Math
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.
// 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";
Math Funzioni
Indice dei contenuti
- abs — Valore assoluto
- acos — Arco coseno
- acosh — Inverso del coseno iperbolico
- asin — Arco seno
- asinh — Inverso del seno iperbolico
- atan2 — Arco tangente di due variabili
- atan — Arco tangente
- atanh — Inverso della tangente iperbolica
- base_convert — Converte un numero fra basi arbitrarie
- bindec — Da binario a decimale
- ceil — arrotonda le frazioni all'intero superiore
- cos — Coseno
- cosh — Coseno iperbolico
- decbin — Da decimale a binario
- dechex — Da decimale a esadecimale
- decoct — Da decimale a ottale
- deg2rad — Converte il numero dato in gradi nell'equivalente espresso in radianti
- exp — Calcola l'esponente di e (la base logaritmica naturale o di Nepero)
- expm1 — Restituisce exp(numero) - 1, computato in maniera tale da essere accurato anche se il valore del numero è vicino a zero
- floor — Arrotonda le frazioni all'intero inferiore
- fmod — Returns the floating point remainder (modulo) of the division of the arguments
- getrandmax — Mostra il più grande numero casuale disponibile
- hexdec — Da esadecimale a decimale
- hypot — Restituisce sqrt(num1*num1 + num2*num2)
- is_finite — Verifica se un numero dato è un numero finito
- is_infinite — Verifica se un dato valore è infinito
- is_nan — Verifica se un dato valore non sia un numero
- lcg_value — Generatore combinato lineare congruenziale
- log10 — Logaritmo base-10
- log1p — Restituisce log(1 + numero), computato in maniera tale da essere accurato anche se il valore del numero è vicino a zero
- log — Logaritmo naturale
- max — Trova il valore massimo
- min — Trova il valore minimo
- mt_getrandmax — Mostra il più grande valore casuale disponibile
- mt_rand — Genera un valore casuale migliore
- mt_srand — Inizializza un generatore di numeri casuali migliore
- octdec — Da ottale a decimale
- pi — Restituisce il valore di pi
- pow — Espressione esponenziale
- rad2deg — Converte un numero in radianti nell'equivalente numero in gradi
- rand — Genera un valore casuale
- round — Arrotonda un numero non intero
- sin — Seno
- sinh — Seno iperbolico
- sqrt — Radice quadrata
- srand — inizializza il generatore di numeri casuali
- tan — Tangente
- tanh — Tangente iperbolica
add a note
User Contributed NotesMath Funzioni
chris at chrisstockton dot org
15-Sep-2008 07:27
15-Sep-2008 07:27
Kollege
13-Aug-2008 04:54
13-Aug-2008 04:54
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 ($dezimal);
}
?>
This can be usefull e.g. if you want to work with unix-timestamps and hexal inputs; e.g. if you want to compute:
time() + [2 houres : 30 minutes]
That is:
time() + (2.5 * 60 * 60)
rubo77 at spacetrace dot org
28-Jul-2008 05:39
28-Jul-2008 05:39
<?php
function lcd($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 $r;
}
?>
PiledHigher at jovi dot net
31-Mar-2008 07:47
31-Mar-2008 07:47
// Ordinal one liner tests good up to PHP_INT_MAX-7 on GNU/Linux
function ordinal($n) {
return $n . gmdate("S", (((abs($n) + 9) % 10) + ((abs($n / 10) % 10) == 1) * 10) * 86400);
}
lummox
02-Feb-2008 05:24
02-Feb-2008 05:24
Wouldn't the following function do the same but a lot easier than the one in the comment before?
function trimInteger($targetNumber,$newLength) {
return $targetNumber%pow(10,$newLength);
}
Mike
10-Jan-2008 05:23
10-Jan-2008 05:23
//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 $newInteger;
}
ddarjany at yahoo dot com
05-Sep-2007 08:25
05-Sep-2007 08:25
Tim's fix of Evan's ordinal function causes another problem, it no longer works for number above 100. (E.g. it returns 111st instead of 111th).
Here is a further modified version which should work for all numbers.
<?PHP
function ordinal($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 09:55
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 07:14
02-Dec-2006 07:14
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 11:36
06-Nov-2006 11:36
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 03:51
27-Oct-2006 03:51
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 09:42
26-Jul-2006 09:42
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 $cardinal.'th';
}
}
?>
edward at edwardsun dot com
20-Jul-2006 04:24
20-Jul-2006 04:24
well just a note.. maybe i'm a bit stupid.. but remember to use pow() rather than the "^" sign for exponents.. as it took me 5 minutes to figure out why it wasn't working.
jaakko dot mantila at sagas dot fi
12-Jul-2006 01:10
12-Jul-2006 01:10
Here is another payment function with working future value($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 07:07
07-Jul-2006 07:07
@ Moikboy:
This may or may not be more simplified factorialization:
<?php
$f=$fact=25;
while ($fact>0)
{$f=$f*$fact--;}
echo $f;
?>
marasek.SPAMLESS at telton.de
08-Jun-2006 03:23
08-Jun-2006 03:23
I could not resist to do a simpler version of the ordinal function:
<?php
function ordinal($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 $num is empty too.
