(moved out of the [Bag of algorithms]) - [RS] started this with:
  proc gcdA {p q} {
     while {1} {
        if {$p==$q} {
            # Termination case
            return $p
        } elseif {$p>$q} {
            # Swap p and q
            set t $p
            set p $q
            set q $t
        }
        # Work out q%p ('cos we're looping...)
        incr q [expr {-$p}]
     }
  } ;#RS, with recursion removed by DKF

It is simpler and faster to use % (reminder) instead of decrementing. (Consider what happens when the above tries to compute the GCD of 1000 and 10.) Furthermore the above control structures can be greatly simplified: 
  proc gcdB {p q} {
     set p [expr {abs($p)}]
     set q [expr {abs($q)}]
     while {$q != 0} {
        set r [expr {$p % $q}]
        set p $q
        set q $r
     }
     set p
  }

There is however an even shorter way of doing it: 
  proc gcdC {p q} {
     set p [expr {abs($p)}]
     set q [expr {abs($q)}]
     while {$q != 0} {set q [expr {$p % [set p $q]}]}
     set p
  }
/Lars Hellstr�m 

[CL] wants to flatten that even more:
   proc gcdE {p q} {
      while {$q != 0} {set q [expr {abs($p) % [set p [expr abs($q)]]}]}
      set p
   } 
----
''[Cameron Laird] wrote in [the comp.lang.tcl newsgroup]:''
Simpler:
  proc gcdD {a b} {
     if {$b==0} {
        return $a
     }
     gcdD $b [expr {$a % $b}]
  }

You can also do it iteratively, with arbitrary-precision integers, ...

''[Tom Poindexter] added:''
... e.g., by using Mpexpr, it's a one-liner:

 % package require Mpexpr
 1.0
 % mpformat %r [mpexpr 60/100.0]
 3/5
Mpexpr:  http://www.NeoSoft.com/tcl/ftparchive/sorted/math/Mpexpr-1.0/

----
Preformance - I ([BBH]) changed the names of the above to be unique and ran this little performance comparison:


 set nums {10 11 15 17 35 95 160 1000 1111 1113}
 puts "  each block contains the time for \[gcdX \$p \$q]/\[gcdX \$q \$p] for 5000 iterations"
 puts " |-----------------------------------------------------------|"
 puts " |   P & Q   |    gcdA   |    gcdB   |    gcdC   |    gcdD   |"
 set i 0
 foreach p $nums {
     incr i
     foreach q [lrange $nums $i end] {
         puts " |-----------+-----------+-----------+-----------+-----------|"
         puts -nonewline  [format " | %4d %4d |" $p $q]
         foreach f {A B C D} {
             # time for p q AND for Q P to see if it makes any difference
             puts -nonewline [format " %4d/%4d |" [lindex [time {gcd$f $p $q} 5000] 0] [lindex [time {gcd$f $q $p} 5000] 0]]
         }
         puts ""
         update
     }
 }
 puts " |-----------------------------------------------------------|"

