PHP: Mathematical Functions

User Contributed Notes
Mathematical Functions

eric at woolhiser dot com
10-Mar-2005 11:41


For all you guys writing mortgage calculators out there:



<?php



function payment($apr,$n,$pv,$fv=0.0,$prec=2){

    /* Calculates the monthly payment rouned to the nearest penny

    ** $apr = the annual percentage rate of the loan.

    ** $n   = number of monthly payments (360 for a 30year loan)

    ** $pv    = present value or principal of the loan

    ** $fv  = future value of the loan

    ** $prec = the precision you wish rounded to

    */

    /****************************************\

    ** No Warranty is expressed or implied. **

    *****************************************/

    

    if ($apr !=0) {

        $alpha = 1/(1+$apr/12);

        $retval =  round($pv * (1 - $alpha) / $alpha / 

        (1 - pow($alpha,$n)),$prec) ;

    } else {

        $retval = round($pv / $n, $prec);

    }

    return($retval);



}

?>

tmpa at yahoo dot com
19-Feb-2005 03:42


while joogat's one line function is short, it is probably better to calculate factorial iteratively instead of recursively. keep in mind if you want large factorials, you'll need to use some sort of arbitrary precision integer or perhaps the BCMath functions. then again, unless you're trying to do large numbers (170! is the highest that you can do that does not return infinity) you probably won't notice any time difference.

<?php

function factorial($in) {

    // 0! = 1! = 1

    $out = 1;



    // Only if $in is >= 2

    for ($i = 2; $i <= $in; $i++) {

        $out *= $i;

    }



    return $out;

}

?>

joogat at hotmail dot com
04-Feb-2005 09:35


factorial:

function f($_){return $_?$_*f(--$_):1;}

thearbitcouncil at gmail dot com
06-Jan-2005 05:32


Two functions I didn't find elsewhere... one to compute mean of an array of numbers, and another to computer variance of a sample of numbers. Both take an array of numbers as arguments. Not much error checking, or optimization...



(note: variance function uses the average function...)



<?php



function average($arr)

{

    if (!count($arr)) return 0;



    $sum = 0;

    for ($i = 0; $i < count($arr); $i++)

    {

        $sum += $arr[$i];

    }



    return $sum / count($arr);

}



function variance($arr)

{

    if (!count($arr)) return 0;



    $mean = average($arr);



    $sos = 0;    // Sum of squares

    for ($i = 0; $i < count($arr); $i++)

    {

        $sos += ($arr[$i] - $mean) * ($arr[$i] - $mean);

    }



    return $sos / (count($arr)-1);  // denominator = n-1; i.e. estimating based on sample 

                                    // n-1 is also what MS Excel takes by default in the

                                    // VAR function

}



echo variance(array(4,6,23,15,18)); // echoes 64.7...correct value :)



?>

info at gavinvincent dot co dot uk
17-Nov-2004 07:34


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;

 }

}

?>

help at gjbdesign dot com
25-Sep-2004 12:05


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

    }

}?>

donnieb819 at hotmail dot NOSPAM dot com
16-Sep-2004 08:58


Method to convert an arbitrary decimal number to its most reduced fraction form (so a string is returned, this method would probably be used for output formatting purposes.)  There were other methods similar to this one on the page, but none did quite what I wanted.  It's maybe not the most elegant code, but it gets the job done.  Hope this helps someone.  An iterative form of Euclid's algorithm is used to find the GCD.



<?php

function dec2frac( $decimal )

{

  $decimal = (string)$decimal;

  $num = '';

  $den = 1;

  $dec = false;

  

  // find least reduced fractional form of number

  for( $i = 0, $ix = strlen( $decimal ); $i < $ix; $i++ )

  {

    // build the denominator as we 'shift' the decimal to the right

    if( $dec ) $den *= 10;

    

    // find the decimal place/ build the numberator

    if( $decimal{$i} == '.' ) $dec = true;

    else $num .= $decimal{$i};

  }

  $num = (int)$num;

    

  // whole number, just return it

  if( $den == 1 ) return $num;

    

  $num2 = $num;

  $den2 = $den;

  $rem  = 1;

  // Euclid's Algorithm (to find the gcd)

  while( $num2 % $den2 ) {

    $rem = $num2 % $den2;

    $num2 = $den2;

    $den2 = $rem;

  }

  if( $den2 != $den ) $rem = $den2;

    

  // now $rem holds the gcd of the numerator and denominator of our fraction

  return ($num / $rem ) . "/" . ($den / $rem);

