exp()

(PHP 4, PHP 5, PHP 7)

计算e的指数

说明

exp(float $arg):float

返回e的$arg次方值。

Note:

用'e'作为自然对数的底 2.718282.

参数

$arg

要处理的参数

返回值

'e' raised to the power of$arg

范例

Example #1exp()例子

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

以上例程会输出：

1.6275E+005
298.87

参见

• log() 自然对数
• pow() 指数表达式

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;
}
?>

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;
 }
?>

PHP does not have the following math function in any extensions:
frexp() - Extract Mantissa and Exponent of the Floating-Point Value
I've digged many C source codes, and found the simplest implementation as follows:
<?php
function frexp ( $float ) {
 $exponent = ( floor(log($float, 2)) + 1 );
 $mantissa = ( $float * pow(2, -$exponent) );
 return(
  array($mantissa, $exponent)
 );
}
print_r(frexp(0.0345));
print_r(frexp(21.539));
?>
Array
(
  [0] => 0.552
  [1] => -4
)
Array
(
  [0] => 0.67309375
  [1] => 5
)
I have compared the results using a lot of floats against C's frexp function - they are the same.
Note that C and PHP uses different float precisions, for example "4619.3" gives:
C: 0.56387939453125, 13
PHP: 0.563879394531, 13
/Assuming default configurations./

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.

Which is the inverse of log(float $arg, e)