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abs> <mailparse_uudecode_all
Last updated: Sun, 25 Nov 2007

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Wiskundige functies

Introductie

Deze wiskundige functies kunnen alleen waarden behandelen die in het bereik van de integer en float types op jouw computer zijn. (dit komt momenteel overeen met resp. de C types long en double). Als je hogere getallen aan moet kunnen, kijk dan eens naar de arbitrary precision math functions.

Afhankelijkheden

Deze functies zijn beschikbaar als onderdeel van de standaard module die altijd beschikbaar is.

Installatie

Er zijn geen handelingen nodig m.b.t. tot installatie voor deze functies, deze maken deel uit van de kern van PHP.

Configuratie tijdens scriptuitvoer

Deze extensie gebruikt geen configuratie regels.

Resource types

Deze extensie maakt geen gebruik van resources.

Voorgedefinieerde constanten

De constanten die hier staan zijn altijd aanwezig als een onderdeel van de PHP kern.

Wiskundige constanten
Constante Waarde Beschrijving
M_PI 3.14159265358979323846 Pi
M_E 2.7182818284590452354 e
M_LOG2E 1.4426950408889634074 log_2 e
M_LOG10E 0.43429448190325182765 log_10 e
M_LN2 0.69314718055994530942 log_e 2
M_LN10 2.30258509299404568402 log_e 10
M_PI_2 1.57079632679489661923 pi/2
M_PI_4 0.78539816339744830962 pi/4
M_1_PI 0.31830988618379067154 1/pi
M_2_PI 0.63661977236758134308 2/pi
M_SQRTPI 1.77245385090551602729 wortel(pi) [4.0.2]
M_2_SQRTPI 1.12837916709551257390 2/wortel(pi)
M_SQRT2 1.41421356237309504880 wortel(2)
M_SQRT3 1.73205080756887729352 wortel(3) [4.0.2]
M_SQRT1_2 0.70710678118654752440 1/wortel(2)
M_LNPI 1.14472988584940017414 log_e(pi) [4.0.2]
M_EULER 0.57721566490153286061 Constante van Euler [4.0.2]
Alleen M_PI is beschikbaar in alle versies van PHP tot en met PHP 4.0.0. Alle andere constanten zijn beschikbaar vanaf PHP 4.0.0. Constanten met [4.0.2] erbij zijn toegevoegd in PHP 4.0.2.

Table of Contents

  • abs — Absolute waarde
  • acos — Arc cosinus
  • acosh — Inverse hyperbolische cosinus
  • asin — Arc sinus
  • asinh — Inverse hyperbolische sinus
  • atan2 — arc tangens van twee variabelen
  • atan — Arc tangens
  • atanh — Inverse hyperbolische tangens
  • base_convert — Converteert een nummer tussen verschillende grondtallen
  • bindec — Binair naar decimaal
  • ceil — Rond af naar boven
  • cos — Cosinus
  • cosh — Hyperbolische cosinus
  • decbin — Decimaal naar binair
  • dechex — Decimaal naar hexadecimaal
  • decoct — Decimaal naar octaal
  • deg2rad — Converteer een getal van graden naar radialen
  • exp — Berekent een exponent van e (het grondtal van de de natuurlijke logaritme of het logaritme van Neper)
  • expm1 — Geeft exp(number) - 1 terug, berekend op een manier die ook nauwkeurig is als de waarde van number dicht bij nul ligt
  • floor — Rond af naar beneden
  • fmod — Returns the floating point remainder (modulo) of the division of the arguments
  • getrandmax — Geeft de grootste mogelijke willekeurige waarde terug
  • hexdec — Hexadecimaal naar decimaal
  • hypot — Geeft de wortel( num1*num1 + num2*num2)
  • is_finite — Beschrijving
  • is_infinite — Beschrijving
  • is_nan — Beschrijving
  • lcg_value — Combined linear congruential generator
  • log10 — Logaritme met grondtal 10
  • log1p — Geeft log(1 + number) terug, berekend op een manier die nauwkeurig is zelfs als de waarde van number dicht bij nul ligt
  • log — Natuurlijke logaritme
  • max — Vind de hoogste waarde
  • min — Vind de laagste waarde
  • mt_getrandmax — Geeft de grootste mogelijke willekeurige waarde terug
  • mt_rand — Genereeer een betere willekeurige waarde
  • mt_srand — 'Bezaai' de betere random number generator
  • octdec — Octaal naar decimaal
  • pi — Verkrijg de waarde van pi
  • pow — Machtsverheffing
  • rad2deg — Converteer een getal van radialen naar graden
  • rand — Genereer een willekeurig waarde
  • round — Rondt een float af
  • sin — Sinus
  • sinh — Hyperbolische sinus
  • sqrt — Worteltrekken
  • srand — 'Bezaai' de random number generator
  • tan — Tangens
  • tanh — Hyperbolic tangens


