Sync

Task/Van-der-Corput-sequence/Erlang/van-der-corput-sequence.erl

@@ -0,0 +1,23 @@
+-module( van_der_corput ).
+
+-export( [sequence/1, sequence/2, task/0] ).
+
+sequence( N ) -> sequence( N, 2 ).
+
+sequence( 0, _Base ) -> 0.0;
+sequence( N, Base ) -> erlang:list_to_float( "0." ++ lists:flatten([erlang:integer_to_list(X) || X <- sequence_loop(N, Base)]) ).
+
+task() -> [task(X) || X <- lists:seq(2, 5)].
+
+
+
+sequence_loop( 0, _Base ) -> [];
+sequence_loop( N, Base ) ->
+	New_n = N div Base,
+	Digit = N rem Base,
+	[Digit | sequence_loop( New_n, Base )].
+
+task( Base ) ->
+	io:fwrite( "Base ~p:", [Base] ),
+	[io:fwrite( " ~p", [sequence(X, Base)] ) || X <- lists:seq(0, 9)],
+	io:fwrite( "~n" ).

Task/Van-der-Corput-sequence/Perl/van-der-corput-sequence.pl

@@ -0,0 +1,15 @@
+sub vdc {
+    my @value = shift;
+    my $base = shift // 2;
+    use integer;
+    push @value, $value[-1] / $base while $value[-1] > 0;
+    my ($x, $sum) = (1, 0);
+    no integer;
+    $sum += ($_ % $base) / ($x *= $base) for @value;
+    return $sum;
+}
+
+for my $base ( 2 .. 5 ) {
+    print "base $base: ", join ' ', map { vdc($_, $base) } 0 .. 10;
+    print "\n";
+}

Task/Van-der-Corput-sequence/Racket/van-der-corput-sequence-1.rkt

@@ -0,0 +1,7 @@
+#lang racket
+(define (van-der-Corput n base)
+  (if (zero? n)
+      0
+      (let-values ([(q r) (quotient/remainder n base)])
+        (/ (+ r (van-der-Corput q base))
+           base))))

Task/Van-der-Corput-sequence/Racket/van-der-corput-sequence-2.rkt

@@ -0,0 +1,7 @@
+#lang racket
+(define (digit-length n base)
+  (if (< n base) 1 (add1 (digit-length (quotient n base) base))))
+(define (digit n i base)
+  (remainder (quotient n (expt base i)) base))
+(define (van-der-Corput n base)
+  (for/sum ([i (digit-length n base)]) (/ (digit n i base) (expt base (+ i 1)))))

Task/Van-der-Corput-sequence/Racket/van-der-corput-sequence-3.rkt

@@ -0,0 +1,10 @@
+(for ([base (in-range 2 (add1 5))])
+  (printf "Base ~a: " base)
+  (for ([n (in-range 0 10)])
+    (printf "~a " (van-der-Corput n base)))
+  (newline))
+
+#| Base 2: 0 1/2 1/4 3/4 1/8 5/8 3/8 7/8 1/16 9/16
+   Base 3: 0 1/3 2/3 1/9 4/9 7/9 2/9 5/9 8/9 1/27
+   Base 4: 0 1/4 1/2 3/4 1/16 5/16 9/16 13/16 1/8 3/8
+   Base 5: 0 1/5 2/5 3/5 4/5 1/25 6/25 11/25 16/25 21/25 |#