class Integer require 'backports/tools/arguments' require 'backports/2.1.0/bignum/bit_length' require 'backports/2.1.0/fixnum/bit_length' def self.sqrt(n) n = Backports.coerce_to_int(n) return Math.sqrt(n).to_i if n <= 9_999_899_999_899_999_322_536_673_279 bits_shift = n.bit_length/2 + 1 bitn_mask = root = 1 << bits_shift while true root ^= bitn_mask if (root * root) > n bitn_mask >>= 1 return root if bitn_mask == 0 root |= bitn_mask end end end unless Integer.respond_to? :sqrt