abs> <mailparse_uudecode_all
Last updated: Sun, 25 Nov 2007
 
add a note add a note User Contributed Notes
Wiskunde
Kollege
12-Aug-2008 06:54
If somebody needs to convert a hexal input (i'm NOT talking about hexaDEZIMAl), e.g. a time like

02:30 h

to dezimal, like - in this case -:

2.5

i can recommend this simple function:
<?
function HexalToDezimal ($hexal) {
 $dezimal = floor($hexal) + round(($hexal - floor($hexal)) * (1 / 0.6), 2);
 return ($dezimal);
 }
?>
This can be usefull e.g. if you want to work with unix-timestamps and hexal inputs; e.g. if you want to compute:

time() + [2 houres : 30 minutes]

That is:

time() + (2.5 * 60 * 60)
rubo77 at spacetrace dot org
28-Jul-2008 07:39
<?php
function lcd($n,$m, $maxvarianzpercent=0){
    // set $maxvarianzpercent=5 to get a small, but approx. result
    /* a better lcd function with varianz:
    for example use
    lcd(141,180,5) to get the approx. lcd '7/9' which is in fact 140/180
    */
    // ATTENTION!!! can be really slow if $m is >1000
   
    $d=$n/$m;
    $f=1;
    while($d*$f!=intval($d*$f)){
        $f++;
    }
    $r=($d*$f).'/'.$f;
    if(($d*$f)<=10 or $f<=10) return $r;
    else if($maxvarianzpercent>0){
        $f=1;
        while($d*$f!=intval($d*$f) and ($d*$f)-intval($d*$f) > $maxvarianzpercent/100){
            $f++;
        }
        return intval($d*$f).'/'.$f;
    } else return $r;
}
?>
PiledHigher at jovi dot net
31-Mar-2008 09:47
// Ordinal one liner tests good up to PHP_INT_MAX-7 on GNU/Linux
function ordinal($n) {                                                                                                                                                  
    return $n . gmdate("S", (((abs($n) + 9) % 10) + ((abs($n / 10) % 10) == 1) * 10) * 86400);                                                                          
}
lummox
02-Feb-2008 07:24
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);
}
Mike
09-Jan-2008 07:23
//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;
}
ddarjany at yahoo dot com
05-Sep-2007 10:25
Tim's fix of Evan's ordinal function causes another problem, it no longer works for number above 100.  (E.g. it returns 111st instead of 111th). 
Here is a further modified version which should work for all numbers.

<?PHP

function ordinal($cardinal)    {
  $cardinal = (int)$cardinal;
  $digit = substr($cardinal, -1, 1);

  if ($cardinal <100) $tens = round($cardinal/10);
  else $tens = substr($cardinal, -2, 1);

  if($tens == 1)  {
    return $cardinal.'th';
  }

  switch($digit) {
    case 1:
      return $cardinal.'st';
    case 2:
      return $cardinal.'nd';
    case 3:
      return $cardinal.'rd';
    default:
      return $cardinal.'th';
  }
}
 ?>
11-Apr-2007 11:55
Here is another way of calculating the nth term of the Fibonacci sequence, based on Binet's formula (see http://en.wikipedia.org/wiki/Fibonacci_series#Closed_form_expression for more information on this).
In this example, it would display the 17th term of the Fibonacci sequence.

<?php

$n = 17; // Sets a value for $n, the nth term
$phi = (1 + sqrt(5)) / 2; // Sets the value of phi for use in the formula
$u = (pow($phi, $n) - pow(1 - $phi, $n)) / sqrt(5);
echo "U<sub>$n</sub> = $u";

?>

Here is a script that lists the Fibonacci sequence from whatever two terms you specify, in this example from the 12th term to the 27th term (inclusive).

