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exp

(PHP 4, PHP 5)

expCalculates the exponent of e

Description

float exp ( float $arg )

Returns e raised to the power of arg.

Note: 'e' is the base of the natural system of logarithms, or approximately 2.718282.

Parameters

arg

The argument to process

Return Values

'e' raised to the power of arg

Examples

Example #1 exp() example

<?php
echo exp(12) . "\n";
echo 
exp(5.7);
?>

The above example will output:

1.6275E+005
298.87

See Also

  • log() - Natural logarithm
  • pow() - Exponential expression


User Contributed Notes
exp
Nitrogen
24-Sep-2009 12:54
Just a note about using the submitted codes below..
Their functions have an optional $precision parameter; however, it's not being used properly..

BCMath functions by default do not use decimal precision unless specified by BCScale($precision); or using the extra parameter in the used BC functions.

For example, a blank PHP file with their code.. executing BCExp('5.7'); returns "47" instead of the correct answer of "298.86740096706..."

So for optimum accuracy, I'd suggest setting BCScale to a healthy length before running their codes.
konrad
24-Jan-2007 11:13
working version (checked) of below code is

<?php
 
// see bccomp for this code (signed and unsigned zero!)
 
function bccomp_zero($amount) {
    return
bccomp($amount, (@$amount{0}=="-"?'-':'').'0.0');
  }

 
// arbitrary precision function (x^n)/(n)!
 
function bcpowfact($x, $n) {
    if (
bccomp_zero($n) == 0) return '1';
    if (
bccomp($n, '1') == 0) return $x;
   
$a = $x; // 1st step: a *= x / 1
   
$i = $n;
    while (
bccomp($i, '1') == 1) {
     
// ith step: a *= x / i
     
$a = bcmul($a, bcdiv($x, $i));
     
$i = bcsub($i, '1'); // bc idiom for $i--
   
}
    return
$a;
  }

 
// arbitrary precision exp() function
 
function bcexp($x, $digits) {
   
$sum = $prev_sum = '0.0';
   
$error = '0.'.str_repeat('0', $digits-1).'1'; // 0.1*10^-k
   
$n = '0.0';
    do {
     
$prev_sum = $sum;
     
$sum = bcadd($sum, bcpowfact($x, $n));
     
$n = bcadd($n, '1'); // bc idiom for $n++
   
} while (bccomp(bcsub($sum, $prev_sum), $error) == 1);
    return
$sum;
  }
?>
boards at gmail dot com
26-Apr-2006 05:18
Note regarding the mathematical function exp(x):

To continue accuracy of the exponential function to an infinite amount of decimal places, one would use the power series definition for exp(x).
(in LaTeX form:)
e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}

So, to do that in PHP (using BC math):

<?php
// arbitrary precision function (x^n)/(n)!
function bcpowfact($x, $n) {
  if (
bccomp($n, '0') == 0) return '1.0';
  if (
bccomp($n, '1') == 1) return $x;
 
$a = $x; // nth step: a *= x / 1
 
$i = $n;
  while (
bccomp($i, '1') == 1) {
   
// ith step: a *= x / i
   
$a = bcmul($a, bcdiv($x, $i));
   
$i = bcsub($i, '1'); // bc idiom for $i--
 
}
  return
$a;
}

// arbitrary precision exp() function
function bcexp($x, $decimal_places) {
 
$sum = $prev_sum = '0.0';
 
$error = bcdiv(bcpow('10', '-'.$decimal_places), 10); // 0.1*10^-k
 
$n = '0';
  do {
   
$prev_sum = $sum;
   
$sum = bcadd($sum, bcpowfact($x, $n));
  }
  while (
bccomp(bcsub($sum, $prev_sum), $error) == 1);
  return
$sum;
}
?>
info at teddycaddy dot com
16-Sep-2004 01:55
This only returns the first 51 digits after the decimal point.
 

 
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