exp

说明

float exp ( float arg )

返回 e 的 arg 次方值。

注: 用 'e' 作为自然对数的底 2.718282.

例子 1. exp() 范例
<?php echo exp(12) . "\n"; echo exp(5.7); ?>
上例将输出：
1.6275E+005 298.87

参见 log() 和 pow()。

add a note User Contributed Notes

boards at gmail dot com
27-Apr-2006 01:18


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 09:55


This only returns the first 51 digits after the decimal point.

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