Initial data commit

Task/Miller-Rabin-primality-test/Go/miller-rabin-primality-test.go

@@ -0,0 +1,66 @@
+package main
+
+import "log"
+
+func main() {
+    // max uint32 is not prime
+    c := uint32(1<<32 - 1)
+    // a few primes near the top of the range.  source: prime pages.
+    for _, p := range []uint32{1<<32 - 5, 1<<32 - 17, 1<<32 - 65, 1<<32 - 99} {
+        for ; c > p; c-- {
+            if prime(c) {
+                log.Fatalf("prime(%d) returned true", c)
+            }
+        }
+        if !prime(p) {
+            log.Fatalf("prime(%d) returned false", p)
+        }
+        c--
+    }
+}
+
+func prime(n uint32) bool {
+    // bases of 2, 7, 61 are sufficient to cover 2^32
+    switch n {
+    case 0, 1:
+        return false
+    case 2, 7, 61:
+        return true
+    }
+    // compute s, d where 2^s * d = n-1
+    nm1 := n - 1
+    d := nm1
+    s := 0
+    for d&1 == 0 {
+        d >>= 1
+        s++
+    }
+    n64 := uint64(n)
+    for _, a := range []uint32{2, 7, 61} {
+        // compute x := a^d % n
+        x := uint64(1)
+        p := uint64(a)
+        for dr := d; dr > 0; dr >>= 1 {
+            if dr&1 != 0 {
+                x = x * p % n64
+            }
+            p = p * p % n64
+        }
+        if x == 1 || uint32(x) == nm1 {
+            continue
+        }
+        for r := 1; ; r++ {
+            if r >= s {
+                return false
+            }
+            x = x * x % n64
+            if x == 1 {
+                return false
+            }
+            if uint32(x) == nm1 {
+                break
+            }
+        }
+    }
+    return true
+}