<?php

$f = 12; // Sets the 'f'th term, the term from which to start listing
$t = 27; //Sets the 't'th term, the term at which to stop listing
$phi = (1 + sqrt(5)) / 2; // Sets the value of phi for use in the formula
while($f <= $t) {
  $u = (pow($phi, $f) - pow(1 - $phi, $f)) / sqrt(5);
  echo "U<sub>$f</sub> = $u<br>\n";
  $f++;
}

?>
barry at megaspace dot com
02-Dec-2006 09:14
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);
tembenite at gmail dot com
06-Nov-2006 01:36
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));
}
tim at durge dot org
27-Oct-2006 05:51
In Evan's ordinal function, the line:

<?php
  $tens = substr($cardinal, -2, 1);
?>

needs to be replaced by:

<?php
  $tens = round($cardinal/10);
?>

or similar. At least on PHP 4.3.10,  substr("1", -2, 1)  returns '1' - so Evan's function gives "1th", as well as "11th".  This is contrary to the documentation, but is noted in the comments on the substr manual page.
Evan Broder
26-Jul-2006 11:42
A slightly more complex but much more accurate cardinal=>ordinal function (the one below doesn't account for 11th, 12th, and 13th, which don't follow the usual rules):

<?php

    function ordinal($cardinal)
    {
        $cardinal = (int)$cardinal;
        $digit = substr($cardinal, -1, 1);
        $tens = substr($cardinal, -2, 1);
        if($tens == 1)
        {
            return $cardinal.'th';
        }
       
        switch($digit)
        {
        case 1:
            return $cardinal.'st';
        case 2:
            return $cardinal.'nd';
        case 3:
            return $cardinal.'rd';
        default:
            return $cardinal.'th';
        }
    }

?>
edward at edwardsun dot com
19-Jul-2006 06:24
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.
jaakko dot mantila at sagas dot fi
12-Jul-2006 03:10
Here is another payment function with working future value($fv) option:

function payment($r,$np,$pv,$fv,$prec) {
   /* Calculates the monthly payment
   ** $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 (after payments)
   ** $prec = the precision you wish rounded to
   */
   /****************************************\
   ** No Warranty is expressed or implied. **
   *****************************************/
if(!$fv) $fv = 0;
$mypmt=$r * (-$fv+pow((1+$r),$np)*$pv)/(-1+pow((1+$r),$np));
return round($mypmt, $prec);
}
twoscoopsofpig at NOSPAM dot gmail dot com
07-Jul-2006 09:07
@ Moikboy:

This may or may not be more simplified factorialization:

<?php
$f=$fact=25;
while ($fact>0)
{$f=$f*$fact--;}
echo $f;
?>
marasek.SPAMLESS at telton.de
08-Jun-2006 05:23
I could not resist to do a simpler version of the ordinal function:
<?php
function ordinal($num)
{
    $num = (int)$num;
    $digit = substr($num, -1, 1);
    $ord = "th";
    switch($digit)
    {
        case 1: $ord = "st"; break;
        case 2: $ord = "nd"; break;
        case 3: $ord = "rd"; break;
    break;
    }
return $num.$ord;
}
?>
One could replace the typecast with

<?php
if($num===NULL or $num==="")
{return NULL;}
?>

to get an empty result instead of "0th" in case $num is empty too.
moikboy (nospam!) moikboy (nospam!) hu
10-May-2006 01:15
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];
};
?>
nessthehero at comcast dot net
21-Mar-2006 02:48
Just a simple function to find the ordinal ending to any number if you're printing for example: "The nth result is..."

function ordinal($num) {
    $digit = substr($num,-1,1);
    $ord = array(
        0 => 'th',
        1 => 'st',
        2 => 'nd',
        3 => 'rd',
        4 => 'th',
        5 => 'th',
        6 => 'th',
        7 => 'th',
        8 => 'th',
        9 => 'th'
    );       
    $string = $num.$ord[$digit];
    return $string;
}
Florian
03-Mar-2006 01:36
A function that simulates the sum operator. (http://en.wikipedia.org/wiki/Sum). Be careful with the expression because it may cause a security hole; note the single quotes to don't parse the "$".
<?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;
}
?>
jos at gtacrime dot nl
17-Feb-2006 01:39
Thanks to Chronial "at" cyberpunkuniverse.de, I was able to create the binompdf(n, p, k) function.

