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LVII. 数学関数(Math)
これらの数学関数は、実行するコンピューターの倍精度整数(long)およ
び倍精度実数(double)の範囲でのみ値を処理します。より大きな数を処
理する必要がある場合には、任意精度数学関数
の使用をお勧めします。
以下の値は PHP の数学拡張機能により定数として定義されています。
表 1. 数学定数 | 定数 | 値 | 説明 |
|---|
| M_PI | 3.14159265358979323846 | 円周率 (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 | オイラー定数 [4.0.2] |
PHP 4RC1までのバージョンのPHPでは、M_PIのみが使用可能です。他の全
ての定数は、PHP 4.0 で使用可能となりました。[4.0.2] とラベルのつい
た定数はPHP 4のCVSコードでのみ使用可能です。
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,$prec=2){
if ($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) {
$out = 1;
for ($i = 2; $i <= $in; $i++) {
$out *= $i;
}
return $out;
}
?>
joogat at hotmail dot com
04-Feb-2005 02:35
factorial:
function f($_){return $_?$_*f(--$_):1;}
thearbitcouncil at gmail dot com
06-Jan-2005 10:32
Two functions I didn't find elsewhere... one to compute mean of an array of numbers, and another to computer variance of a sample of numbers. Both take an array of numbers as arguments. Not much error checking, or optimization...
(note: variance function uses the average function...)
<?php
function average($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);
$sos = 0; for ($i = 0; $i < count($arr); $i++)
{
$sos += ($arr[$i] - $mean) * ($arr[$i] - $mean);
}
return $sos / (count($arr)-1); }
echo variance(array(4,6,23,15,18)); ?>
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
<?
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 $polar;
}
else return false;
}
function polar2rect($r,$theta)
{
if(is_numeric($r)&&is_numeric($theta))
{
$x=$r*cos($theta);
$y=$r*sin($theta);
$rect=array("x"=>$x,"y"=>$y);
}
else
{
return false;
}
}
?>
help at gjbdesign dot com
25-Sep-2004 04:05
Occasionally a user must enter a number in a form. This function converts fractions to decimals and leaves decimals untouched. Of course, you may wish to round the final output, but that is not included here.
<?php
function Deci_Con($q){
if(strstr($q, ' ')){
$wa = strrev($q);
$wb = strrev(strstr($wa, ' '));
$whole = true;}
if(strstr($q, '/')){
if($whole==true){$q = strstr($q, ' ');
}
$b = str_replace("/","",strstr($q, '/'));$c = strrev($q);
$d = strstr($c, '/');
$e = strrev($d);
$a = str_replace("/","",$e);if($whole==true){$a = $a+($wb*$b);}
$q = $a/$b;return $q;
}else{
return $q;}
}?>
donnieb819 at hotmail dot NOSPAM dot com
16-Sep-2004 12:58
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;
for( $i = 0, $ix = strlen( $decimal ); $i < $ix; $i++ )
{
if( $dec ) $den *= 10;
if( $decimal{$i} == '.' ) $dec = true;
else $num .= $decimal{$i};
}
$num = (int)$num;
if( $den == 1 ) return $num;
$num2 = $num;
$den2 = $den;
$rem = 1;
while( $num2 % $den2 ) {
$rem = $num2 % $den2;
$num2 = $den2;
$den2 = $rem;
}
if( $den2 != $den ) $rem = $den2;
return ($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 02:36
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); $i++)
{
if($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)
{
$final .= $equa{$i}."*";
}
elseif(is_numeric($equa{$i}) && $i > 0 && $equa{$i-1} != "^")
{
$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};
}
}
}
$finalMul = "";
for($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: ".$finalMul;
}
?>
I know this is not optimal but i've done this quick :)
If you guys have any comment just email me.
I also want to do this fonction In C to add to phpCore maybe soon...
Patoff
moc.erawtfostym@evad
27-May-2004 02:04
The fastest O(1) factorial function has a lookup table of all the factorials that fit within the output range. With an array of the first 34 (float) or 170 (double) factorials, you get identical results in a fraction of the time.
churkl at hotmail dot com
26-May-2004 08:32
Here is my factorial function which i think is very simple and without any confusion. email me comments if you like if i had something wrong.
<?php
function factorial($number)
{
$temp = 1;
while ($number > 1){
$temp *= $number--;
}
return $temp;
}
?>
ausvald at tut dot by
01-May-2004 12:48
I see there are some factorial functions below.
I'll provide the best one:
<?
function factorial($n){ $n=(int)$n;
$f=1;
for(;$n>0;--$n) $f*=$n;
return $f;
}
?>
florian at shellfire dot de
28-Apr-2004 09:48
Please note that shorter is not always better
(meaning that really short faculty implementation above).
In my opinion, a clearer way to code this is, including a check
for negative or non-integer values.
In order to calculate the faculty of a positive integer,
an iterative way (which might be harder to understand)
is usually a bit faster, but I am using it only for small
values so it is not really important to me:
<?php
function iFaculty($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 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 04:37
to "convert" scientific notation to a float simply cast it:
<?php
$val = '3.5e4';
$val = (float) $val;
echo $val;
?>
output:
35000
jl85 at yahoo dot com
05-Oct-2003 11:00
Here's yet another greatest common denominator (gcd) function, a reeeeally small one.
function gcd($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,$m));
}
fabien_mornand at yahoo dot fr
30-Sep-2003 10:46
here is an algorithm to calculate gcd of a number. This is Euclid algorithm i was studying in Maths. I've converted it in php for the fun.
<?php
if($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 03:07
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 $num % 2 would work as well i think :).
matthew_gaddis at yahoo dot com
24-Apr-2003 09:23
Here is a cleaner factorial function:
function factorial($s){
if($s) $r = $s * factorial($s - 1);
else $r = 1;
return $r;
}
jerry dot wilborn at fast dot net
16-Apr-2003 06:10
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
$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 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 $simpl_fract;
function decimalToFraction($decimal,$count,$result) {
$a = (1/$decimal);
$b = ( $a - floor($a) );
$count++;
if ($b > .01 && $count <= 5) decimalToFraction($b,$count,&$result);
$result[$count] = floor($a);
}
function simplifyFraction($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) {
$shift = pow(10, $digits);
return ((floor($num * $shift)) / $shift);
}
?>
patience at worldonline dot nl
05-Aug-2002 04:08
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( $r );
}
?>
shanx at shanx dot com
08-Jul-2002 08:13
<?
function base36($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($newval);
}
echo "The string for 46655, for instance, is " . base36(46655, 36);
?>
webkid%webkid.com
31-May-2002 10:54
And the reason I needed a Factorial function is because I there were no nPr or nCr functions native to PHP, either.
function n_pick_r($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($r));}
Hope that helps someone!
webkid%webkid.com
31-May-2002 10:49
I found it kind of irritating that PHP had no native functionality for a calculating Factorials. Since I really didn't feel like loading the GMP library, I figured I'd write my own function.
function fact($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 09:03
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) {
n=abs(n); m=abs(m);
if (n==0 and m==0)
return 1; 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));
}
?>
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 02:55
Converting non-standard form:
you can use something like this:
<?php
$v=0.3e-9;
$v=sprintf ( "%2.9f", $v);
?>
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mailparse_uudecode_all