moikboy (nospam!) moikboy (nospam!) hu
10-May-2006 11:15
10-May-2006 11:15
I think, this is the optimal code for calculating factorials:
<?php
function fact($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[$int];
};
?>
nessthehero at comcast dot net
22-Mar-2006 12:48
22-Mar-2006 12:48
Just a simple function to find the ordinal ending to any number if you're printing for example: "The nth result is..."
function ordinal($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 $string;
}
Florian
03-Mar-2006 11:36
03-Mar-2006 11:36
A function that simulates the sum operator. (http://en.wikipedia.org/wiki/Sum). Be careful with the expression because it may cause a security hole; note the single quotes to don't parse the "$".
<?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 11:39
17-Feb-2006 11:39
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 $return;
}
?>
peter-stangl at t-online dot de
02-Feb-2006 01:16
02-Feb-2006 01:16
I needed to approximate an integral because i was not able to calculate it, so i wrote this function. It approximates an integral with the composite Simpson's rule.
More information on Simpson's rule: http://en.wikipedia.org/wiki/Simpson%27s_rule
<?php
function simpsonf($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 08:01
01-Dec-2005 08:01
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
27-Oct-2005 12:27
27-Oct-2005 12:27
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 04:37
18-Oct-2005 04:37
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 05:50
27-Jul-2005 05:50
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 $median;
}
?>
bjcffnet at gmail dot com
27-Jul-2005 02:57
27-Jul-2005 02:57
thearbitcouncil at gmail dot com, you could just use array_sum():
<?php
function average($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 10:48
01-Jun-2005 10:48
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 06:41
11-Mar-2005 06:41
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 10:42
19-Feb-2005 10:42
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 $out;
}
?>
thearbitcouncil at gmail dot com
07-Jan-2005 12:32
07-Jan-2005 12:32
Two functions I didn't find elsewhere... one to compute mean of an array of numbers, and another to computer variance of a sample of numbers. Both take an array of numbers as arguments. Not much error checking, or optimization...
(note: variance function uses the average function...)
<?php
function average($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 02:34
17-Nov-2004 02:34
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 07:05
25-Sep-2004 07:05
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 03:58
16-Sep-2004 03:58
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 05:36
09-Jun-2004 05:36
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: ".$finalMul;
}
?>
I know this is not optimal but i've done this quick :)
If you guys have any comment just email me.
I also want to do this fonction In C to add to phpCore maybe soon...
Patoff
moc.erawtfostym@evad
27-May-2004 05:04
27-May-2004 05:04
The fastest O(1) factorial function has a lookup table of all the factorials that fit within the output range. With an array of the first 34 (float) or 170 (double) factorials, you get identical results in a fraction of the time.
churkl at hotmail dot com
26-May-2004 11:32
26-May-2004 11:32
Here is my factorial function which i think is very simple and without any confusion. email me comments if you like if i had something wrong.
<?php
function factorial($number)
{
$temp = 1;
while ($number > 1){
$temp *= $number--;
}
return $temp;
}
?>
ausvald at tut dot by
01-May-2004 03:48
01-May-2004 03:48
I see there are some factorial functions below.
I'll provide the best one:
<?
function factorial($n){ $n=(int)$n;
$f=1;
for(;$n>0;--$n) $f*=$n;
return $f;
}
?>
florian at shellfire dot de
29-Apr-2004 12:48
29-Apr-2004 12:48
Please note that shorter is not always better
(meaning that really short faculty implementation above).
In my opinion, a clearer way to code this is, including a check
for negative or non-integer values.
In order to calculate the faculty of a positive integer,
an iterative way (which might be harder to understand)
is usually a bit faster, but I am using it only for small
values so it is not really important to me:
<?php
// Calculate the Faculty of a positive int-value
function iFaculty($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 11:47
13-Jan-2004 11:47
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 07:37
07-Oct-2003 07:37
to "convert" scientific notation to a float simply cast it:
<?php
$val = '3.5e4';
$val = (float) $val;
echo $val;
?>
output:
35000
jl85 at yahoo dot com
05-Oct-2003 02:00
05-Oct-2003 02:00
Here's yet another greatest common denominator (gcd) function, a reeeeally small one.
function gcd($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,$m));
}
fabien_mornand at yahoo dot fr
01-Oct-2003 01:46
01-Oct-2003 01:46
here is an algorithm to calculate gcd of a number. This is Euclid algorithm i was studying in Maths. I've converted it in php for the fun.
<?php
if($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 06:07
27-Aug-2003 06:07
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 $num % 2 would work as well i think :).
matthew_gaddis at yahoo dot com
25-Apr-2003 12:23
25-Apr-2003 12:23
Here is a cleaner factorial function:
function factorial($s){
if($s) $r = $s * factorial($s - 1);
else $r = 1;
return $r;
}