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LI. Mathematische FunktionenEinleitung
Die mathematischen Funktionen behandeln nur Werte im Bereich der
Datentypen long und double der jeweiligen Architektur. Wenn Sie
gr��ere Zahlen oder Werte mit h�herer Genauigkeit ben�tigen,
sollten Sie sich die mathematische
Funktionen mit beliebiger Genauigkeit ansehen.
Mathematische Konstanten
Die folgenden Werte werden von diesem Packet definiert:
Tabelle 1. Mathematische Konstanten | Konstante | Wert | Beschreibung |
|---|
| M_PI | 3.14159265358979323846 | Der Wert � (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_2_SQRTPI | 1.12837916709551257390 | 2/sqrt(pi) | | M_SQRT2 | 1.41421356237309504880 | sqrt(2) | | M_SQRT1_2 | 0.70710678118654752440 | 1/sqrt(2) |
Bis auf M_PI sind diese Konstanten erst ab PHP4.0 verf�gbar.
- Inhaltsverzeichnis
- abs -- Absolutwert
- acos -- Arcuscosinus
- acosh -- Inverse hyperbolic cosine
- asin -- Arcussinus
- asinh -- Inverse hyperbolic sine
- atan2 -- Arcustangens aus zwei Werten
- atan -- Arcustangens
- atanh -- Inverse hyperbolic tangent
- base_convert -- Konvertiert Werte zwischen Zahlensystemen unterschiedlicher Basis
- bindec -- Bin�r zu dezimal Konvertierung
- ceil -- Aufrunden
- cos -- Cosinus
- cosh -- Hyperbolic cosine
- decbin -- Dezimal zu bin�r Konvertierung
- dechex -- Dezimal zu hexadezimal Konvertierung
- decoct -- Dezimal zu oktal Konvertierung
- deg2rad -- Grad in Bogenma� wandeln
- exp -- e hoch ...
- expm1 --
Returns exp(number) - 1, computed in a way that is accurate even
when the value of number is close to zero
- floor -- Abrunden
- fmod -- Returns the floating point remainder (modulo) of the division
of the arguments
- getrandmax -- Gr��tm�glicher Zufallswert
- hexdec -- Hexadezimal zu dezimal Konvertierung
- hypot --
Returns sqrt( num1*num1 + num2*num2)
- is_finite --
- is_infinite --
- is_nan --
- lcg_value -- Combined linear congruential generator
- log10 -- Zehner-Logarithmus
- log1p --
Returns log(1 + number), computed in a way that accurate even when the val
ue of number is close to zero
- log -- Nat�rlicher Logarithmus
- max -- Maximalwert bestimmen
- min -- Minimalwert bestimmen
- mt_getrandmax -- show largest possible random value
- mt_rand -- Erzeugt 'bessere' Zufallszahlen
- mt_srand -- seed the better random number generator
- octdec -- Oktal zu dezimal Konvertierung
- pi -- Wert von PI
- pow -- Exponentialfunktion
- rad2deg -- Bogenma� in Grad wandeln
- rand -- (Pseudo-) Zufallszahl generieren
- round -- Runden eines Wertes
- sin -- Sinus
- sinh -- Hyperbolic sine
- sqrt -- Quadratwurzel
- srand -- Startwert f�r den Zufallsgenerator festlegen
- tan -- Tangens
- tanh -- Hyperbolic tangent
User Contributed Notes
Mathematische Funktionen |
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cathody at mail dot ru
11-Aug-2000 02:55 |
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Converting non-standard form:
you can use something like
this:
$v=0.3e-9;
$v=sprintf ( "%2.9f", $v);
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ian at mp3 dot com
19-Feb-2001 10:43 |
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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){
$valid = 0;
}
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cornelius at skjoldhoej dot dk
12-Jun-2001 09:03 |
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I found that when dealing with tables, a 'least common multiple'
function is sometimes useful for abusing tablespan and the
likes.
So here goes (you may choose to remove the first part of
the gcd function if the function call is well-behaved):
function
gcd(n, m) //greatest common divisor
{
n=abs(n);
m=abs(m);
if (n==0 and m==0)
return 1; //avoid infinite
recursion
if (n==m and n>=1)
return n;
return
m<n?gcd(n-m,n):gcd(n,m-n);
}
function lcm(n, m) //least
common multiple
{
return m*(n/gcd(n,m));
}
This
may or may not be something to consider adding to the mathematical
function library.
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webkid%webkid.com
31-May-2002 10:49 |
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I found it kind of irritating that PHP had no native functionality for a
calculating Factorials. Since I really didn't feel like loading the GMP
library, I figured I'd write my own function.
function
fact($s){$r=(int)$s; for ($i=$r;$i--;$i>1){$r=$r*$i;} return
$r;}
I think that's right... I havn't tested it extensively but it
should work.
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webkid%webkid.com
31-May-2002 10:54 |
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And the reason I needed a Factorial function is because I there were no nPr
or nCr functions native to PHP, either.
function
n_pick_r($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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shanx at shanx dot com
08-Jul-2002 08:13 |
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<?
/**
* Function to calculate base36 values from a number.
Very
* useful if you wish to generate IDs from numbers.
*
*
@param $value The number
* @param $base The base to be applied (16,
36 or 64)
* @return The calculated string
* @author Shashank
Tripathi ([email protected])
* @version 0.1 - Let me know if something
doesnt work
*
*/
function base36($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);
?>
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lepkio at spanltd dot com
11-Jul-2002 12:13 |
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I couldn't have found mod function, but it is there as % sign. For
example; 6%3=0, 7%3=1 and so on.
Oliver Lepki
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patience at worldonline dot nl
05-Aug-2002 04:08 |
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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( $r );
}
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jbeardsl [found_at] gte [d0t] net
08-Nov-2002 08:15 |
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I was looking for a truncate function. Not finding one, I wrote my own.
Since it deals with everything as a number, I imagine it's faster than the
alternative of using string functions. HTH...
function truncate
($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)) /
$shift);
}
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jbeardsl at gte dot net
09-Nov-2002 05:36 |
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I needed a truncate function to operate on real numbers. I preferred not to
use a string-manipulation method, so here's my solution.
HTH...
function truncate ($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);
}
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nazgul26 (at_sign) windfox dot net
08-Dec-2002 09:58 |
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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>";
}
}
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php at casaforge dot com (Hal)
01-Feb-2003 12:25 |
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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
// get some numbers to play with
$x
= rand(0,130000)/10;
$y = rand(0,1200);
$z = rand(0,4)/64;
$array
= array($x, $x, $x, $y, $y, $z, 324.19, 425/7, sqrt(2), pi(),
pi());
// functions
function mult($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";}
}
// make a table
echo
'<table>';
$array = array_map("mult",
$array);
$array = (array_filter($array, strval)); //get rid of
zeros
$array = (array_count_values ($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>';
?>
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jl85 at yahoo dot com
22-Feb-2003 03:04 |
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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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jerry dot wilborn at fast dot net
16-Apr-2003 06:10 |
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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)
/ $sample_count), 2));
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matthew_gaddis at yahoo dot com
24-Apr-2003 09:23 |
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Here is a cleaner factorial function:
function
factorial($s){
if($s) $r = $s * factorial($s - 1);
else $r =
1;
return $r;
}
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