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

function binompdf($n, $p, $k){
    $return = nCr($n, $k) * pow($p, $k) * pow((1 - $p), ($n - $k));
    return $return;
}
?>
peter-stangl at t-online dot de
01-Feb-2006 03:16
I needed to approximate an integral because i was not able to calculate it, so i wrote this function. It approximates an integral with the composite Simpson's rule.
More information on Simpson's rule: http://en.wikipedia.org/wiki/Simpson%27s_rule

<?php

function simpsonf($x){
// returns f(x) for integral approximation with composite Simpson's rule
   return(pow((1+pow($x, (-4))), 0.5));
}
function simpsonsrule($a, $b, $n){
// approximates integral_a_b f(x) dx with composite Simpson's rule with $n intervals
// $n has to be an even number
// f(x) is defined in "function simpsonf($x)"
   if($n%2==0){
      $h=($b-$a)/$n;
      $S=simpsonf($a)+simpsonf($b);
      $i=1;
      while($i <= ($n-1)){
         $xi=$a+$h*$i;
         if($i%2==0){
            $S=$S+2*simpsonf($xi);
         }
         else{
            $S=$S+4*simpsonf($xi);
         }
         $i++;
      }
      return($h/3*$S);
      }
   else{
      return('$n has to be an even number');
   }
}

?>
daniel at g-loc dot org
01-Dec-2005 10:01
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!
nbraczek at bsds dot de
26-Oct-2005 02:27
Under some circumstances, it is appropriate to round floats to a given number of significant digits. This function will do it for you:

/**
 * Round to significant digits
 *
 * @param float   $f The number to be rounded
 * @param integer $n Number of significant digits
 */
function round_significant($f, $n)
{
    if ($f==0) return $f;
    return round($f, $n-floor(log10(abs($f)))-1);
}
monte at ohrt dot com
18-Oct-2005 06:37
This is an efficient method of calculating the binomial coefficient C(n,k). This code was derived from Owant: Mastering Algorithms with Perl.

<?php
   // calculate binomial coefficient
   function binomial_coeff($n, $k) {

      $j = $res = 1;

      if($k < 0 || $k > $n)
         return 0;
      if(($n - $k) < $k)
         $k = $n - $k;

      while($j <= $k) {
         $res *= $n--;
         $res /= $j++;
      }

      return $res;

   }
?>

If you compiled php with --enable-bcmath, you can get full integer values of extremely large numbers by replacing:

$res *= $n--;
$res /= $j++;

with:

$res = bcmul($res, $n--);
$res = bcdiv($res, $j++);
crescentfreshpot at yahoo dot com
26-Jul-2005 07:50
Median:

number median ( number arg1, number arg2 [, number ...] )

number median ( array numbers )

<?php

function median()
{
    $args = func_get_args();

    switch(func_num_args())
    {
        case 0:
            trigger_error('median() requires at least one parameter',E_USER_WARNING);
            return false;
            break;

        case 1:
            $args = array_pop($args);
            // fallthrough

        default:
            if(!is_array($args)) {
                trigger_error('median() requires a list of numbers to operate on or an array of numbers',E_USER_NOTICE);
                return false;
            }

            sort($args);
           
            $n = count($args);
            $h = intval($n / 2);

            if($n % 2 == 0) {
                $median = ($args[$h] + $args[$h-1]) / 2;
            } else {
                $median = $args[$h];
            }

            break;
    }
   
    return $median;
}

?>
bjcffnet at gmail dot com
26-Jul-2005 04:57
thearbitcouncil at gmail dot com, you could just use array_sum():
<?php
function average($arr)
{
   if (!is_array($arr)) return false;

   return array_sum($arr)/count($arr);
}

$array = array(5, 10, 15);
echo average($array); // 10
?>
graywh at gmail DELETE dot com
01-Jun-2005 12:48
If you're really concerned about speed, you could compute the factorial of large numbers using the Gamma function of n-1.

Integral y^(t-1)*Exp(-y) for y from 0 to Infinity

For Fibonacci numbers, there's a better-than-recursive way.

((1+sqrt(5))/2)^(n/sqrt(5)) - ((1-sqrt(5))/2)^(n/sqrt(5))
eric at woolhiser dot com
10-Mar-2005 08:41
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 12:42
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;
}
?>
thearbitcouncil at gmail dot com
06-Jan-2005 02:32
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 04:34
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 09:05
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 05:58
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 07:36
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 07:04
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 01:32
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 05:48
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 02:48
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