Math Functions

    Table of Contents

    • abs — Absolute value
    • acos — Arc cosine
    • acosh — Inverse hyperbolic cosine
    • asin — Arc sine
    • asinh — Inverse hyperbolic sine
    • atan2 — Arc tangent of two variables
    • atan — Arc tangent
    • atanh — Inverse hyperbolic tangent
    • base_convert — Convert a number between arbitrary bases
    • bindec — Binary to decimal
    • ceil — Round fractions up
    • cos — Cosine
    • cosh — Hyperbolic cosine
    • decbin — Decimal to binary
    • dechex — Decimal to hexadecimal
    • decoct — Decimal to octal
    • deg2rad — Converts the number in degrees to the radian equivalent
    • exp — Calculates the exponent of e
    • expm1 — Returns exp($num) - 1, computed in a way that is accurate even when the value of number is close to zero
    • fdiv — Divides two numbers, according to IEEE 754
    • floor — Round fractions down
    • fmod — Returns the floating point remainder (modulo) of the division of the arguments
    • hexdec — Hexadecimal to decimal
    • hypot — Calculate the length of the hypotenuse of a right-angle triangle
    • intdiv — Integer division
    • is_finite — Checks whether a float is finite
    • is_infinite — Checks whether a float is infinite
    • is_nan — Checks whether a float is NAN
    • log10 — Base-10 logarithm
    • log1p — Returns log(1 + number), computed in a way that is accurate even when the value of number is close to zero
    • log — Natural logarithm
    • max — Find highest value
    • min — Find lowest value
    • octdec — Octal to decimal
    • pi — Get value of pi
    • pow — Exponential expression
    • rad2deg — Converts the radian number to the equivalent number in degrees
    • round — Rounds a float
    • sin — Sine
    • sinh — Hyperbolic sine
    • sqrt — Square root
    • tan — Tangent
    • tanh — Hyperbolic tangent

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    User Contributed Notes 35 notes

    up
    12
    pat.mat AT sympatico DOT com
    20 years ago
    For people interest in Differential Equations, I've done a function that receive a string like: x^2+x^3 and put it in
    2x+3x^2 witch is the differantial of the previous equation.

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

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

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

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

    I know this is not optimal but i've done this quick :)
    If you guys have any comment just email me.
    I also want to do this fonction In C to add to phpCore maybe soon...
    Patoff
    up
    7
    daniel at g-loc dot org
    18 years ago
    If you're an aviator and needs to calculate windcorrection angles and groundspeed (e.g. during flightplanning) this can be very useful.

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

    You can probably write these lines more beautiful, but they work!
    up
    5
    lummox
    16 years ago
    Wouldn't the following function do the same but a lot easier than the one in the comment before?

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

    //r must be in radians, returns array of x,y
    function polar2rect($r,$theta)
    {
    if(is_numeric($r)&&is_numeric($theta))
    {
    $x=$r*cos($theta);
    $y=$r*sin($theta);
    $rect=array("x"=>$x,"y"=>$y);
    }
    else
    {
    return false;
    }
    }
    ?>
    up
    -1
    Anonymous
    6 years ago
    And the reason I needed a Factorial function is because I there were no nPr or nCr functions native to PHP, either.

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

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

    <?php
    sprintf    ( "%d%s", $t, array_pop( array_slice( array_merge( array( "th","st","nd","rd"), array_fill( 4,6,"th")), $t%10, 1)));'
    ?>
    up
    -3
    Mike
    16 years ago
    //had a mistake in last post, heres the corrected version

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

    function trimInteger($targetNumber,$newLength) {

    $digits = pow(10,$newLength);

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

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

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

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

    return $newInteger;
    }
    up
    -3
    florian at shellfire dot de
    20 years ago
    Please note that shorter is not always better
    (meaning that really short faculty implementation above).

