Initial data commit

Task/Zeckendorf-arithmetic/Nim/zeckendorf-arithmetic.nim

@@ -0,0 +1,142 @@
+type Zeckendorf = object
+  dVal: Natural
+  dLen: Natural
+
+const
+  Dig = ["00", "01", "10"]
+  Dig1 = ["", "1", "10"]
+
+# Forward references.
+func b(z: var Zeckendorf; pos: Natural)
+func inc(z: var Zeckendorf)
+
+
+func a(z: var Zeckendorf; n: Natural) =
+  var i = n
+  while true:
+
+    if z.dLen < i: z.dLen = i
+    let j = z.dVal shr (i * 2) and 3
+
+    case j
+    of 0, 1:
+      return
+    of 2:
+      if (z.dVal shr ((i + 1) * 2) and 1) != 1: return
+      z.dVal += 1 shl (i * 2 + 1)
+      return
+    of 3:
+      z.dVal = z.dVal and not (3 shl (i * 2))
+      z.b((i + 1) * 2)
+    else:
+        assert(false)
+
+    inc i
+
+
+func b(z: var Zeckendorf; pos: Natural) =
+  if pos == 0:
+    inc z
+    return
+
+  if (z.dVal shr pos and 1) == 0:
+    z.dVal += 1 shl pos
+    z.a(pos div 2)
+    if pos > 1: z.a(pos div 2 - 1)
+  else:
+    z.dVal = z.dVal and not(1 shl pos)
+    z.b(pos + 1)
+    z.b(pos - (if pos > 1: 2 else: 1))
+
+
+func c(z: var Zeckendorf; pos: Natural) =
+  if (z.dVal shr pos and 1) == 1:
+    z.dVal = z.dVal and not(1 shl pos)
+    return
+
+  z.c(pos + 1)
+  if pos > 0:
+    z.b(pos - 1)
+  else:
+    inc z
+
+
+func initZeckendorf(s = "0"): Zeckendorf =
+  var q = 1
+  var i = s.high
+  result.dLen = i div 2
+  while i >= 0:
+    result.dVal += (ord(s[i]) - ord('0')) * q
+    q *= 2
+    dec i
+
+
+func inc(z: var Zeckendorf) =
+  inc z.dVal
+  z.a(0)
+
+
+func `+=`(z1: var Zeckendorf; z2: Zeckendorf) =
+  for gn in 0 .. (2 * z2.dLen + 1):
+    if (z2.dVal shr gn and 1) == 1:
+      z1.b(gn)
+
+
+func `-=`(z1: var Zeckendorf; z2: Zeckendorf) =
+  for gn in 0 .. (2 * z2.dLen + 1):
+    if (z2.dVal shr gn and 1) == 1:
+      z1.c(gn)
+
+  while z1.dLen > 0 and (z1.dVal shr (z1.dLen * 2) and 3) == 0:
+    dec z1.dLen
+
+
+func `*=`(z1: var Zeckendorf; z2: Zeckendorf) =
+  var na, nb = z2
+  var nr: Zeckendorf
+  for i in 0 .. (z1.dLen + 1) * 2:
+    if (z1.dVal shr i and 1) > 0: nr += nb
+    let nt = nb
+    nb += na
+    na = nt
+  z1 = nr
+
+func`$`(z: var Zeckendorf): string =
+  if z.dVal == 0: return "0"
+  result.add Dig1[z.dVal shr (z.dLen * 2) and 3]
+  for i in countdown(z.dLen - 1, 0):
+    result.add Dig[z.dVal shr (i * 2) and 3]
+
+when isMainModule:
+
+  var g: Zeckendorf
+
+  echo "Addition:"
+  g = initZeckendorf("10")
+  g += initZeckendorf("10")
+  echo g
+  g += initZeckendorf("10")
+  echo g
+  g += initZeckendorf("1001")
+  echo g
+  g += initZeckendorf("1000")
+  echo g
+  g += initZeckendorf("10101")
+  echo g
+
+
+  echo "\nSubtraction:"
+  g = initZeckendorf("1000")
+  g -= initZeckendorf("101")
+  echo g
+  g = initZeckendorf("10101010")
+  g -= initZeckendorf("1010101")
+  echo g
+
+  echo "\nMultiplication:"
+  g = initZeckendorf("1001")
+  g *= initZeckendorf("101")
+  echo g
+  g = initZeckendorf("101010")
+  g += initZeckendorf("101")
+  echo g