使用PHP/GMP计算整数的第n个根

问题描述

如何使用PHP/GMP计算整数的第n个根?

How can I calculate the n-th root of an integer using PHP/GMP?

尽管我在gmp_root(a, nth)的函数nofollow> PHP来源，似乎该功能尚未在任何发行版中发布*: http://3v4l.org/8FjU7

Although I found a function called gmp_root(a, nth) in the PHP source, it seems that this function has not been published in any release yet*: http://3v4l.org/8FjU7

*)5.6.0alpha2是撰写本文时的最新版本

*) 5.6.0alpha2 being the most recent one at the time of writing

推荐答案

原始来源:在PHP中使用bcmath计算第N个根–感谢和感谢 HamZa ！

Original source: Calculating Nth root with bcmath in PHP – thanks and credits to HamZa!

我已经重写了使用GMP而不是BCMath的代码:

I've rewritten the code to use GMP instead of BCMath:

function gmp_nth_root($num, $n) {
    if ($n < 1) return 0; // we want positive exponents
    if ($num <= 0) return 0; // we want positive numbers
    if ($num < 2) return 1; // n-th root of 1 or 2 give 1

    // g is our guess number
    $g = 2;

    // while (g^n < num) g=g*2
    while (gmp_cmp(gmp_pow($g, $n), $num) < 0) {
        $g = gmp_mul($g, 2);
    }
    // if (g^n==num) num is a power of 2, we're lucky, end of job
    if (gmp_cmp(gmp_pow($g, $n), $num) == 0) {
        return $g;
    }

    // if we're here num wasn't a power of 2 :(
    $og = $g; // og means original guess and here is our upper bound
    $g = gmp_div($g, 2); // g is set to be our lower bound
    $step = gmp_div(gmp_sub($og, $g), 2); // step is the half of upper bound - lower bound
    $g = gmp_add($g, $step); // we start at lower bound + step , basically in the middle of our interval

    // while step != 1

    while (gmp_cmp($step, 1) > 0) {
        $guess = gmp_pow($g, $n);
        $step = gmp_div($step, 2);
        $comp = gmp_cmp($guess, $num); // compare our guess with real number
        if ($comp < 0) { // if guess is lower we add the new step
            $g = gmp_add($g, $step);
        } else if ($comp == 1) { // if guess is higher we sub the new step
            $g = gmp_sub($g, $step);
        } else { // if guess is exactly the num we're done, we return the value
            return $g;
        }
    }

    // whatever happened, g is the closest guess we can make so return it
    return $g;
}

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