Funções Matemáticas

Índice

abs — Valor absoluto
acos — Arco cosseno
acosh — Arco cosseno hiperbólico
asin — Arco seno
asinh — Arco seno hiperbólico
atan — Arco tangente
atan2 — Arco tangente de duas variáveis
atanh — Arco tangente hiperbólico
base_convert — Converte um número entre bases arbitrárias
bindec — Binário para decimal
ceil — Arredonda frações para cima
cos — Cosseno
cosh — Cosseno hiperbólico
decbin — Decimal para binário
dechex — Decimal para hexadecimal
decoct — Decimal para octal
deg2rad — Converte o número em graus para o equivalente em radianos
exp — Calcula o expoente de e
expm1 — Retorna exp($num) - 1, computado de forma precisa mesmo quando o valor do número está próximo de zero.
fdiv — Divide dois números de acordo com a IEEE 754
floor — Arredonda frações para baixo
fmod — Retorna o resto (módulo) em ponto flutuante da divisão dos argumentos
hexdec — Hexadecimal para decimal
hypot — Calcula o comprimento da hipotenusa de triângulo retângulo
intdiv — Divisão de inteiros
is_finite — Verifica se um float é finito
is_infinite — Verifica se um float é infinito
is_nan — Verifica se um float é NAN
log — Logaritmo natural
log10 — Logaritmo na base 10
log1p — Retorna log(1 + número), calculado de forma que seja preciso mesmo quando o valor do número seja próximo de zero.
max — Localiza o maior valor
min — Encontra o menor valor
octdec — Octal para decimal
pi — Obtém o valor de pi
pow — Expressão exponencial
rad2deg — Converte o número em radianos para o equivalente em graus
round — Arredonda um float
sin — Seno
sinh — Seno hiperbólico
sqrt — Raiz quadrada
tan — Tangente
tanh — Tangente hiperbólica

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Notas Enviadas por Usuários (em inglês) 26 notes

down

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

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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!

down

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); 
}

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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;
 }
}
?>

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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/

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-1

php at keith tyler dot com ¶

14 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)));'
?>

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-1

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;
}

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-1

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') ) ) )

?>

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-1

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));    

    } 



?>

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-1

jordanolsommer at imap dot cc ¶

21 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 :).

down

-2

capripot at gmail dot com ¶

12 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.

down

-2

edward at edwardsun dot com ¶

18 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.

down

-2

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];
};
?>

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-2

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;
}
?>

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-3

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.

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-4

help at gjbdesign dot com ¶

20 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
    }
}?>

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-3

tembenite at gmail dot com ¶

18 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));
}

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-4

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!

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-4

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));

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-3

patience at worldonline dot nl ¶

22 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 );

}

?>

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-3

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);

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-3

jl85 at yahoo dot com ¶

21 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));
}

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-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;

}

?>

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-4

fabien_mornand at yahoo dot fr ¶

21 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;
?>

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-4

Aiden880 ¶

9 years ago

Lowest Common Denominator:
function lcd($num, $start) {
    while($num % $start != 0) {
        $start++;
    }
    return $start;
}

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-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;
}
?>

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