Continued fraction arithmetic
The purpose of this task is to write a function 





r
2
c
f


(

i
n
t



{\displaystyle {\mathit {r2cf}}(\mathrm {int} }

 




N

1


,

i
n
t



{\displaystyle N_{1},\mathrm {int} }

 




N

2


)


{\displaystyle N_{2})}

, or 





r
2
c
f


(

F
r
a
c
t
i
o
n



{\displaystyle {\mathit {r2cf}}(\mathrm {Fraction} }

 



N
)


{\displaystyle N)}

, which will output a continued fraction assuming:






N

1




{\displaystyle N_{1}}

 is the numerator





N

2




{\displaystyle N_{2}}

 is the denominator
The function should output its results one digit at a time each time it is called, in a manner sometimes described as lazy evaluation.

To achieve this it must determine: the integer part; and remainder part, of 




N

1




{\displaystyle N_{1}}

 divided by 




N

2




{\displaystyle N_{2}}

. It then sets 




N

1




{\displaystyle N_{1}}

 to 




N

2




{\displaystyle N_{2}}

 and 




N

2




{\displaystyle N_{2}}

 to the determined remainder part. It then outputs the determined integer part. It does this until 




a
b
s

(

N

2


)


{\displaystyle \mathrm {abs} (N_{2})}

 is zero.

Demonstrate the function by outputing the continued fraction for:

 1/2
 3
 23/8
 13/11
 22/7
 -151/77






2




{\displaystyle {\sqrt {2}}}

 should approach 



[
1
;
2
,
2
,
2
,
2
,
…
]


{\displaystyle [1;2,2,2,2,\ldots ]}

 try ever closer rational approximations until boredom gets the better of you:

 14142,10000
 141421,100000
 1414214,1000000
 14142136,10000000
Try :

 31,10
 314,100
 3142,1000
 31428,10000
 314285,100000
 3142857,1000000
 31428571,10000000
 314285714,100000000
Observe how this rational number behaves differently to 





2




{\displaystyle {\sqrt {2}}}

 and convince yourself that, in the same way as 



3.7


{\displaystyle 3.7}

 may be represented as 



3.70


{\displaystyle 3.70}

 when an extra decimal place is required, 



[
3
;
7
]


{\displaystyle [3;7]}

 may be represented as 



[
3
;
7
,
∞
]


{\displaystyle [3;7,\infty ]}

 when an extra term is required.

// version 1.1.2
// compile with -Xcoroutines=enable flag from command line
 
import kotlin.coroutines.experimental.buildSequence
 
fun r2cf(frac: Pair<Int, Int>) =
    buildSequence {
        var num = frac.first
        var den = frac.second
        while (Math.abs(den) != 0) {
            val div = num / den
            val rem = num % den
            num = den
            den = rem
            yield(div)
        }
    }
 
fun iterate(seq: Sequence<Int>) {
    for (i in seq) print("$i ")
    println()
}
 
fun main(args: Array<String>) {
    val fracs = arrayOf(1 to 2, 3 to 1, 23 to 8, 13 to 11, 22 to 7, -151 to 77)
    for (frac in fracs) {
        print("${"%4d".format(frac.first)} / ${"%-2d".format(frac.second)} = ")
        iterate(r2cf(frac))
    }
    val root2 = arrayOf(14142 to 10000, 141421 to 100000,
                        1414214 to 1000000, 14142136 to 10000000)
    println("\nSqrt(2) ->")
    for (frac in root2) {
        print("${"%8d".format(frac.first)} / ${"%-8d".format(frac.second)} = ")
        iterate(r2cf(frac))
    }
    val pi = arrayOf(31 to 10, 314 to 100, 3142 to 1000, 31428 to 10000,
                     314285 to 100000, 3142857 to 1000000,
                     31428571 to 10000000, 314285714 to 100000000)
    println("\nPi ->")
    for (frac in pi) {
        print("${"%9d".format(frac.first)} / ${"%-9d".format(frac.second)} = ")
        iterate(r2cf(frac))
    }
}