exp

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

    exp — Calculates the exponent of e

    Description

    exp(float $num): float

    Returns e raised to the power of num.

    Note:

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

    Parameters

    num

    The argument to process

    Return Values

    'e' raised to the power of num

    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

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    User Contributed Notes 4 notes

    up
    3
    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./
    up
    0
    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;
    }
    ?>
    up
    -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;
    }
    ?>
    up
    -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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