Continued fraction/Arithmetic/Construct from rational number: Difference between revisions

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3141592653589793 / 1000000000000000 : 3 7 15 1 292 1 1 1 2 1 3 1 14 4 2 3 1 12 5 1 5 20 1 11 1 1 1 2 ok</pre>
3141592653589793 / 1000000000000000 : 3 7 15 1 292 1 1 1 2 1 3 1 14 4 2 3 1 12 5 1 5 20 1 11 1 1 1 2 ok</pre>




=={{header|Fortran}}==
<syntaxhighlight lang="f90">
program r2cf_demo
implicit none

call write_r2cf (1, 2)
call write_r2cf (3, 1)
call write_r2cf (23, 8)
call write_r2cf (13, 11)
call write_r2cf (22, 7)
call write_r2cf (-151, 77)

call write_r2cf (14142, 10000)
call write_r2cf (141421, 100000)
call write_r2cf (1414214, 1000000)
call write_r2cf (14142136, 10000000)

call write_r2cf (31, 10)
call write_r2cf (314, 100)
call write_r2cf (3142, 1000)
call write_r2cf (31428, 10000)
call write_r2cf (314285, 100000)
call write_r2cf (3142857, 1000000)
call write_r2cf (31428571, 10000000)
call write_r2cf (314285714, 100000000)

contains

! This implementation of r2cf both modifies its arguments and
! returns a value.
function r2cf (N1, N2) result (q)
integer, intent(inout) :: N1, N2
integer :: q

integer r

! We will use floor division, where the quotient is rounded
! towards negative infinity. Whenever the divisor is positive,
! this type of division gives a non-negative remainder.
r = modulo (N1, N2)
q = (N1 - r) / N2

N1 = N2
N2 = r
end function r2cf

subroutine write_r2cf (N1, N2)
integer, intent(in) :: N1, N2

integer :: digit, M1, M2
character(len = :), allocatable :: sep

write (*, '(I0, "/", I0, " => ")', advance = "no") N1, N2

M1 = N1
M2 = N2
sep = "["
do while (M2 /= 0)
digit = r2cf (M1, M2)
write (*, '(A, I0)', advance = "no") sep, digit
if (sep == "[") then
sep = "; "
else
sep = ", "
end if
end do
write (*, '("]")', advance = "yes")
end subroutine write_r2cf

end program r2cf_demo
</syntaxhighlight>

{{out}}
<pre>$ gfortran -std=f2018 continued-fraction-from-rational.f90 && ./a.out
1/2 => [0; 2]
3/1 => [3]
23/8 => [2; 1, 7]
13/11 => [1; 5, 2]
22/7 => [3; 7]
-151/77 => [-2; 25, 1, 2]
14142/10000 => [1; 2, 2, 2, 2, 2, 1, 1, 29]
141421/100000 => [1; 2, 2, 2, 2, 2, 2, 3, 1, 1, 3, 1, 7, 2]
1414214/1000000 => [1; 2, 2, 2, 2, 2, 2, 2, 3, 6, 1, 2, 1, 12]
14142136/10000000 => [1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 1, 2, 4, 1, 1, 2]
31/10 => [3; 10]
314/100 => [3; 7, 7]
3142/1000 => [3; 7, 23, 1, 2]
31428/10000 => [3; 7, 357]
314285/100000 => [3; 7, 2857]
3142857/1000000 => [3; 7, 142857]
31428571/10000000 => [3; 7, 476190, 3]
314285714/100000000 => [3; 7, 7142857]</pre>




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