 4-> (ie. 987654 => 7654)
    */

    function trimInteger($targetNumber,$newLength) {

    $digits = pow(10,$newLength);

    $s = ($targetNumber/ $digits); //make the last X digits the decimal part

    $t = floor($targetNumber / $digits); //drop the last X digits (the decimal part)

    $h = $s - $t; //remove all but the decimal part

    $newInteger = ($h*$digits); //make the everything after the decimal point the new number

    return $newInteger;
    }
    up
    -1
    AsherMaximum gmail
    13 years ago
    Here's a simple way way to convert a number to an ordinal number I created:

    $i == the number to convert. Put this inside a for loop if you need to populate an array.

    <?php
    // change increment variable to ordinal number.
    $n1 = $i % 100; //first remove all but the last two digits

    $n2 = ($n1 < 20 ? $1 : $i % 10; //remove all but last digit unless the number is in the teens, which all should be 'th'

    //$n is now used to determine the suffix.
    $ord = ($n2==1 ? $i.'st' : ( ($n2==2 ? $i.'nd' : ($n2==3 ? $i.'rd' : $i.'th') ) ) )
    ?>
    up
    -1
    florian at shellfire dot de
    20 years ago
    Please note that shorter is not always better
    (meaning that really short faculty implementation above).

    In my opinion, a clearer way to code this is, including a check
    for negative or non-integer values.

    In order to calculate the faculty of a positive integer,
    an iterative way (which might be harder to understand)
    is usually a bit faster, but I am using it only for small
    values so it is not really important to me:

    <?php

    // Calculate the Faculty of a positive int-value
    function iFaculty($a_iFac)
    {
    if (    $a_iFac > 0)
    {
    return     $a_iFac * $this->iFaculty($a_iFac - 1);
    }
    elseif (    $a_iFac == 0)
    {
    return     1;
    }
    else
    {
    return     0; // Wrong argument!
    }
    }
    ?>

    I've also written another function to calculate the
    binomial coefficient of 2 values, I didn't find it anywhere yet so I hope it might help someone (works fine with the above stated faculty-function and ready to be used inside of your own classes!)

    <?php

    // calculates the binomial coefficient "n over k" of 2 positive int values
    // for n >= k
    function iBinCoeff($a_iN, $a_iK)
    {
    // the binomial coefficient is defined as n! / [ (n-k)! * k! ]
    return $this->iFaculty($a_iN) / ($this->iFaculty($a_iN - $a_iK) * $this->iFaculty($a_iK));
    }

    ?>
    up
    -1
    jordanolsommer at imap dot cc
    21 years ago
    The reason the bitwise AND ("&") operator works to determine whether a number is odd or even is because odd numbers expressed in binary always have the rightmost (2^0) bit = 1 and even numbers always have the 2^0 bit = 0.

    So if you do a " 1 & $num", it will return zero if the number is even (since xxxxxxx0 [the even number in binary] and 00000001 [the 1]) don't share any bits, and will return 1 if the number is odd (xxxxxx1 and 000001).

    a clever way of doing things, but $num % 2 would work as well i think :).
    up
    -2
    capripot at gmail dot com
    12 years ago
    Another simpler function to check a number with the luhn algorithm :

    <?php
    function luhn($num){
    if(!    $num)
    return     false;
    $num = array_reverse(str_split($num));
    $add = 0;
    foreach(    $num as $k => $v){
    if(    $k%2)
    $v = $v*2;
    $add += ($v >= 10 ? $v - 9 : $v);
    }
    return (    $add%10 == 0);
    }
    ?>

    Don't know if foreach and arrays operations are faster than while and substr, but I feel it clearer.
    up
    -2
    edward at edwardsun dot com
    18 years ago
    well just a note.. maybe i'm a bit stupid.. but remember to use pow() rather than the "^" sign for exponents.. as it took me 5 minutes to figure out why it wasn't working.
    up
    -2
    moikboy (nospam!) moikboy (nospam!) hu
    18 years ago
    I think, this is the optimal code for calculating factorials:

    <?php
    function fact($int){
    if(    $int<2)return 1;
    for(    $f=2;$int-1>1;$f*=$int--);
    return     $f;
    };
    ?>

    And another one for calculating the $int-th Fibonacci-number:

