Data commit

Task/Farey-sequence/Nim/farey-sequence.nim

@@ -0,0 +1,45 @@
+import strformat
+
+proc farey(n: int) =
+  var f1 = (d: 0, n: 1)
+  var f2 = (d: 1, n: n)
+  write(stdout, fmt"0/1 1/{n}")
+  while f2.n > 1:
+    let k = (n + f1.n) div f2.n
+    let aux = f1
+    f1 = f2
+    f2 = (f2.d * k - aux.d, f2.n * k - aux.n)
+    write(stdout, fmt" {f2.d}/{f2.n}")
+  write(stdout, "\n")
+
+proc fareyLength(n: int, cache: var seq[int]): int =
+  if n >= cache.len:
+    var newLen = cache.len
+    if newLen == 0:
+      newLen = 16
+    while newLen <= n:
+      newLen *= 2
+    cache.setLen(newLen)
+  elif cache[n] != 0:
+    return cache[n]
+
+  var length = n * (n + 3) div 2
+  var p = 2
+  var q = 0
+  while p <= n:
+    q = n div (n div p) + 1
+    dec length, fareyLength(n div p, cache) * (q - p)
+    p = q
+  cache[n] = length
+  return length
+
+for n in 1..11:
+  write(stdout, fmt"{n:>8}: ")
+  farey(n)
+
+var cache: seq[int] = @[]
+for n in countup(100, 1000, step=100):
+  echo fmt"{n:>8}: {fareyLength(n, cache):14} items"
+
+let n = 10_000_000
+echo fmt"{n}: {fareyLength(n, cache):14} items"