%!PS

% begin library code

/test {
    /test.count test.count 1 add def
    {
        /test.pass test.pass 1 add def
    } {
        ( ) print
        test.count (....) cvs print
        (-fail) print
    } ifelse
} bind def

/test.start {
    print (:) print
    /test.pass 0 def
    /test.count 0 def
} bind def

/test.end {
    ( ) print
    test.count 0 gt {
        (Passed ) print
        test.pass (...) cvs print
        (/) print
        test.count (...) cvs print
        ( \() print
        test.pass 100 mul test.count idiv (...) cvs print
        (%\)) print
        (\r\n) print
    } if
} bind def

/deepeq {
    2 dict begin
    /a exch def
    /b exch def
    a type b type eq {
        a type /dicttype eq {
            a length b length eq {
                <<
                    a {
                        pop
                        true
                    } forall
                    b {
                        pop
                        true
                    } forall
                >>
                true exch
                {
                    pop
                    dup a exch known {
                        dup b exch known {
                            dup a exch get exch b exch get deepeq not {
                                pop false
                            } if
                        } {
                            false
                        } ifelse
                    } {
                        false
                    } ifelse
                } forall
            } {
                false
            } ifelse
        } {
            a type dup /arraytype eq exch /stringtype eq or {
                a length b length eq {
                    true
                    0 1 a length 1 sub {
                        dup a exch get exch b exch get deepeq not {
                            pop false
                            exit
                        } if
                    } for
                } {
                    false
                } ifelse
            } {
                a b eq
            } ifelse
        } ifelse
    } {
        false
    } ifelse
    end
} bind def

/quicksort { % [ a c b ] -> [ a b c ]
    1 dict begin
    /arr exch def
    0 arr length 1 sub quicksort.main
    arr
    end
} bind def

/quicksort.main { % lo hi -> (null)
    3 dict begin
    /hi exch def
    /lo exch def
    /xit false def
    lo 0 lt {
        /xit true def
    } if
    hi 0 lt {
        /xit true def
    } if
    lo hi ge {
        /xit true def
    } if
    xit not {
        /p quicksort.partition def
        lo p quicksort.main
        p 1 add hi quicksort.main
    } if
    end
} bind def

/quicksort.partition {
    3 dict begin
    /pivot arr hi lo add 2 idiv get def
    /i lo 1 sub def
    /j hi 1 add def
    {
        {
            /i i 1 add def
            arr i get pivot ge {
                exit
            } if
        } loop
        {
            /j j 1 sub def
            arr j get pivot le {
                exit
            } if
        } loop
        i j ge {
            j
            exit
        } if
        i j quicksort.swap
    } loop
    end
} bind def

/quicksort.swap {
    2 dict begin
    /bi exch def
    /ai exch def
    arr ai get
    arr bi get
    arr exch ai exch put
    arr exch bi exch put
    end
} bind def

/reduce { % array proc -> value
    2 dict begin
    /p exch def
    /a exch def
    a 0 get
    1 1 a length 1 sub {
        a exch get
        p
    } for
    end
} bind def


/apush { % [a b] c -> [a b c]
    exch
    [ exch aload length 2 add -1 roll ]
} bind def

/map { % array proc -> array
    2 dict begin
    /p exch def
    [ exch
      {
          p
      } forall
    ]
} bind def

/keys { % dict -> array of dict keys
    [ exch
      {
          pop
      } forall
    ]
} bind def

% end library code

/gcd {
    {
        dup
        3 1 roll
        mod
        dup 0 eq {
            pop exit
        } if
    } loop
} bind def

/lcm {
    dup 3 -1 roll
    dup 4 -1 roll
    gcd idiv mul
} bind def

/lcmseries {
    { lcm } reduce
} bind def

/farey {
    7 dict begin
    /n exch def
    /l [ 2 1 n { } for ] lcmseries def
    /d n dup mul dict def
    1 1 n {
        /i exch def
        /m l i idiv def
        0 1 i {
            /j exch def
            /k m j mul def
            d k known not {
                d k [ j i ] put
            } if
        } for
    } for
    d keys quicksort { d exch get } map
    end
} bind def

(farey) test.start

5 farey
[ [0 1] [1 5] [1 4] [1 3] [2 5] [1 2] [3 5] [2 3] [3 4] [4 5] [1 1] ]
deepeq test

7 farey
[ [0 1] [1 7] [1 6] [1 5] [1 4] [2 7] [1 3] [2 5] [3 7] [1 2] [4 7]
  [3 5] [2 3] [5 7] [3 4] [4 5] [5 6] [6 7] [1 1] ]
deepeq test

4 farey
[ [0 1] [1 4] [1 3] [1 2] [2 3] [3 4] [1 1] ]
deepeq test

test.end