    <?php
    function fib($int){
    static     $fibTable=array();
    return empty(    $fibTable[$int])?$fibTable[$int] = $int>1?fib($int-2)+fib($int-1):1:$fibTable[$int];
    };
    ?>
    up
    -2
    Chronial "at" cyberpunkuniverse.de
    20 years ago
    Here are are a nPr and a nPc function
    (had to define NaN - don't know, how to this the "rigth" way)

    <?php
    define     (NaN,acos(1.01));

    function     nCr($n,$r){
    if (    $r > $n)
    return     NaN;
    if ((    $n-$r) < $r)
    return     nCr($n,($n-$r));
    $return = 1;
    for (    $i=0;$i < $r;$i++){
    $return *= ($n-$i)/($i+1);
    }
    return     $return;
    }

    function     nPr($n,$r){
    if (    $r > $n)
    return     NaN;
    if (    $r)
    return     $n*(nPr($n-1,$r-1));
    else
    return     1;
    }
    ?>
    up
    -3
    jl85 at yahoo dot com
    21 years ago
    Theres another faster way of doing even/odd number checking by using bitwise operators. Don't ask me how it works, I just found this out by experimenting with it (could the editor possibly explain?)

    if ((1&$num)) {
    echo "$num is odd";
    }

    if (!(1&$num)) {
    echo "$num is even";
    }

    How it works is (1&$num) returns a 1 for odd numbers and returns 0 when it's an even number.
    up
    -4
    help at gjbdesign dot com
    20 years ago
    Occasionally a user must enter a number in a form. This function converts fractions to decimals and leaves decimals untouched. Of course, you may wish to round the final output, but that is not included here.

    <?php
    /*Some example values of $q
    $q = "2.5";
    $q = "2 1/2";
    $q = "5/2";
    */
    function Deci_Con($q){
    //check for a space, signifying a whole number with a fraction
    if(strstr($q, ' ')){
    $wa = strrev($q);
    $wb = strrev(strstr($wa, ' '));
    $whole = true;//this is a whole number
    }
    //now check the fraction part
    if(strstr($q, '/')){
    if(    $whole==true){//if whole number, then remove the whole number and space from the calculations
    $q = strstr($q, ' ');
    }
    $b = str_replace("/","",strstr($q, '/'));//this is the divisor
    //isolate the numerator
    $c = strrev($q);
    $d = strstr($c, '/');
    $e = strrev($d);
    $a = str_replace("/","",$e);//the pre-final numerator
    if($whole==true){//add the whole number to the calculations
    $a = $a+($wb*$b);//new numerator is whole number multiplied by denominator plus original numerator
    }
    $q = $a/$b;//this is now your decimal
    return $q;
    }else{
    return     $q;//not a fraction, just return the decimal
    }
    }    ?>
    up
    -3
    tembenite at gmail dot com
    18 years ago
    To add to what Cornelius had, I have written a function that will take an array of numbers and return the least common multiple of them:

    function lcm_arr($items){
    //Input: An Array of numbers
    //Output: The LCM of the numbers
    while(2 <= count($items)){
    array_push($items, lcm(array_shift($items), array_shift($items)));
    }
    return reset($items);
    }

    //His Code below with $'s added for vars

    function gcd($n, $m) {
    $n=abs($n); $m=abs($m);
    if ($n==0 and $m==0)
    return 1; //avoid infinite recursion
    if ($n==$m and $n>=1)
    return $n;
    return $m<$n?gcd($n-$m,$n):gcd($n,$m-$n);
    }

    function lcm($n, $m) {
    return $m * ($n/gcd($n,$m));
    }
    up
    -4
    webkid%webkid.com
    22 years ago
    And the reason I needed a Factorial function is because I there were no nPr or nCr functions native to PHP, either.

    function n_pick_r($n,$r){$n=(int)$n; $r=(int)$r;return (fact($n)/fact($n-$r));}
    function n_choose_r($n,$r){$n=(int)$n; $r=(int)$r;return (n_pick_r($n,$r)/fact($r));}

    Hope that helps someone!
    up
    -4
    jerry dot wilborn at fast dot net
    21 years ago
    Here is how to calculate standard deviation in PHP where $samples is an array of incrementing numeric keys and the values are your samples:

    $sample_count = count($samples);

    for ($current_sample = 0; $sample_count > $current_sample; ++$current_sample) $sample_square[$current_sample] = pow($samples[$current_sample], 2);

    $standard_deviation = sqrt(array_sum($sample_square) / $sample_count - pow((array_sum($samples) / $sample_count), 2));
    up
    -3
    patience at worldonline dot nl
    22 years ago
    The example for Factorials given above is wrong. Here a correct version, so that you do not have to reinvent the wheel again...

