September 2017 Update

Task/Van-der-Corput-sequence/Jq/van-der-corput-sequence-1.jq

@@ -0,0 +1,16 @@
+# vdc(base) converts an input decimal integer to a decimal number based on the van der
+# Corput sequence using base 'base', e.g. (4 | vdc(2)) is 0.125.
+#
+def vdc(base):
+
+  # The helper function converts a stream of residuals to a decimal,
+  # e.g. if base is 2, then decimalize( (0,0,1) ) yields 0.125
+  def decimalize(stream):
+    reduce stream as $d   # state: [accumulator, power]
+      ( [0, 1/base];
+       .[1] as $power | [ .[0] + ($d * $power), $power / base] )
+    | .[0];
+
+  if . == 0 then 0
+  else decimalize(recurse( if . == 0 then empty else ./base | floor end ) % base)
+  end ;

Task/Van-der-Corput-sequence/Jq/van-der-corput-sequence-2.jq

@@ -0,0 +1,5 @@
+def round(n):
+  (if . < 0 then -1 else 1 end) as $s
+  | $s*10*.*n | if (floor%10)>4 then (.+5) else . end | ./10 | floor/n | .*$s;
+
+range(2;6) | . as $base | "Base \(.): \( [ range(0;11) | vdc($base)|round(1000) ] )"

Task/Van-der-Corput-sequence/Jq/van-der-corput-sequence-3.jq

@@ -0,0 +1,5 @@
+$ jq -n -f -c -r van_der_corput_sequence.jq
+Base 2: [0,0.5,0.25,0.75,0.125,0.625,0.375,0.875,0.063,0.563,0.313]
+Base 3: [0,0.333,0.667,0.111,0.444,0.778,0.222,0.556,0.889,0.037,0.37]
+Base 4: [0,0.25,0.5,0.75,0.063,0.313,0.563,0.813,0.125,0.375,0.625]
+Base 5: [0,0.2,0.4,0.6,0.8,0.04,0.24,0.44,0.64,0.84,0.08]