}

?>



Examples:

echo dec2frac( 10 );

echo dec2frac( .5 );

echo dec2frac( 5.25 );

echo dec2frac( .333333333 );



yields:

10

1/2

21/4

333333333/1000000000

pat.mat AT sympatico DOT com
08-Jun-2004 10:36


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

moc.erawtfostym@evad
26-May-2004 10:04


The fastest O(1) factorial function has a lookup table of all the factorials that fit within the output range. With an array of the first 34 (float) or 170 (double) factorials, you get identical results in a fraction of the time.

churkl at hotmail dot com
26-May-2004 04:32


Here is my factorial function which i think is very simple and without any confusion. email me comments if you like if i had something wrong.





<?php


function factorial($number)


{


    $temp = 1;


    while ($number > 1){


        $temp *= $number--;


    }


    return $temp;


}


?>

ausvald at tut dot by
30-Apr-2004 08:48


I see there are some factorial functions below.



I'll provide the best one:



<?

function factorial($n){ $n=(int)$n;

  $f=1;

  for(;$n>0;--$n) $f*=$n;

  return $f;

}

?>

florian at shellfire dot de
28-Apr-2004 05:48


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

    // f�r 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));    

    } 



?>

Chronial "at" cyberpunkuniverse.de
13-Jan-2004 04:47


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;

}

?>

chris at free-source dot com
07-Oct-2003 12:37


to "convert" scientific notation to a float simply cast it:

<?php

$val = '3.5e4';

$val = (float) $val;

echo $val;

?>



output:

35000

jl85 at yahoo dot com
05-Oct-2003 07:00


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));

}

fabien_mornand at yahoo dot fr
30-Sep-2003 06:46


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;

?>

jordanolsommer at imap dot cc
27-Aug-2003 11:07


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 :).

matthew_gaddis at yahoo dot com
24-Apr-2003 05:23


Here is a cleaner factorial function:



function factorial($s){

    if($s) $r = $s * factorial($s - 1);

    else $r = 1;

    return $r;

}

jerry dot wilborn at fast dot net
16-Apr-2003 02:10


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));

jl85 at yahoo dot com
22-Feb-2003 11:04


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.

php at casaforge dot com (Hal)
31-Jan-2003 08:25


This might be useful in generating fractional numbers for construction, if only because most carpenters would rather put a nail in your foot than hear about any number that ends with .8125".



Since I couldn't figure out the fraction code above, this is my simple-minded take on the problem. Also, align by "char" doesn't seem to work yet in html, so it seems necessary to use tables (egad!) to make numbers align properly. The following code illustrates a way to make a dynamically sized table with aligned fractions from an array of random numbers. Since I don't care about fractions less than 1/16, this rounds them into oblivion. Also, it sorts the list from long to short and collates multiples in the array. One bit of cleverness here (gleaned from these pages) that might not be obvious: I'm using 1 *bitwise and* (1 &) to determine odd numbers.



If you copy and paste the following code, try refreshing the page a few times to see how the table adjusts itself.



<?php



// get some numbers to play with



$x = rand(0,130000)/10;

$y = rand(0,1200);

$z = rand(0,4)/64;

$array = array($x, $x, $x, $y, $y, $z, 324.19, 425/7, sqrt(2), pi(), pi());



// functions



function mult($n) { return intval (round ($n*16)); }



function frac($num) { $mod = fmod ($num,1)*16; 

if (1 & $mod) { return " - ".$mod."/16"; } 

else $mod = $mod/2;

if (1 & $mod) { return " - ".$mod."/8"; }

else $mod = $mod/2;

if (1 & $mod) { return " - ".$mod."/4"; }

else $mod = $mod/2;

if (1 & $mod) {return " - ".$mod."/2";}

}



// make a table



echo '<table>';

$array = array_map("mult", $array);

$array = (array_filter($array, strval)); //get rid of zeros

$array = (array_count_values ($array));

krsort ($array);

while (list ($key, $val) = each ($array)) {

$key = $key/16;

echo "<tr><td>$val</td><td>&nbsp; @ &nbsp;</td><td align=\"right\">".intval($key)." </td><td> ".frac($key)." </td></tr>";

}

echo '</table>';



?>

nazgul26 (at_sign) windfox dot net
08-Dec-2002 05:58


This code will convert a decimal to it's fraction equivalent. The precision can be set by changing PRECISION.





