Data commit

Task/Minkowski-question-mark-function/Nim/minkowski-question-mark-function.nim

@@ -0,0 +1,87 @@
+import math, strformat
+
+const MaxIter = 151
+
+
+func minkowski(x: float): float =
+
+  if x notin 0.0..1.0:
+    return floor(x) + minkowski(x - floor(x))
+
+  var
+    p = x.uint64
+    r = p + 1
+    q, s = 1u64
+    d = 1.0
+    y = p.float
+
+  while true:
+    d /= 2
+    if y + d == y: break
+    let m = p + r
+    if m < 0 or p < 0: break
+    let n = q + s
+    if n < 0: break
+    if x < m.float / n.float:
+      r = m
+      s = n
+    else:
+      y += d
+      p = m
+      q = n
+
+  result = y + d
+
+
+func minkowskiInv(x: float): float =
+
+  if x notin 0.0..1.0:
+    return floor(x) + minkowskiInv(x - floor(x))
+  if x == 1 or x == 0:
+    return x
+
+  var
+    contFrac: seq[uint32]
+    curr = 0u32
+    count = 1u32
+    i = 0
+    x = x
+
+  while true:
+    x *= 2
+    if curr == 0:
+      if x < 1:
+        inc count
+      else:
+        inc i
+        contFrac.setLen(i + 1)
+        contFrac[i - 1] = count
+        count = 1
+        curr = 1
+        x -= 1
+    else:
+      if x > 1:
+        inc count
+        x -= 1
+      else:
+        inc i
+        contFrac.setLen(i + 1)
+        contFrac[i - 1] = count
+        count = 1
+        curr = 0
+    if x == floor(x):
+      contFrac[i] = count
+      break
+    if i == MaxIter:
+      break
+
+  var ret = 1 / contFrac[i].float
+  for j in countdown(i - 1, 0):
+    ret = contFrac[j].float + 1 / ret
+  result = 1 / ret
+
+
+echo &"{minkowski(0.5*(1+sqrt(5.0))):19.16f}, {5/3:19.16f}"
+echo &"{minkowskiInv(-5/9):19.16f}, {(sqrt(13.0)-7)/6:19.16f}"
+echo &"{minkowski(minkowskiInv(0.718281828)):19.16f}, " &
+     &"{minkowskiInv(minkowski(0.1213141516171819)):19.16f}"