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

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

    <?php

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

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

    <?php

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

    ?>
    up
    -3
    edward at edwardsun dot com
    17 years ago
    well just a note.. maybe i'm a bit stupid.. but remember to use pow() rather than the "^" sign for exponents.. as it took me 5 minutes to figure out why it wasn't working.
    up
    -3
    moikboy (nospam!) moikboy (nospam!) hu
    18 years ago
    I think, this is the optimal code for calculating factorials:

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

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

    <?php
    function fib($int){
    static     $fibTable=array();
    return empty(    $fibTable[$int])?$fibTable[$int] = $int>1?fib($int-2)+fib($int-1):1:$fibTable[$int];
    };
    ?>
    up
    -3
    Chronial "at" cyberpunkuniverse.de
    20 years ago
    Here are are a nPr and a nPc function
    (had to define NaN - don't know, how to this the "rigth" way)

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

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

    function     nPr($n,$r){
    if (    $r > $n)
    return     NaN;
    if (    $r)
    return     $n*(nPr($n-1,$r-1));
    else
    return     1;
    }
    ?>
    up
    -3
    AsherMaximum gmail
    13 years ago
    Here's a simple way way to convert a number to an ordinal number I created:

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

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

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

    //$n is now used to determine the suffix.
    $ord = ($n2==1 ? $i.'st' : ( ($n2==2 ? $i.'nd' : ($n2==3 ? $i.'rd' : $i.'th') ) ) )
    ?>
    up
    -4
    help at gjbdesign dot com
    19 years ago
    Occasionally a user must enter a number in a form. This function converts fractions to decimals and leaves decimals untouched. Of course, you may wish to round the final output, but that is not included here.

    <?php
    /*Some example values of $q
    $q = "2.5";
    $q = "2 1/2";
    $q = "5/2";
    */
    function Deci_Con($q){
    //check for a space, signifying a whole number with a fraction
    if(strstr($q, ' ')){
    $wa = strrev($q);
    $wb = strrev(strstr($wa, ' '));
    $whole = true;//this is a whole number
    }
    //now check the fraction part
    if(strstr($q, '/')){
    if(    $whole==true){//if whole number, then remove the whole number and space from the calculations
    $q = strstr($q, ' ');
    }
    $b = str_replace("/","",strstr($q, '/'));//this is the divisor
    //isolate the numerator
    $c = strrev($q);
    $d = strstr($c, '/');
    $e = strrev($d);
    $a = str_replace("/","",$e);//the pre-final numerator
    if($whole==true){//add the whole number to the calculations
    $a = $a+($wb*$b);//new numerator is whole number multiplied by denominator plus original numerator
    }
    $q = $a/$b;//this is now your decimal
    return $q;
    }else{
    return     $q;//not a fraction, just return the decimal
    }
    }    ?>
    up
    -4
    capripot at gmail dot com
    11 years ago
    Another simpler function to check a number with the luhn algorithm :

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

    Don't know if foreach and arrays operations are faster than while and substr, but I feel it clearer.
    up
    -6
    peter-stangl at t-online dot de
    18 years ago
    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');
    }
    }

    ?>
    up
    -6
    jbeardsl [found_at] gte [d0t] net
    21 years ago
    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);
    }
    ?>
    up
    -3
    patience at worldonline dot nl
    21 years ago
    The example for Factorials given above is wrong. Here a correct version, so that you do not have to reinvent the wheel again...

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

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

    return(     $r );
    }
    ?>
    up
    -6
    nazgul26 (at_sign) windfox dot net
    21 years ago
    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>";
    }
    }
    ?>
    up
    -5
    webkid%webkid.com
    22 years ago
    And the reason I needed a Factorial function is because I there were no nPr or nCr functions native to PHP, either.

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

    Hope that helps someone!
    up
    -3
    jl85 at yahoo dot com
    20 years ago
    Here's yet another greatest common denominator (gcd) function, a reeeeally small one.

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

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

    function gcd($n,$m){
    if(!$m)return$n;return gcd($m,fmod($n,$m));
    }
    up
    -6
    bjcffnet at gmail dot com
    18 years ago
    thearbitcouncil at gmail dot com, you could just use array_sum():
    <?php
    function average($arr)
    {
    if (!    is_array($arr)) return false;

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

    $array = array(5, 10, 15);
    echo     average($array); // 10
    ?>
    up
    -3
    ian at mp3 dot com
    23 years ago
    for those looking for a credit card verification function i wrote a simple LUHN Formula algorithm:

    <?php
    $valid     = 1;

    $numOfDigits = 0 - strlen($ccNumber);