<?php


define(PRECISION, .01);





$count=0;


$result=array();


decimalToFraction($_REQUEST['dec'],$count,&$result);


$count = count($result);


$simp_fract = simplifyFraction($result,$count,1,$result[$count]);





echo $simpl_fract;





// Start of functions





/*


   Converts a decimal to unsimplified fraction represented in an array


*/


function decimalToFraction($decimal,$count,$result) {


    $a = (1/$decimal);


    $b = ( $a - floor($a)  );


    $count++;


    if ($b > .01 && $count <= 5) decimalToFraction($b,$count,&$result);


    $result[$count] = floor($a);


}





/* 


    Simplifies a fraction in an array form that is returned from  


    decimalToFraction


*/


function simplifyFraction($fraction,$count,$top,$bottom) {


    $next = $fraction[$count-1];


    $a = ($bottom * $next) + $top;


    $top = $bottom;


    $bottom = $a;


    $count--;


    if ($count > 0) simplifyFraction($fraction,$count,$top,$bottom);


    else {


        return "<font size=1>$bottom/$top</font>";


    }


}


?>

jbeardsl at gte dot net
09-Nov-2002 01:36


I needed a truncate function to operate on real numbers. I preferred not to use a string-manipulation method, so here's my solution. HTH...



function truncate ($num, $digits = 0) {



    //provide the real number, and the number of 

    //digits right of the decimal you want to keep.



    $shift = pow(10 , $digits);

    return ((floor($num * $shift)) / $shift);



}

jbeardsl [found_at] gte [d0t] net
08-Nov-2002 04:15


I was looking for a truncate function. Not finding one, I wrote my own. Since it deals with everything as a number, I imagine it's faster than the alternative of using string functions. HTH...





<?php


function truncate ($num, $digits = 0) {





    //provide the real number, and the number of 


    //digits right of the decimal you want to keep.





    $shift = pow(10, $digits);


    return ((floor($num * $shift)) / $shift);


}


?>

patience at worldonline dot nl
05-Aug-2002 12:08


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 );


}


?>

shanx at shanx dot com
08-Jul-2002 04:13


<?



/**

 * Function to calculate base36 values from a number. Very 

 * useful if you wish to generate IDs from numbers. 

 * 

 * @param $value The number 

 * @param $base The base to be applied (16, 36 or 64)

 * @return The calculated string 

 * @author Shashank Tripathi (shanx@shanx.com)

 * @version 0.1 - Let me know if something doesnt work

 * 

 */

 

function base36($value, $base) 

{

    $baseChars = array('0', '1', '2', '3', '4', '5',

                       '6', '7', '8', '9', 'a', 'b',

                       'c', 'd', 'e', 'f', 'g', 'h',

                       'i', 'j', 'k', 'l', 'm', 'n',

                       'o', 'p', 'q', 'r', 's', 't',

                       'u', 'v', 'w', 'x', 'y', 'z'

                     );



    $remainder = 0;

    $newval = "";

    

    while ( $value > 0 ) 

    {

        $remainder = $value % $base;

        $value = ( ($value - $remainder)/ $base );

        $newval .= $baseChars[$remainder];

    }

    return strrev($newval);

    

}



echo "The string for 46655, for instance, is " . base36(46655, 36);



?>

webkid%webkid.com
31-May-2002 06:54


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!

webkid%webkid.com
31-May-2002 06:49


I found it kind of irritating that PHP had no native functionality for a calculating Factorials. Since I really didn't feel like loading the GMP library, I figured I'd write my own function.



function fact($s){$r=(int)$s; for ($i=$r;$i--;$i>1){$r=$r*$i;} return $r;}



I think that's right... I havn't tested it extensively but it should work.

cornelius at skjoldhoej dot dk
12-Jun-2001 05:03


I found that when dealing with tables, a 'least common multiple' function is sometimes useful for abusing tablespan and the likes.





So here goes (you may choose to remove the first part of the gcd function if the function call is well-behaved):





<?php


function gcd(n, m) //greatest common divisor


{


    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) //least common multiple


{


    return m*(n/gcd(n,m));


}


?>





This may or may not be something to consider adding to the mathematical function library.

ian at mp3 dot com
19-Feb-2001 06:43


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;


}


?>

cathody at mail dot ru
10-Aug-2000 10:55


Converting non-standard form:





you can use something like this:





<?php


$v=0.3e-9;


$v=sprintf ( "%2.9f", $v);


?>

LXIV. Mathematical Functions

Introduction

Requirements

Installation

Runtime Configuration

Resource Types

Predefined Constants