factor::miller_rabin: Extract dividers from the primality test

Another 36% improvement.

src/uu/factor/src/miller_rabin.rs

@@ -4,14 +4,29 @@ use crate::numeric::*;
 //  discovered by Jim Sinclair on 2011-04-20, see miller-rabin.appspot.com
 const BASIS: [u64; 7] = [2, 325, 9375, 28178, 450775, 9780504, 1795265022];
 
+#[derive(Eq, PartialEq)]
+pub(crate) enum Result {
+    Prime,
+    Pseudoprime,
+    Composite(u64),
+}
+
+impl Result {
+    pub(crate) fn is_prime(&self) -> bool {
+        return *self == Result::Prime;
+    }
+}
+
 // Deterministic Miller-Rabin primality-checking algorithm, adapted to extract
 // (some) dividers; it will fail to factor strong pseudoprimes.
-pub(crate) fn is_prime(n: u64) -> bool {
+pub(crate) fn test(n: u64) -> Result {
+    use self::Result::*;
+
     if n < 2 {
-        return false;
+        return Pseudoprime;
     }
     if n % 2 == 0 {
-        return n == 2;
+        return if n == 2 { Prime } else { Composite(2) };
     }
 
     let d = (n - 1).trailing_zeros();
@@ -30,7 +45,7 @@ pub(crate) fn is_prime(n: u64) -> bool {
         }
 
         if pow(x, n - 1, n, mul) != 1 {
-            return false;
+            return Pseudoprime;
         }
         x = pow(x, r, n, mul);
         if x == 1 || x == n - 1 {
@@ -40,7 +55,7 @@ pub(crate) fn is_prime(n: u64) -> bool {
         loop {
             let y = mul(x, x, n);
             if y == 1 {
-                return false;
+                return Composite(gcd(x - 1, n));
             }
             if y == n - 1 {
                 // This basis element is not a witness of `n` being composite.
@@ -51,5 +66,11 @@ pub(crate) fn is_prime(n: u64) -> bool {
         }
     }
 
-    true
+    Prime
+}
+
+// Used by build.rs' tests
+#[allow(dead_code)]
+pub(crate) fn is_prime(n: u64) -> bool {
+    test(n).is_prime()
 }

src/uu/factor/src/rho.rs

@@ -1,3 +1,4 @@
+use crate::miller_rabin::Result::*;
 use crate::{miller_rabin, Factors};
 use numeric::*;
 use rand::distributions::{Distribution, Uniform};
@@ -39,16 +40,25 @@ fn find_divisor(num: u64) -> u64 {
     }
 }
 
-pub(crate) fn factor(num: u64) -> Factors {
+pub(crate) fn factor(mut num: u64) -> Factors {
     let mut factors = Factors::new();
     if num == 1 {
         return factors;
     }
 
-    if miller_rabin::is_prime(num) {
-        factors.push(num);
-        return factors;
-    }
+    match miller_rabin::test(num) {
+        Prime => {
+            factors.push(num);
+            return factors;
+        }
+
+        Composite(d) => {
+            num = num / d;
+            factors *= factor(d);
+        }
+
+        Pseudoprime => {}
+    };
 
     let divisor = find_divisor(num);
     factors *= factor(divisor);