Math
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Math 函数

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Math
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PHP手册 - N: Math 函数

用户评论:

milo at mdlwebsolutions dot com (04-Apr-2012 10:45)

@crescentfreshpot
Regarding your median function, if you use $n % 2 == 0, you won't get what you think.
Use is_int($n) instead.
<?php

var_dump(2.5 % 2); //int(0)
var_dump(4.5 % 2); //int(0)
var_dump(5.5 % 2); //int(1)
var_dump((5/2) % 2); //int(0)
$n = 5 / 2;var_dump($n % 2); //int(0)
$n = 4 / 2;var_dump($n % 2); //int(0)
$n = 7 / 2;var_dump($n % 2); //int(1)
$n = 9 / 2;var_dump($n % 2); //int(0)
$n = 9 / 2;var_dump(is_int($n)); //bool(false)
$n = 8 / 2;var_dump(is_int($n)); //bool(true)
$n = 9 / 2;var_dump(floor($n)); //float(4)
/**
 *  @function median returns the median of an array of numeric values.
 *  @param $data must have 1 or more values, all of which are numeric.
 *  @variable $c_data is the number of items in the data set.
 *  @variable $middle is the number of items divided by 2.  This is
 *    used to find the index of the middle value.
 *  @return The median of the data set.
 *  @example
 *  On the complex example of an even number of values:
 *  $data = array(0, 1, 2, 3);
 *  $c_data = 4;
 *  $middle = 2;
 *  return 1.5; //($data[1] + $data[2]) / 2
 *  @example
 *  On the complex example with an odd number of values:
 *  $data = array(0, 1, 2, 3, 4);
 *  $c_data = 5;
 *  $middle = 2.5;
 *  return 2; //$data[floor($middle)]
 * 
 */
function median($data) {
    $c_data = count($data);
    $middle = $c_data / 2;
   
    if ($c_data == 0) {
        return false;
    }//END IF
   
    if ($c_data < 2) {
       
        return $data[0];
       
    } elseif (is_int($middle)) {
       
        return (($data[$middle - 1] + $data[$middle]) / 2);
       
    } else {
       
        return $data[floor($middle)];
       
    }//END IF
       
}//END FUNCTION

AsherMaximum gmail (19-Apr-2011 05:40)

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') ) ) )
?>

php at keith tyler dot com (04-Nov-2010 07:09)

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)));'
?>

zero dot affect at hotmail dot com (07-May-2010 11:16)

I was editing some code and made up two functions which may come in handy, they are to work out the average value of multiple values.

Working with array:
<?php
function avgval($avg_vals) {
 if ( is_array($avg_vals) && count($avg_vals) > 1 ) {
        $return_vals = ( array_sum($avg_vals) / count($avg_vals) );
 } elseif ( is_array($avg_vals) && count($avg_vals) == 1 ) {
        $return_vals = current($avg_vals);
 } else {
        $return_vals = FALSE;
 }
   return $return_vals;
}
   echo avgval(array(6,11,7)); // outputs 8
   echo avgval(array(6)); // outputs 6
?>

Working with string:
<?php
function avgvals($avg_vals,$avg_delimiter=',') {
 if ( (is_string($avg_vals) && strlen($avg_vals) > 2) && (is_string($avg_delimiter) && !empty($avg_delimiter)) ) {
    $average_vals = explode($avg_delimiter, $avg_vals);
        $return_vals = ( array_sum($average_vals) / count($average_vals) );
 } elseif ( (is_string($avg_vals) && strlen($avg_vals) <= 2) && (is_string($avg_delimiter) && !empty($avg_delimiter)) ) {
        $return_vals = $avg_vals;
 } else {
        $return_vals = FALSE;
 }
   return $return_vals;
}
   echo avgvals('6,11,7'); // outputs 8
   echo avgvals('6-11-7', '-'); // outputs 8
   echo avgvals('6'); // outputs 6
?>

chris at chrisstockton dot org (15-Sep-2008 05:27)

Recently I needed to determine the size of N is unknown, only the state of N is known. May seem like a weird thing to need, but a example is finding the maximum size of sending email to a SMTP server when the maximum size is currently unknown. You  can send $size email each iteration and the direction will be TRUE if the email is to big and is rejected by the server, or FALSE if the email is accepted.

Below is a example.

<?php
// our arbitrary number that if not being used in this example, would be
// otherwise unknown
$n = 1;
echo "Finding: $n\n";

$direction = FALSE;
$step = 1;
$size = $sizeLeast = $sizeMax = $i = 0;

while(1) {
    // small var for counting, could be taken out if you don't care how many
    // iterations it took (in common use you wouldn't)
    $i++;

    // this should be a function call or something that says what the current
    // state of N is, above (true) or below (false), here $n is just a arbitrary
    // number and to determine the state we compare it against current $size
    $direction = ($size > $n);

    // simple steps based on the current state of n (direction), the call could
    // be here instead of assigning direction for more performance
    if($direction) {
        $sizeMax = $size;
        $step = (int) round($step/2);
        $size -= $step;
    } else {
        $sizeLeast = $size;
        $step = $step*2;
        $size += $step;
    }

    // if sizemax - sizeleast is 1, then obviously the size is sizeLeast
    if(1 === ($sizeMax - $sizeLeast) && 1 === $step) {
        break;
    }
}

echo "Found: $size in $i iterations\n";
?>

Kollege (13-Aug-2008 02:54)

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 03:39)

<?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 04:47)

// 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 03:24)

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 (10-Jan-2008 03:23)

//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 06:25)

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 07:55)

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 05:14)

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 09:36)

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 01:51)

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 07:42)

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 (20-Jul-2006 02:24)

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 11:10)

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 05:07)

@ 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 01:23)

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 09:15)

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 10:48)

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 09:36)

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 09:39)

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 11:16)

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 06:01)

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 10:27)

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 02:37)

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 (27-Jul-2005 03:50)

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 (27-Jul-2005 12:57)

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 08:48)

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 (11-Mar-2005 04:41)

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 08:42)

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 10:32)

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 12:34)

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 05:05)

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 01:58)

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 (09-Jun-2004 03:36)

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 (27-May-2004 03:04)

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 09:32)

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 (01-May-2004 01:48)

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 10:48)

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
    // 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));   
    }

?>

Chronial "at" cyberpunkuniverse.de (13-Jan-2004 09:47)

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 05:37)

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 12:00)

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 11:46)

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 04:07)

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 10:23)

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 07:10)

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 04:04)

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) (01-Feb-2003 01:25)

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 10:58)

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 06:36)

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 09:15)

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 05:08)

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 09:13)

<?

/**
 * 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 11:54)

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 11:49)

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 10:03)

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 11:43)

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 (11-Aug-2000 03:55)

Converting non-standard form:

you can use something like this:

<?php
$v=0.3e-9;
$v=sprintf ( "%2.9f", $v);
?>