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LII. Funzioni MatematicheRequisitiNon sono necessarie librerie esterne per utilizzare questo modulo. InstallazioneNon è necessaria nessuna installazione per usare queste
funzioni, esse fanno parte del core di PHP. Configurazione di RuntimeQuesta estensione non definisce
alcuna direttiva di configurazione in php.ini Tipi di risorseQuesta estensione non definisce alcun tipo di risorsa. Costanti predefinite
Le costanti qui elencate sono sempre disponibili in quanto parte del core di PHP.
Tabella 1. Costanti Matematiche | Costante | Valore | Descrizione |
|---|
| M_PI | 3.14159265358979323846 | Pi | | M_E | 2.7182818284590452354 | e | | M_LOG2E | 1.4426950408889634074 | log_2 e | | M_LOG10E | 0.43429448190325182765 | log_10 e | | M_LN2 | 0.69314718055994530942 | log_e 2 | | M_LN10 | 2.30258509299404568402 | log_e 10 | | M_PI_2 | 1.57079632679489661923 | pi/2 | | M_PI_4 | 0.78539816339744830962 | pi/4 | | M_1_PI | 0.31830988618379067154 | 1/pi | | M_2_PI | 0.63661977236758134308 | 2/pi | | M_SQRTPI | 1.77245385090551602729 | sqrt(pi) [4.0.2] | | M_2_SQRTPI | 1.12837916709551257390 | 2/sqrt(pi) | | M_SQRT2 | 1.41421356237309504880 | sqrt(2) | | M_SQRT3 | 1.73205080756887729352 | sqrt(3) [4.0.2] | | M_SQRT1_2 | 0.70710678118654752440 | 1/sqrt(2) | | M_LNPI | 1.14472988584940017414 | log_e(pi) [4.0.2] | | M_EULER | 0.57721566490153286061 | Costante di Eulero [4.0.2] |
Soltanto M_PI è disponibile nelle versioni precedenti alla PHP 4.0.0 (compresa).
Tutte le rimanenti costanti sono disponibili a partire dal PHP 4.0.0. Le costanti
indicate con [4.0.2] sono state aggiunte nel PHP 4.0.2.
- Sommario
- 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 Notes
Funzioni Matematiche
ausvald at tut dot by
30-Apr-2004 11:48
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 $f;
}
?>
florian at shellfire dot de
28-Apr-2004 08:48
Please note that shorter is not always better
(meaning that really short faculty implementation above).
In my opinion, a clearer way to code this is, including a check
for negative or non-integer values.
In order to calculate the faculty of a positive integer,
an iterative way (which might be harder to understand)
is usually a bit faster, but I am using it only for small
values so it is not really important to me:
<?php
function iFaculty($a_iFac)
{
if ($a_iFac > 0)
{
return $a_iFac * $this->iFaculty($a_iFac - 1);
}
elseif ($a_iFac == 0)
{
return 1;
}
else
{
return 0; }
}
?>
I've also written another function to calculate the
binomial coefficient of 2 values, I didn't find it anywhere yet so I hope it might help someone (works fine with the above stated faculty-function and ready to be used inside of your own classes!)
<?php
function iBinCoeff($a_iN, $a_iK)
{
return $this->iFaculty($a_iN) / ($this->iFaculty($a_iN - $a_iK) * $this->iFaculty($a_iK));
}
?>
Chronial "at" cyberpunkuniverse.de
13-Jan-2004 07:47
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 03:37
to "convert" scientific notation to a float simply cast it:
<?php
$val = '3.5e4';
$val = (float) $val;
echo $val;
?>
output:
35000
jl85 at yahoo dot com
05-Oct-2003 10:00
Here's yet another greatest common denominator (gcd) function, a reeeeally small one.
function gcd($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,$m));
}
fabien_mornand at yahoo dot fr
30-Sep-2003 09:46
here is an algorithm to calculate gcd of a number. This is Euclid algorithm i was studying in Maths. I've converted it in php for the fun.
<?php
if($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 02:07
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 $num % 2 would work as well i think :).
matthew_gaddis at yahoo dot com
24-Apr-2003 08:23
Here is a cleaner factorial function:
function factorial($s){
if($s) $r = $s * factorial($s - 1);
else $r = 1;
return $r;
}
jerry dot wilborn at fast dot net
16-Apr-2003 05:10
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) / $sample_count), 2));
jl85 at yahoo dot com
22-Feb-2003 02:04
Theres another faster way of doing even/odd number checking by using bitwise operators. Don't ask me how it works, I just found this out by experimenting with it (could the editor possibly explain?)
if ((1&$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)
31-Jan-2003 11:25
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
$x = rand(0,130000)/10;
$y = rand(0,1200);
$z = rand(0,4)/64;
$array = array($x, $x, $x, $y, $y, $z, 324.19, 425/7, sqrt(2), pi(), pi());
function mult($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";}
}
echo '<table>';
$array = array_map("mult", $array);
$array = (array_filter($array, strval)); $array = (array_count_values ($array));
krsort ($array);
while (list ($key, $val) = each ($array)) {
$key = $key/16;
echo "<tr><td>$val</td><td> @ </td><td align=\"right\">".intval($key)." </td><td> ".frac($key)." </td></tr>";
}
echo '</table>';
?>
nazgul26 (at_sign) windfox dot net
08-Dec-2002 08:58
This code will convert a decimal to it's fraction equivalent. The precision can be set by changing PRECISION.
-----------------------------------------------------------------
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 04:36
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)) / $shift);
}
jbeardsl [found_at] gte [d0t] net
08-Nov-2002 07:15
I was looking for a truncate function. Not finding one, I wrote my own. Since it deals with everything as a number, I imagine it's faster than the alternative of using string functions. HTH...
function truncate ($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 03:08
The example for Factorials given above is wrong. Here a correct version, so that you do not have to reinvent the wheel again...
function mathFact( $s )
{
$r = (int) $s;
if ( $r < 2 )
$r = 1;
else {
for ( $i = $r-1; $i > 1; $i-- )
$r = $r * $i;
}
return( $r );
}
shanx at shanx dot com
08-Jul-2002 07:13
<?
function base36($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($newval);
}
echo "The string for 46655, for instance, is " . base36(46655, 36);
?>
webkid%webkid.com
31-May-2002 09:54
And the reason I needed a Factorial function is because I there were no nPr or nCr functions native to PHP, either.
function n_pick_r($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($r));}
Hope that helps someone!
webkid%webkid.com
31-May-2002 09:49
I found it kind of irritating that PHP had no native functionality for a calculating Factorials. Since I really didn't feel like loading the GMP library, I figured I'd write my own function.
function fact($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 08:03
<P>I found that when dealing with tables, a 'least common multiple' function is sometimes useful for abusing tablespan and the likes.</P>
<P>So here goes (you may choose to remove the first part of the gcd function if the function call is well-behaved):</P>
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));
}
<P>This may or may not be something to consider adding to the mathematical function library.</P>
ian at mp3 dot com
19-Feb-2001 09:43
for those looking for a credit card verification function i wrote a simple LUHN Formula algorithm:
$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 01:55
Converting non-standard form:
you can use something like this:
$v=0.3e-9;
$v=sprintf ( "%2.9f", $v);
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mailparse_uudecode_all
