transform.php

<?php




function continued($x, $terms = 22, $rel_tol = 1e-9, $abs_tol = 0.0) {
    // Initialize, using Khinchin's notation
    $a = [];       // continued fraction terms
    $p = [0, 1];   // convergent numerator terms (-2 and -1 indices)
    $q = [1, 0];   // convergent denominator terms (-2 and -1 indices)
    $s = [];       // convergent terms
    $remainder = $x;

    // Collect the continued fraction and convergent terms
    for ($i = 0; $i < $terms; $i++) {
        // Compute the next terms
        $whole = floor($remainder);
        $frac = bcsub($remainder,$whole,20);
        $an = (int)$whole;
        /*if($i==16){
            $an=5;
        }*/
        $pn = $an * $p[count($p) - 1] + $p[count($p) - 2];
        $qn = $an * $q[count($q) - 1] + $q[count($q) - 2];
        $sn = [$pn,$qn];

        // Add terms to lists
        $a[] = $an;
        $p[] = $pn;
        $q[] = $qn;
        $s[] = $sn;

        // Convergence check
       /* if (is_close($x, floatval($sn), $rel_tol, $abs_tol)) {
            break;
        }*/

        // Get ready for next iteration
        $remainder = bcdiv(1,$frac,20);
    }

    // Return the tuple of the continued fraction and the convergents
    return [$a, $s];
}

print_r(continued('1.01964950736352181566869548344827172826353172896898'));
//print_r(continued('0.2312076819339227309219662514224185'));

//536870912
//526524956

//134217728
//131631239


//536870912/134217728