Greatest common divisor
Greatest common divisor
You are encouraged to solve this task according to the task description, using any language you may know.
You are encouraged to solve this task according to the task description, using any language you may know.
This task requires the finding of the greatest common divisor of two integers.
Ada
with Ada.Text_Io; use Ada.Text_Io; procedure Gcd_Test is function Gcd (A, B : Integer) return Integer is begin if A = 0 then return B; end if; if B = 0 then return A; end if; if A > B then return Gcd(B, A mod B); else return Gcd(A, B mod A); end if; end Gcd; begin Put_Line("GCD of 100, 5 is" & Integer'Image(Gcd(100, 5))); Put_Line("GCD of 5, 100 is" & Integer'Image(Gcd(5, 100))); Put_Line("GCD of 7, 23 is" & Integer'Image(Gcd(7, 23))); end Gcd_Test;
Output:
GCD of 100, 5 is 5 GCD of 5, 100 is 5 GCD of 7, 23 is 1
ALGOL 68
PROC gcd = (INT a, b) INT: ( IF a = 0 THEN b ELIF b = 0 THEN a ELIF a > b THEN gcd(b, a MOD b) ELSE gcd(a, b MOD a) FI ); main : ( INT a = 33, b = 77; printf(($x"The gcd of"g" and "g" is "gl$,a,b,gcd(a,b))); INT c = 49865, d = 69811; printf(($x"The gcd of"g" and "g" is "gl$,c,d,gcd(c,d))) )
The output is:
The gcd of +33 and +77 is +11 The gcd of +49865 and +69811 is +9973
C
Iterative Euclid algorithm
int gcd_iter(int u, int v) { int t; while (v) { t = u; u = v; v = t % v; } return u < 0 ? -u : u; /* abs(u) */ }
Recursive Euclid algorithm
int gcd(int u, int v) { if (v) return gcd(v, u % v); else return u < 0 ? -u : u; /* abs(u) */ }
Iterative binary algorithm
int gcd_bin(int u, int v) { int t, k; u = u < 0 ? -u : u; /* abs(u) */ v = v < 0 ? -v : v; if (u < v) { t = u; u = v; v = t; } if (v == 0) return u; k = 1; while (u & 1 == 0 && v & 1 == 0) { /* u, v - even */ u >>= 1; v >>= 1; k <<= 1; } t = (u & 1) ? -v : u; while (t) { while (t & 1 == 0) t >>= 1; if (t > 0) u = t; else v = -t; t = u - v; } return u * k; }
Notes on performance
gcd_iter(40902, 24140)
takes us about 2.87 usec
gcd_bin(40902, 24140)
takes us about 2.47 usec
gcd(40902, 24140)
takes us about 2.86 usec
Forth
: gcd ( a b -- n ) begin dup while tuck mod repeat drop ;
Fortran
Iterative Euclid algorithm
subroutine gcd_iter(value, u, v) Cf2py integer, intent(out) :: value integer value, u, v, t intrinsic abs, mod C do while( v.NE.0 ) t = u u = v v = mod(t, v) enddo value = abs(u) end subroutine gcd_iter
Iterative binary algorithm
subroutine gcd_bin(value, u, v) Cf2py integer, intent(out) :: value integer value, u, v, k, t, abs, mod intrinsic abs, mod u = abs(u) v = abs(v) if( u.lt.v ) then t = u u = v v = t endif if( v.eq.0 ) then value = u return endif k = 1 do while( (mod(u, 2).eq.0).and.(mod(v, 2).eq.0) ) u = u / 2 v = v / 2 k = k * 2 enddo if( (mod(u, 2).eq.0) ) then t = u else t = -v endif do while( t.ne.0 ) do while( (mod(t, 2).eq.0) ) t = t / 2 enddo if( t.gt.0 ) then u = t else v = -t endif t = u - v enddo value = u * k end subroutine gcd_bin
Notes on performance
gcd_iter(40902, 24140)
takes us about 2.8 usec
