3 

     4 // adding two binary strings very, very lazy manner

     5 

     6 def badd(s1: String, s2: String) : String = 

     7   (BigInt(s1, 2) + BigInt(s2, 2)).toString(2)

     8 

     9 

    10 // collatz function on binary numbers

    11 

    12 def bcollatz(s: String) : Long = (s.dropRight(1), s.last) match {

    13   case ("", '1') => 1                                  // we reached 1

    14   case (rest, '0') => 1 + bcollatz(rest)               // even number => divide by two

    15   case (rest, '1') => 1 + bcollatz(badd(s + '1', s))   // odd number => s + '1' is 2 * s + 1

    16                                                        //               add another s gives 3 * s + 1  

    17 } 

    18 

    19 bcollatz(9.toBinaryString)

    20 bcollatz(837799.toBinaryString)

    21 bcollatz(100000000000000000L.toBinaryString)

    22 bcollatz(BigInt("1000000000000000000000000000000000000000000000000000000000000000000000000000").toString(2))

    23 

    24 def conv(c: Char) : Int = c match {

    25   case '0' => 0

    26   case '1' => 1

    27 }

    28 

    29 def badds(s1: String, s2: String, carry: Int) : String = (s1, s2, carry) match {

    30   case ("", "", 1) => "1"

    31   case ("", "", 0) => ""

    32   case (cs1, cs2, carry) => (conv(cs1.last) + conv(cs2.last) + carry) match {

    33     case 3 => badds(cs1.dropRight(1), cs2.dropRight(1), 1) + '1'

    34     case 2 => badds(cs1.dropRight(1), cs2.dropRight(1), 1) + '0'

    35     case 1 => badds(cs1.dropRight(1), cs2.dropRight(1), 0) + '1'

    36     case 0 => badds(cs1.dropRight(1), cs2.dropRight(1), 0) + '0'

    37   }

    38 } 

    39 

    40 def bcollatz2(s: String) : Long = (s.dropRight(1), s.last) match {

    41   case ("", '1') => 1                                          // we reached 1

    42   case (rest, '0') => 1 + bcollatz2(rest)                      // even number => divide by two

    43   case (rest, '1') => 1 + bcollatz2(badds(s + '1', '0' + s, 0))   // odd number => s + '1' is 2 * s + 1

    44                                                                   //         add another s gives 3 * s + 1  

    45 } 

    46 

    47 bcollatz2(9.toBinaryString)

    48 bcollatz2(837799.toBinaryString)

    49 bcollatz2(100000000000000000L.toBinaryString)

    50 bcollatz2(BigInt("1000000000000000000000000000000000000000000000000000000000000000000000000000").toString(2))

    51