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<?php /** * Created by PhpStorm. * User: Mch * Date: 8/10/18 * Time: 23:51 * 只用位运算不用算数运算实现整数的 + - * / */ class Arithmetic { const MAX_INTEGER = 2147483647; const MIN_INTEGER = -2147483648; /** * @param int $a * @param int $b * @return int $a + $b; */ public static function add(int $a, int $b) : int { $sum = $a; while ($b) { $sum = $a ^ $b; // 不考虑进位 $b = ($a & $b) << 1; // 只考虑进位 $a = $sum; } return $sum; } /** * 相反数 <= 二进制表达取反+1(补码) * @param int $n * @return int */ private static function negateNumber(int $n) : int { return self::add(~$n, 1); } /** * a-b = a + (-b) * @param int $a * @param int $b * @return int */ public static function minus(int $a, int $b) : int { return self::add($a, self::negateNumber($b)); } /** * @param int $a * @param int $b * @return int $a * $b */ public static function multiple(int $a, int $b) : int { $res = 0; while ($b) { if (($b & 1)) { $res = self::add($res, $a); } $a <<= 1; $b >>= 1; } return $res; } private static function isNegative(int $n) : bool { return $n < 0; } /** * a/b a = MIN_INTEGER, b!=MIN_INTEGER ? * @param int $a * @param int $b * @return int */ private static function p(int $a, int $b) : int { $x = self::isNegative($a) ? self::negateNumber($a) : $a; $y = self::isNegative($b) ? self::negateNumber($b) : $b; $res = 0; for ($i = 31; $i >-1; $i = self::minus($i, 1)) { if (($x >> $i)>=$y) { $res |= (1 << $i); $x = self::minus($x, $y<<$i); } } return self::isNegative($a) ^ self::isNegative($b) ? self::negateNumber($res):$res; } /** * @param int $a * @param int $b * @return int $a / $b */ public static function pide(int $a, int $b) : int { if ($b === 0) { throw new RuntimeException("pisor is 0"); } if ($a === self::MIN_INTEGER && $b === self::MIN_INTEGER) { return 1; } else if ($b === self::MIN_INTEGER) { return 0; } else if ($a === self::MIN_INTEGER) { $res = self::p(self::add($a, 1), $b); return self::add($res, self::p(self::minus($a, self::multiple($res, $b)), $b)); } else { return self::p($a, $b); } } }
TEST:
echo Arithmetic::add(1, 2).PHP_EOL; // 3 echo Arithmetic::minus(10, 3).PHP_EOL; // 7 echo Arithmetic::multiple(5, 3).PHP_EOL; // 15 echo Arithmetic::pide(-2147483648, 1).PHP_EOL; // -2147483648 echo Arithmetic::pide(-15, 3).PHP_EOL; // -5
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