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

    if ((    $total % 10) != 0){
    $valid = 0;
    }
    ?>
    up
    -4
    Florian
    18 years ago
    A function that simulates the sum operator. (http://en.wikipedia.org/wiki/Sum). Be careful with the expression because it may cause a security hole; note the single quotes to don't parse the "$".
    <?php
    # @param string $expr expression to evaluate (for example (2*$x)^2+1)
    # @param string $var dummy variable (for example "x")
    # @param integer $start
    # @param integer $end
    # @param integer $step

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

    for (    $i = $start; $i <= $end; $i = $i + $step) {
    $_expr = str_replace('$'.$var,$i,$expr);
    $_eval = '$_result = '.$_expr.'; return $_result;';
    $_result = eval($_eval);
    if(    $result === FALSE) return "SYNTAX ERROR : $expr";
    $sum += $_result;
    }
    return (int)    $sum;
    }
    ?>
    up
    -6
    tmpa at yahoo dot com
    19 years ago
    while joogat's one line function is short, it is probably better to calculate factorial iteratively instead of recursively. keep in mind if you want large factorials, you'll need to use some sort of arbitrary precision integer or perhaps the BCMath functions. then again, unless you're trying to do large numbers (170! is the highest that you can do that does not return infinity) you probably won't notice any time difference.
    <?php
    function factorial($in) {
    // 0! = 1! = 1
    $out = 1;

    // Only if $in is >= 2
    for ($i = 2; $i <= $in; $i++) {
    $out *= $i;
    }

    return     $out;
    }
    ?>
    up
    -5
    jerry dot wilborn at fast dot net
    21 years ago
    Here is how to calculate standard deviation in PHP where $samples is an array of incrementing numeric keys and the values are your samples:

    $sample_count = count($samples);

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

    $standard_deviation = sqrt(array_sum($sample_square) / $sample_count - pow((array_sum($samples) / $sample_count), 2));
    up
    -4
    fabien_mornand at yahoo dot fr
    20 years ago
    here is an algorithm to calculate gcd of a number. This is Euclid algorithm i was studying in Maths. I've converted it in php for the fun.

    <?php
    if($a && $b)
    {     $ax=$a; $bx=$b;
    $r=fmod($a,$b);
    if(!    $r){$rx=$r;}
    while(    $r){
    $rx=$r;
    $a=$b;
    $b=$r;
    $r=fmod($a,$b);
    }
    }
    echo     'PGCD ('.$ax.' , '.$bx.' ) = '.$rx;
    ?>
    up
    -4
    jl85 at yahoo dot com
    21 years ago
    Theres another faster way of doing even/odd number checking by using bitwise operators. Don't ask me how it works, I just found this out by experimenting with it (could the editor possibly explain?)

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

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

    How it works is (1&$num) returns a 1 for odd numbers and returns 0 when it's an even number.
    up
    -4
    tembenite at gmail dot com
    17 years ago
    To add to what Cornelius had, I have written a function that will take an array of numbers and return the least common multiple of them:

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

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

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

    function lcm($n, $m) {
    return $m * ($n/gcd($n,$m));
    }
    up
    -7
    thearbitcouncil at gmail dot com
    19 years ago
    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 :)

    ?>
    up
    -5
    marasek.SPAMLESS at telton.de
    18 years ago
    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.
    up
    -4
    barry at megaspace dot com
    17 years ago
    Here's a least common denominator (lcd) function:

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

    function lcd($array,$x) {

    $mod_sum = 0;

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

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

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

    }

    lcd($array,1);
    up
    -5
    Aiden880
    9 years ago
    Lowest Common Denominator:
    function lcd($num, $start) {
    while($num % $start != 0) {
    $start++;
    }
    return $start;
    }
    up
    -4
    jordanolsommer at imap dot cc
    20 years ago
    The reason the bitwise AND ("&") operator works to determine whether a number is odd or even is because odd numbers expressed in binary always have the rightmost (2^0) bit = 1 and even numbers always have the 2^0 bit = 0.

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

    a clever way of doing things, but $num % 2 would work as well i think :).
    up
    -7
    monte at ohrt dot com
    18 years ago
    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++);
    up
    -16
    pradhumansaini2 at gmail dot com
    3 years ago
    Ajay Singh Deol is commonly known as Sunny Deol which is a famous Indian Television actor and a Politician as well. Want to know about the info then you can check it in your browser such as Sunny Deol age where you can get about his complete information.
    For your information, Sunny Deol is the person who won the Filmfare award for the best actor
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