Continued fraction/Arithmetic/Construct from rational number

Continued fraction/Arithmetic/Construct from rational number
You are encouraged to solve this task according to the task description, using any language you may know.

To understand this task in context please see Continued fraction arithmetic

The purpose of this task is to write a function r2cf(int N1, int N2), or r2cf(Fraction N), which will output a continued fraction assuming:

N1 is the numerator

N2 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 N1 divided by N2. It then sets N1 to N2 and N2 to the determined remainder part. It then outputs the determined integer part. It does this until N2 is zero.

Demonstrate the function by outputing the continued fraction for:

1/2

3

23/8

13/11

22/7

${\sqrt {2}}$ should approach [1; 2, 2, 2, 2, ...] try ever closer rational approximations until bordom gets the better of you:

14142,10000

141421,100000

1414214,1000000

4142136,10000000

Demonstrate that this function may be used as generator a in [Continued fraction] and obtain a floating point value for 23/8, 13/11, and 22/7

Perl 6

Straightforward implementation: <lang perl 6>sub r2cf(Rat $x is copy) {

   gather while True {

$x -= take $x.Int; last unless $x > 0; $x = 1 / $x;

   }

}

say r2cf(Rat($_)) for <1/2 3 23/8 13/11 22/7 1.41 1.4142136>;</lang>

Output:

0 2
3
2 1 7
1 5 2
3 7
1 2 2 3 1 1 2
1 2 2 2 2 2 2 2 2 2 6 1 2 4 1 1 2

Ruby

=begin

 Generate a continued fraction from a rational number

 Nigel Galloway, February 4th., 2013

=end <lang ruby> def r2cf(n1,n2)

 while n2 > 0
   t1 = n1/n2; t2 = n2; n2 = n1 - t1 * n2; n1 = t2; yield t1 
 end

end </lang>

Testing

1/2 <lang ruby>r2cf(1,2) {|n| print "#{n} "}</lang>

Output:

0 2 

3

<lang ruby>r2cf(3,1) {|n| print "#{n} "}</lang>

Output:

3 

23/8 <lang ruby>r2cf(23,8) {|n| print "#{n} "}</lang>

Output:

2 1 7 

13/11 <lang ruby>r2cf(13,11) {|n| print "#{n} "}</lang>

Output:

1 5 2 

22/7 <lang ruby>r2cf(22,7) {|n| print "#{n} "}</lang>

Output:

3 7 

1.4142 <lang ruby>r2cf(14142,10000) {|n| print "#{n} "}</lang>

Output:

1 2 2 2 2 2 1 1 29 

1.4142 <lang ruby>r2cf(141421,100000) {|n| print "#{n} "}</lang>

Output:

1 2 2 2 2 2 2 3 1 1 3 1 7 2 

1.414214 <lang ruby>r2cf(1414214,1000000) {|n| print "#{n} "}</lang>

Output:

1 2 2 2 2 2 2 2 3 6 1 2 1 12 

1.4142136 <lang ruby>r2cf(14142136,10000000) {|n| print "#{n} "}</lang>

Output:

1 2 2 2 2 2 2 2 2 2 6 1 2 4 1 1 2