and the results on my PIII running Win2K tcl 8.3.4 on 23 Jan 2002 were

 |-----------------------------------------------------------|
 |   P & Q   |    gcdA   |    gcdB   |    gcdC   |    gcdD   |
 |-----------+-----------+-----------+-----------+-----------|
 |   10   11 |   52/  56 |   28/  22 |   24/  20 |   28/  22 |
 |-----------+-----------+-----------+-----------+-----------|
 |   10   15 |   26/  28 |   26/  24 |   26/  20 |   28/  24 |
 |-----------+-----------+-----------+-----------+-----------|
 |   10   17 |   44/  46 |   32/  28 |   28/  26 |   36/  32 |
 |-----------+-----------+-----------+-----------+-----------|
 |   10   35 |   34/  36 |   26/  22 |   24/  20 |   28/  24 |
 |-----------+-----------+-----------+-----------+-----------|
 |   10   95 |   54/  54 |   26/  22 |   24/  20 |   28/  22 |
 |-----------+-----------+-----------+-----------+-----------|
 |   10  160 |   68/  68 |   22/  20 |   20/  20 |   22/  20 |
 |-----------+-----------+-----------+-----------+-----------|
 |   10 1000 |  341/ 350 |   24/  20 |   22/  18 |   22/  20 |
 |-----------+-----------+-----------+-----------+-----------|
 |   10 1111 |  415/ 437 |   24/  24 |   22/  20 |   28/  22 |
 |-----------+-----------+-----------+-----------+-----------|
 |   10 1113 |  401/ 403 |   28/  28 |   24/  22 |   32/  28 |
 |-----------+-----------+-----------+-----------+-----------|
 |   11   15 |   44/  46 |   30/  30 |   28/  24 |   36/  30 |
 |-----------+-----------+-----------+-----------+-----------|
 |   11   17 |   46/  50 |   32/  28 |   28/  24 |   36/  34 |
 |-----------+-----------+-----------+-----------+-----------|
 |   11   35 |   54/  52 |   30/  26 |   24/  24 |   30/  28 |
 |-----------+-----------+-----------+-----------+-----------|
 |   11   95 |   70/  70 |   34/  32 |   28/  28 |   40/  36 |
 |-----------+-----------+-----------+-----------+-----------|
 |   11  160 |   90/  92 |   32/  28 |   26/  24 |   34/  32 |
 |-----------+-----------+-----------+-----------+-----------|
 |   11 1000 |  348/ 351 |   28/  26 |   24/  22 |   32/  32 |
 |-----------+-----------+-----------+-----------+-----------|
 |   11 1111 |  364/ 365 |   22/  20 |   20/  18 |   24/  18 |
 |-----------+-----------+-----------+-----------+-----------|
 |   11 1113 |  372/ 373 |   30/  24 |   28/  22 |   36/  30 |
 |-----------+-----------+-----------+-----------+-----------|
 |   15   17 |   54/  58 |   28/  28 |   24/  22 |   34/  28 |
 |-----------+-----------+-----------+-----------+-----------|
 |   15   35 |   34/  34 |   26/  24 |   22/  24 |   34/  32 |
 |-----------+-----------+-----------+-----------+-----------|
 |   15   95 |   54/  48 |   26/  24 |   22/  20 |   28/  24 |
 |-----------+-----------+-----------+-----------+-----------|
 |   15  160 |   62/  62 |   30/  26 |   24/  22 |   32/  28 |
 |-----------+-----------+-----------+-----------+-----------|
 |   15 1000 |  246/ 244 |   30/  24 |   26/  22 |   32/  26 |
 |-----------+-----------+-----------+-----------+-----------|
 |   15 1111 |  306/ 310 |   26/  24 |   24/  20 |   26/  24 |
 |-----------+-----------+-----------+-----------+-----------|
 |   15 1113 |  300/ 294 |   30/  22 |   22/  22 |   26/  24 |
 |-----------+-----------+-----------+-----------+-----------|
 |   17   35 |   80/  82 |   24/  24 |   22/  20 |   28/  22 |
 |-----------+-----------+-----------+-----------+-----------|
 |   17   95 |   64/  64 |   38/  32 |   30/  28 |   40/  36 |
 |-----------+-----------+-----------+-----------+-----------|
 |   17  160 |   72/  76 |   32/  28 |   28/  24 |   36/  30 |
 |-----------+-----------+-----------+-----------+-----------|
 |   17 1000 |  238/ 238 |   34/  32 |   28/  28 |   40/  36 |
 |-----------+-----------+-----------+-----------+-----------|
 |   17 1111 |  258/ 260 |   32/  28 |   26/  26 |   36/  30 |
 |-----------+-----------+-----------+-----------+-----------|
 |   17 1113 |  262/ 266 |   28/  26 |   24/  24 |   32/  26 |
 |-----------+-----------+-----------+-----------+-----------|
 |   35   95 |   44/  44 |   32/  30 |   26/  26 |   36/  32 |
 |-----------+-----------+-----------+-----------+-----------|
 |   35  160 |   54/  68 |   36/  30 |   26/  26 |   36/  30 |
 |-----------+-----------+-----------+-----------+-----------|
 |   35 1000 |  128/ 130 |   32/  28 |   26/  26 |   34/  30 |
 |-----------+-----------+-----------+-----------+-----------|
 |   35 1111 |  162/ 166 |   34/  32 |   28/  26 |   40/  36 |
 |-----------+-----------+-----------+-----------+-----------|
 |   35 1113 |  136/ 138 |   30/  24 |   26/  22 |   32/  26 |
 |-----------+-----------+-----------+-----------+-----------|
 |   95  160 |   54/  54 |   32/  30 |   26/  24 |   36/  32 |
 |-----------+-----------+-----------+-----------+-----------|
 |   95 1000 |   92/  94 |   32/  28 |   26/  24 |   36/  32 |
 |-----------+-----------+-----------+-----------+-----------|
 |   95 1111 |  100/ 102 |   42/  42 |   34/  32 |   54/  50 |
 |-----------+-----------+-----------+-----------+-----------|
 |   95 1113 |  128/ 128 |   38/  36 |   34/  30 |   44/  40 |
 |-----------+-----------+-----------+-----------+-----------|
 |  160 1000 |   50/  52 |   26/  22 |   24/  20 |   28/  22 |
 |-----------+-----------+-----------+-----------+-----------|
 |  160 1111 |  120/ 120 |   38/  34 |   30/  30 |   44/  40 |
 |-----------+-----------+-----------+-----------+-----------|
 |  160 1113 |  144/ 148 |   36/  34 |   28/  28 |   42/  36 |
 |-----------+-----------+-----------+-----------+-----------|
 | 1000 1111 |  475/ 475 |   28/  36 |   44/  24 |   32/  32 |
 |-----------+-----------+-----------+-----------+-----------|
 | 1000 1113 |  104/ 104 |   44/  42 |   36/  34 |   54/  48 |
 |-----------+-----------+-----------+-----------+-----------|
 | 1111 1113 | 2303/2143 |   32/  26 |   26/  28 |   34/  26 |
 |-----------------------------------------------------------|

----
[Category Mathematics] - [Arts and crafts of Tcl-Tk programming]