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Task/Prime-decomposition/Nim/prime-decomposition.nim

@@ -0,0 +1,47 @@
+import strutils, math, sequtils, times
+
+proc getStep(n: int64) : int64 {.inline.} =
+   result = 1 + n*4 - int64(n /% 2)*2
+
+proc primeFac(n: int64): seq[int64] =
+    var res: seq[int64] = @[]
+    var maxq = int64(floor(sqrt(float(n))))
+    var d = 1
+    var q: int64 = (n %% 2) and 2 or 3    # either 2 or 3, alternating
+    while (q <= maxq) and ((n %% q) != 0):
+        q = getStep(d)
+        d += 1
+    if q <= maxq:
+        var q1: seq[int64] = primeFac(n /% q)
+        var q2: seq[int64] = primeFac(q)
+        res = concat(q2, q1, res)
+    else:
+        res.add(n)
+    result = res
+
+var is_prime: seq[Bool] = @[]
+is_prime.add(False)
+is_prime.add(False)
+
+iterator primes(limit: int): int =
+    for n in high(is_prime) .. limit+2: is_prime.add(True)
+    for n in 2 .. limit + 1:
+        if is_prime[n]:
+            yield n
+            for i in countup((n *% n), limit+1, n): # start at ``n`` squared
+                try:
+                    is_prime[i] = False
+                except EInvalidIndex: break
+
+# Example: calculate factors of Mersenne numbers to M59 #
+
+for m in primes(59):
+    var p = int64(pow(2.0,float(m)) - 1)
+    write(stdout,"2**$1-1 = $2, with factors: " % [$m, $p] )
+    var start = cpuTime()
+    var f = primeFac(p)
+    for factor in f:
+        write(stdout, factor)
+        write(stdout, ", ")
+        FlushFile(stdout)
+    writeln(stdout, "=> $#ms" % $int(1000*(cpuTime()-start)) )