Data commit

Task/Jacobi-symbol/Nim/jacobi-symbol.nim

@@ -0,0 +1,34 @@
+template isOdd(n: int): bool = (n and 1) != 0
+template isEven(n: int): bool = (n and 1) == 0
+
+
+func jacobi(n, k: int): range[-1..1] =
+  assert k > 0 and k.isOdd
+  var n = n mod k
+  var k = k
+  result = 1
+  while n != 0:
+    while n.isEven:
+      n = n shr 1
+      if (k and 7) in [3, 5]:
+        result = -result
+    swap n, k
+    if (n and 3) == 3 and (k and 3) == 3:
+      result = -result
+    n = n mod k
+  if k != 1: result = 0
+
+when isMainModule:
+
+  import strutils
+
+  stdout.write "n/k|"
+  for n in 1..20:
+    stdout.write align($n, 3)
+  echo '\n' & repeat("—", 64)
+
+  for k in countup(1, 21, 2):
+    stdout.write align($k, 2), " |"
+    for n in 1..20:
+      stdout.write align($jacobi(n, k), 3)
+    echo ""