gcd_bin(40902, 24140)
takes us about 2.5 usec
Haskell
That is already available as the function gcd in the Prelude. Here's the implementation:
gcd :: (Integral a) => a -> a -> a gcd 0 0 = error "Prelude.gcd: gcd 0 0 is undefined" gcd x y = gcd' (abs x) (abs y) where gcd' a 0 = a gcd' a b = gcd' b (a `rem` b)
J
x+.y
Java
Iterative
public static long gcd(long a, long b){ long factor= 0; factor= Math.max(a, b); for(long loop= factor;loop > 1;loop--){ if(a % loop == 0 && b % loop == 0){ return loop; } } return 1; }
Recursive
public static long gcd(long a, long b){ if(a == 0) return b; if(b == 0) return a; if(a > b) return gcd(b, a % b); return gcd(a, b % a); }
OCaml
let rec gcd a b = if a = 0 then b else if b = 0 then a else if a > b then gcd b (a mod b) else gcd a (b mod a)
Perl
Iterative Euclid algorithm
sub gcd_iter($$) { ($u, $v) = @_; while ($v) { $t = $u; $u = $v; $v = $t % $v; } return abs($u); }
Recursive Euclid algorithm
sub gcd($$) { ($u, $v) = @_; if ($v) { return gcd($v, $u % $v); } else { return abs($u); } }
Iterative binary algorithm
sub gcd_bin($$) { ($u, $v) = @_; $u = abs($u); $v = abs($v); if ($u < $v) { $t = $u; $u = $v; $v = $t; } if ($v == 0) { return $u; } $k = 1; while ($u & 1 == 0 && $v & 1 == 0) { $u >>= 1; $v >>= 1; $k <<= 1; } $t = ($u & 1) ? -$v : $u; while ($t) { while ($t & 1 == 0) { $t >>= 1; } if ($t > 0) { $u = $t; } else { $v = -$t; } $t = $u - $v; } return $u * $k; }
Notes on performance
use Benchmark qw(cmpthese); $u = 40902; $v = 24140; (-5, { 'gcd' => sub { gcd($u, $v); }, 'gcd_iter' => sub { gcd_iter($u, $v); }, 'gcd_bin' => sub { gcd_bin($u, $v); }, });
Output on 'Intel(R) Pentium(R) 4 CPU 1.50GHz' / Linux / Perl 5.8.8:
Rate gcd_bin gcd_iter gcd gcd_bin 321639/s -- -12% -20% gcd_iter 366890/s 14% -- -9% gcd 401149/s 25% 9% --
Python
Iterative Euclid algorithm
def gcd_iter(u, v): while v: u, v = v, u % v return abs(u)
Recursive Euclid algorithm
Interpreter: Python 2.5
def gcd(u, v): return gcd(v, u % v) if v else abs(u)
Tests
>>> gcd(0,0) 0 >>> gcd(0, 10) == gcd(10, 0) == gcd(-10, 0) == gcd(0, -10) == 10 True >>> gcd(9, 6) == gcd(6, 9) == gcd(-6, 9) == gcd(9, -6) == gcd(6, -9) == gcd(-9, 6) == 3 True >>> gcd(8, 45) == gcd(45, 8) == gcd(-45, 8) == gcd(8, -45) == gcd(-8, 45) == gcd(45, -8) == 1 True >>> gcd(40902, 24140) # check Knuth :) 34
Iterative binary algorithm
See The Art of Computer Programming by Knuth (Vol.2)
def gcd_bin(u, v): u, v = abs(u), abs(v) # u >= 0, v >= 0 if u < v: u, v = v, u # u >= v >= 0 if v == 0: return u # u >= v > 0 k = 1 while u & 1 == 0 and v & 1 == 0: # u, v - even u >>= 1; v >>= 1 k <<= 1 t = -v if u & 1 else u while t: while t & 1 == 0: t >>= 1 if t > 0: u = t else: v = -t t = u - v return u * k
Notes on performance
gcd(40902, 24140)
takes us about 17 usec
gcd_iter(40902, 24140)
takes us about 11 usec
gcd_bin(40902, 24140)
takes us about 41 usec
Scheme
(define (gcd a b) (cond ((= a 0) b) ((= b 0) a) ((> a b) (gcd b (modulo a b))) (else (gcd a (modulo b a)))))