Data update

2026-04-30 12:34:36 -04:00 · 2026-04-30 12:34:36 -04:00 · cbaf4c4b64
commit cbaf4c4b64
parent 4bb20c9b71
12390 changed files with 318560 additions and 27248 deletions
--- a/Task/Farey-sequence/Fortran/farey-sequence.f
+++ b/Task/Farey-sequence/Fortran/farey-sequence.f
@ -0,0 +1,100 @@
+! Farey Sequence
+!
+! tested with Intel ifx (IFX) 2025.2.1 20250806             on Kubuntu 25.10
+!             GNU gfortran (Ubuntu 15.2.0-4ubuntu4)  15.2.0 on Kubuntu 25.10
+!             VSI Fortran x86-64 V8.7-001                   on OpenVMS V9.2-3
+! U.B., March 2026
+!
+program Farey
+
+implicit none
+
+! These variables are used in "contained" subtoutines and functions
+integer :: n,a,b,c,d    ! Order, and current 2 terms of a Farey Sequence
+
+! Local variables here in Main program:
+integer :: ii, count  ! Loop index, counter for terms in sequence
+
+! compute and show the Farey sequence for orders 1 through 11 (inclusive).
+
+do ii=1, 11
+  call startNew (ii)
+  write (*, '(I2, ": ")', advance='no') n         ! Advance 'no' to print all in 1 line
+  count = 0
+  do
+    count = count + 1                             ! Count to limit line length
+    write (*,'(i0, "/",i0)', advance='no') a, b   ! Advance 'no' to print them in 1 line
+    if (.not. expectNext())    Exit               ! Finish when sequence complete
+    write (*, '(", ")', advance='no')             ! more is coming - print separator
+    if (count .eq. 10) then                       ! By default, OpenVMS does not like
+      count = 0                                   ! long output lines and produces a run-time
+      write (*,'(/,4x)', advance='no')            ! error when line length exceeds 132
+    endif
+    call next()                                   ! Calculate next term
+  enddo
+  write (*, *)                                    ! Terminate line
+enddo
+
+! compute and display the number of fractions in the Farey sequence for order 100 through 1,000 inclusive)   by hundreds.
+write (*,*)                                       ! empty line
+do ii=100, 1000, 100
+  count = 0
+  call startNew (ii)
+  write (*, '(I4, ": ")', advance='no') n
+  do
+    count = count + 1                             ! Dont print the terms, just count them
+    if (.not. expectNext()) Exit
+    call next()
+  enddo
+  write (*, '(I0)')   count
+ end do
+contains
+
+
+! =========================================
+! Start a new Farey Sequence or order newN
+! =========================================
+subroutine startNew(newN)
+integer, intent(in) :: newN
+
+n = newN
+a = 0       ! 1st term is a/b=0/1
+b = 1
+c = 1       ! 2nd term is c/d=(1/n)
+d = n
+
+end subroutine startNew
+
+! =================================================
+! Calculate next term in the current Farey Sequence
+! =================================================
+subroutine next()
+!
+! The algorithm to calculate next term a/b of the sequence is
+! described in Wikipedia, https://en.wikipedia.org/wiki/Farey_sequence
+
+integer :: fact, nextC, nextD
+
+fact = (n+b) / d
+nextC = fact*c - a
+nextD = fact*d - b
+
+a = c
+b = d
+c = nextC
+d = nextD
+
+end subroutine next
+
+! ==========================================================
+! Say Yes if more terms in current sequence can be expected
+! ==========================================================
+function expectNext() result (YN)
+
+! The end is reached when the last term (1/1) is encountered.
+logical :: YN
+
+YN = a .ne. 1 .or. b .ne. 1
+end function expectNext
+
+end program Farey