exp

(PHP 4, PHP 5, PHP 7, PHP 8)

exp — e の累乗を計算する

説明

exp(float $num): float

e を num 乗した値を返します。

注意:
'e' は自然対数の底で、およそ 2.718282 です。

パラメータ

num: 処理する引数。

戻り値

'e' の num 乗を返します。

例

例1 exp() の例

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

上の例の出力は以下となります。

1.6275E+005
298.87

参考

log() - 自然対数
pow() - 指数表現

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User Contributed Notes 4 notes

down

zooly at globmi dot com ¶

13 years ago

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./

down

boards at gmail dot com ¶

18 years ago

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;
}
?>

down

-3

konrad ¶

17 years ago

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;
  }
?>

down

-5

Nitrogen ¶

15 years ago

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.

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