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Added root, pow, max, min, loopforeach functions and tests.
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danogentili
Daniil Gentili
parent
c12500cace
commit
7cf300984c
@ -3674,4 +3674,241 @@ class BigInteger
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// self::$base === 31
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return ($x - ($x % $y)) / $y;
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}
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/**
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* Calculates the nth root of a biginteger.
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*
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* Returns the nth root of a positive biginteger, where n defaults to 2
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*
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* Here's an example:
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* <code>
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* <?php
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* $a = new \phpseclib\Math\BigInteger('625');
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*
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* $root = $a->root();
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*
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* echo $root->toString(); // outputs 25
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* ?>
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* </code>
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*
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* @param \phpseclib\Math\BigInteger $n
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* @access public
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* @return \phpseclib\Math\BigInteger
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*
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* @internal This function is based off of {@link http://mathforum.org/library/drmath/view/52605.html this page} and {@link http://stackoverflow.com/questions/11242920/calculating-nth-root-with-bcmath-in-php this stackoverflow question}.
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*/
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function root($n = null)
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{
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$one = new static(1);
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$two = new static(2);
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if ($n === null) {
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$n = $two;
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}
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if ($n->compare($one) == -1) {
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return new static(0);
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} // we want positive exponents
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if ($this->compare($one) == -1) {
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return new static(0);
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} // we want positive numbers
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if ($this->compare($two) == -1) {
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return $one;
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} // n-th root of 1 or 2 is 1
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$root = new static();
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switch (MATH_BIGINTEGER_MODE) {
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case self::MODE_BCMATH:
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// g is our guess number
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$g = 2;
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// while (g^n < num) g=g*2
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while (bccomp(bcpow($g, $n->value), $this->value) == -1) {
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$g = bcmul($g, '2');
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}
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// if (g^n==num) num is a power of 2, we're lucky, end of job
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if (bccomp(bcpow($g, $n->value), $this->value) == 0) {
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$root->value = $g;
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break;
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}
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// if we're here num wasn't a power of 2 :(
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$og = $g; // og means original guess and here is our upper bound
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$g = bcdiv($g, '2'); // g is set to be our lower bound
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$step = bcdiv(bcsub($og, $g), '2'); // step is the half of upper bound - lower bound
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$g = bcadd($g, $step); // we start at lower bound + step , basically in the middle of our interval
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// while step!=1
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while (bccomp($step, '1') == 1) {
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$guess = bcpow($g, $n);
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$step = bcdiv($step, '2');
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$comp = bccomp($guess, $this->value); // compare our guess with real number
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if ($comp == -1) { // if guess is lower we add the new step
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$g = bcadd($g, $step);
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} elseif ($comp == 1) { // if guess is higher we sub the new step
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$g = bcsub($g, $step);
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} else { // if guess is exactly the num we're done, we return the value
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$root->value = $g;
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break;
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}
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}
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// whatever happened, g is the closest guess we can make so return it
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$root->value = $g;
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break;
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case self::MODE_GMP:
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if (function_exists('gmp_root')) {
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$root->value = gmp_root($this->value, gmp_intval($n->value));
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break;
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}
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default:
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// g is our guess number
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$g = $two;
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// while (g^n < num) g=g*2
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while ($g->pow($n)->compare($this) == -1) {
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$g = $g->multiply($two);
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}
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// if (g^n==num) num is a power of 2, we're lucky, end of job
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// == 0 bccomp(bcpow($g,$n), $n->value)==0
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if ($g->pow($n)->equals($this)) {
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$root = $g;
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break;
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}
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// if we're here num wasn't a power of 2 :(
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$og = $g; // og means original guess and here is our upper bound
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$g = $g->divide($two)[0]; // g is set to be our lower bound
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$step = $og->subtract($g)->divide($two)[0]; // step is the half of upper bound - lower bound
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$g = $g->add($step); // we start at lower bound + step , basically in the middle of our interval
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// while step!=1
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while ($step->compare($one) == 1) {
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$guess = $g->pow($n);
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$step = $step->divide($two)[0];
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$comp = $guess->compare($this); // compare our guess with real number
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if ($comp == -1) { // if guess is lower we add the new step
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$g = $g->add($step);
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} elseif ($comp == 1) { // if guess is higher we sub the new step
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$g = $g->subtract($step);
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} else { // if guess is exactly the num we're done, we return the value
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$root = $g;
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break;
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}
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}
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// whatever happened, g is the closest guess we can make so return it
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$root = $g;
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break;
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}
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return $this->_normalize($root);
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}
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/**
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* Performs exponentiation.
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*
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*
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* @param \phpseclib\Math\BigInteger $n
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* @access public
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* @return \phpseclib\Math\BigInteger
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*/
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function pow($n)
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{
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$zero = new static(0);
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if ($n->compare($zero) == 0) {
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return new static(1);
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} // n^0 = 1
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$res = new static();
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switch (MATH_BIGINTEGER_MODE) {
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case self::MODE_GMP:
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$res->value = gmp_pow($this->value, gmp_intval($n->value));
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return $this->_normalize($res);
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case self::MODE_BCMATH:
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$res->value = bcpow($this->value, $n->value);
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return $this->_normalize($res);
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default:
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$one = new static(1);
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$res = $this;
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while (!$n->equals($one)) {
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$res = $res->multiply($this);
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$n = $n->subtract($one);
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}
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return $res;
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break;
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}
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}
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/**
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* Return the minimum BigInteger between two BigIntegers.
