Data update

Task/Fermat-numbers/ALGOL-68/fermat-numbers.alg

@@ -0,0 +1,71 @@
+BEGIN # find and factorise some Fermat numbers: F(n) = 2^(2^n) + 1            #
+
+    PR read "primes.incl.a68" PR                    # include prime utilities #
+    PR precision 256 PR                  # set the precision of LONG LONG INT #
+
+    PROC gcd = ( LONG LONG INT x, y )LONG LONG INT:           # iterative gcd #
+         BEGIN
+            LONG LONG INT a := x, b := y;
+            WHILE b /= 0 DO
+               LONG LONG INT next a = b;
+               b := a MOD b;
+               a := next a
+            OD;
+            ABS a
+         END # gcd # ;
+
+    # returns a prime factor (if possible) of n, if n is prime, n is returned #
+    PROC pollard rho = ( LONG LONG INT n )LONG LONG INT:
+         IF   is probably prime( n )
+         THEN n
+         ELIF LONG LONG INT x := 2, y := 2, d := 1;
+              PROC g = ( LONG LONG INT x )LONG LONG INT: ( ( x * x ) + 1 ) MOD n;
+              WHILE d = 1 DO
+                  x := g( x );
+                  y := g( g( y ) );
+                  d := gcd( ABS( x - y ), n )
+              OD;
+              d = n
+         THEN print( ( "pollard rho found non probably prime n for: ", n, newline ) );
+              n
+         ELIF LONG LONG INT other d = n OVER d;
+              d > other d
+         THEN other d
+         ELSE d
+         FI # pollard rho # ;
+
+    # returns the lowest prime factor of n, or n if n is prime                #
+    PROC prime factor = ( LONG LONG INT n )LONG LONG INT:
+         IF   LONG LONG INT d := pollard rho( n );
+              d = n
+         THEN d
+         ELSE # check for a lower factor                                      #
+              LONG LONG INT other d := n OVER d;
+              LONG LONG INT d1      := pollard rho( other d );
+              WHILE d1 < d DO
+                  d       := d1;
+                  other d := other d OVER d;
+                  d1      := pollard rho( other d )
+              OD;
+              IF d1 < d THEN d1 ELSE d FI
+         FI # prime factor # ;
+
+    # task                                                                    #
+    INT p2 := 1;
+    FOR i FROM 0 TO 9 DO
+        LONG LONG INT fn = 1 + ( LONG LONG 2 )^p2;
+        print( ( "F(", whole( i, 0 ), "): ", whole( fn, 0 ) ) );
+        IF i < 7 THEN
+            print( ( ", " ) );
+            LONG LONG INT pf = prime factor( fn );
+            IF pf = fn THEN
+                print( ( "prime" ) )
+            ELSE
+                print( ( whole( pf, 0 ), " x ", whole( fn OVER pf, 0 ) ) )
+            FI
+        FI;
+        print( ( newline ) );
+        p2 *:= 2
+    OD
+
+END

Task/Fermat-numbers/Langur/fermat-numbers.langur

@@ -1,6 +1,6 @@
-val .fermat = f 2 ^ 2 ^ .i + 1
+val .fermat = fn(.i) 2 ^ 2 ^ .i + 1
 
-val .factors = f(var .x) {
+val .factors = fn(var .x) {
     for[.f=[]] .i, .s = 2, trunc .x ^/ 2; .i < .s; .i += 1 {
         if .x div .i {
             .f ~= [.i]