    <?php
    function mathFact( $s )
    {
    $r = (int) $s;

    if (     $r < 2 )
    $r = 1;
    else {
    for (     $i = $r-1; $i > 1; $i-- )
    $r = $r * $i;
    }

    return(     $r );
    }
    ?>
    up
    -3
    barry at megaspace dot com
    17 years ago
    Here's a least common denominator (lcd) function:

    $array = array(3,4,6,8,18,2);

    function lcd($array,$x) {

    $mod_sum = 0;

    for($int=1;$int < count($array);$int++) {
    $modulus[$int] = ($array[0]*$x) % ($array[$int]);
    $mod_sum = $mod_sum + $modulus[$int];
    }

    if (!$mod_sum) {
    echo "LCD: ".($array[0]*$x)."\n";
    }

    else {
    lcd($array,$x+1);
    }

    }

    lcd($array,1);
    up
    -3
    jl85 at yahoo dot com
    21 years ago
    Here's yet another greatest common denominator (gcd) function, a reeeeally small one.

    function gcd($n,$m){
    if(!$m)return$n;return gcd($m,$n%$m);
    }

    It works by recursion. Not really sure about it's speed, but it's really small! This won't work on floating point numbers accurately though. If you want a floating point one, you need to have at least PHP 4, and the code would be

    function gcd($n,$m){
    if(!$m)return$n;return gcd($m,fmod($n,$m));
    }
    up
    -3
    ian at mp3 dot com
    23 years ago
    for those looking for a credit card verification function i wrote a simple LUHN Formula algorithm:

    <?php
    $valid     = 1;

    $numOfDigits = 0 - strlen($ccNumber);

    $i = -1;
    while (    $i>=$numOfDigits){
    if ((    $i % 2) == 0){
    $double = 2*(substr($ccNumber, $i, 1));
    $total += substr($double,0,1);
    if (    strlen($double > 1)){
    $total += substr($double,1,1);
    }
    } else {
    $total += substr($ccNumber, $i, 1);
    }
    $i--;
    }

    if ((    $total % 10) != 0){
    $valid = 0;
    }
    ?>
    up
    -4
    fabien_mornand at yahoo dot fr
    21 years ago
    here is an algorithm to calculate gcd of a number. This is Euclid algorithm i was studying in Maths. I've converted it in php for the fun.

    <?php
    if($a && $b)
    {     $ax=$a; $bx=$b;
    $r=fmod($a,$b);
    if(!    $r){$rx=$r;}
    while(    $r){
    $rx=$r;
    $a=$b;
    $b=$r;
    $r=fmod($a,$b);
    }
    }
    echo     'PGCD ('.$ax.' , '.$bx.' ) = '.$rx;
    ?>
    up
    -4
    Aiden880
    9 years ago
    Lowest Common Denominator:
    function lcd($num, $start) {
    while($num % $start != 0) {
    $start++;
    }
    return $start;
    }
    up
    -4
    Florian
    18 years ago
    A function that simulates the sum operator. (http://en.wikipedia.org/wiki/Sum). Be careful with the expression because it may cause a security hole; note the single quotes to don't parse the "$".
    <?php
    # @param string $expr expression to evaluate (for example (2*$x)^2+1)
    # @param string $var dummy variable (for example "x")
    # @param integer $start
    # @param integer $end
    # @param integer $step

    function sum($expr,$var,$start,$end,$step = 1) {
    $expr = str_replace(';','',$expr);
    $var = str_replace('$','',$var);
    $start = (int)$start; $end = (int)$end; $step = (int)$step; $sum = 0;

    for (    $i = $start; $i <= $end; $i = $i + $step) {
    $_expr = str_replace('$'.$var,$i,$expr);
    $_eval = '$_result = '.$_expr.'; return $_result;';
    $_result = eval($_eval);
    if(    $result === FALSE) return "SYNTAX ERROR : $expr";
    $sum += $_result;
    }
    return (int)    $sum;
    }
    ?>
    ＋add a note
    To Top