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*
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*
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* @param \phpseclib\Math\BigInteger $a
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* @param \phpseclib\Math\BigInteger $b
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* @access public
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*
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*
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* @return \phpseclib\Math\BigInteger
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*/
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function min($b)
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{
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if ($this->compare($b) == '1') {
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return $b;
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}
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return $this;
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}
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/**
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* Return the maximum BigInteger between two BigIntegers.
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*
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*
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* @param \phpseclib\Math\BigInteger $b
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* @access public
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*
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* @return \phpseclib\Math\BigInteger
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*/
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function max($b)
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{
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if ($this->compare($b) == '1') {
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return $this;
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}
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return $b;
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}
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/**
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* Execute a function n times, where n is the current BigInteger.
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* The passed function must accept a paremeter that will be set to the the current number
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* (that number will range from zero to BigInteger - 1 if the BigInteger is positive, and from BigInteger - 1 to zero if the BigInteger is negative).
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* You can also set it to accept an optional parameter, that will be equal to the optional $userdata parameter.
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*
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* @access public
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* @param callable $function
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* @param &$userdata
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*
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* @return \phpseclib\Math\BigInteger
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*/
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function loopforeach(callable $function, &$userdata = null)
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{
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if ($this->compare(new static(0)) < 0) { // negative
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$limit = new static(-PHP_INT_MAX - 1);
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$one = new static(-1);
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} else { // positive
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$limit = new static(PHP_INT_MAX);
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$one = new static(1);
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}
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if ($this->compare($limit) == -((int) $one->toString())) {
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$oneint = (int) $one->toString();
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$thisint = (int) $this->toString();
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for ($loop = 0; $loop != $thisint; $loop += $oneint) {
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$function($loop, $userdata);
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}
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} else {
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for ($loop = new static(0); !$loop->equals($this); $loop = $loop->add($one)) {
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$function((string) $loop, $userdata);
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}
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}
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}
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}
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@ -380,4 +380,105 @@ abstract class Unit_Math_BigInteger_TestCase extends PhpseclibTestCase
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$n = $this->getInstance(2);
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$x->powMod($e, $n);
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}
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public function testRoot()
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{
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$bigInteger = new \phpseclib\Math\BigInteger('64000000'); // (20^2)^3
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$three = new \phpseclib\Math\BigInteger('3');
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$bigInteger = $bigInteger->root();
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$this->assertSame('8000', (string) $bigInteger);
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$bigInteger = $bigInteger->root($three);
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$this->assertSame('20', (string) $bigInteger);
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}
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public function testPow()
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{
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$bigInteger = new \phpseclib\Math\BigInteger('20');
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$two = new \phpseclib\Math\BigInteger('2');
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$three = new \phpseclib\Math\BigInteger('3');
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$bigInteger = $bigInteger->pow($two);
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$this->assertSame('400', (string) $bigInteger);
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$bigInteger = $bigInteger->pow($three);
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$this->assertSame('64000000', (string) $bigInteger); // (20^2)^3
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}
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public function testMax()
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{
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$min = new \phpseclib\Math\BigInteger('20');
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$max = new \phpseclib\Math\BigInteger('20000');
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$this->assertSame((string) $max, (string) $min->max($max));
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$this->assertSame((string) $max, (string) $max->max($min));
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}
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public function testMin()
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{
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$min = new \phpseclib\Math\BigInteger('20');
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$max = new \phpseclib\Math\BigInteger('20000');
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$this->assertSame((string) $min, (string) $min->min($max));
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$this->assertSame((string) $min, (string) $max->min($min));
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}
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public function testLoopForeach()
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{
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$maxBigInteger = new \phpseclib\Math\BigInteger('34');
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$one = new \phpseclib\Math\BigInteger('1');
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$vars = [];
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$maxBigInteger->loopforeach(
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function ($i, &$vars) {
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if ($i == 0) {
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$vars['first'] = $i;
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} else {
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$vars['last'] = $i;
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}
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},
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$vars
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);
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$this->assertSame(0, $vars['first']);
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$this->assertSame(33, $vars['last']);
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/* Nope, too slow
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$maxBigInteger = new \phpseclib\Math\BigInteger(PHP_INT_MAX);
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$maxBigInteger = $maxBigInteger->add($one);
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$maxBigInteger->loopforeach(
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function ($i, &$vars) {
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if ($i == 0) {
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$vars["first"] = $i;
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} else {
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$vars["last"] = $i;
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}
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},
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$vars
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);
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$this->assertSame("0", $vars["first"]);
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$this->assertSame((string)$maxBigInteger->subtract($one), $vars["last"]);*/
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$maxBigInteger = new \phpseclib\Math\BigInteger(-34);
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$maxBigInteger->loopforeach(
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function ($i, &$vars) {
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if ($i == 0) {
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$vars['first'] = $i;
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} else {
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$vars['last'] = $i;
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}
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},
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$vars
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);
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$this->assertSame(0, $vars['first']);
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$this->assertSame(-33, $vars['last']);
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/* Nope, too slow
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$maxBigInteger = new \phpseclib\Math\BigInteger(-PHP_INT_MAX - 1);
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$maxBigInteger = $maxBigInteger->subtract($one);
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$maxBigInteger->loopforeach(
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function ($i, &$vars) {
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if ($i == 0) {
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$vars["first"] = $i;
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} else {
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$vars["last"] = $i;
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}
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},
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$vars
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);
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$this->assertSame("0", $vars["first"]);
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$this->assertSame((string)$maxBigInteger->add($one), $vars["last"]);*/
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}
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}
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